The Pennsylvania State University
The Graduate School
Department of Geosciences
DETRITAL-MINERAL THERMOCHRONOLOGY: INVESTIGATIONS
OF OROGENIC DENUDATION IN THE HIMALAYA OF CENTRAL NEPAL
A Thesis in
Geosciences
by
Ian D. Brewer
2005 Ian D. Brewer
Submitted in Partial Fulfillment of the Requirements
for the Degree of
Doctor of Philosophy
August 2005
The thesis of Ian D. Brewer was reviewed and approved* by the following:
Douglas W. Burbank Professor of Geosciences
Thesis Advisor Chair of Committee
Rudy L. Slingerland Professor of Geosciences Head of Department of Geosciences
Peter B. Flemings Professor of Geosciences
Derek Elsworth Professor of Mineral Engineering Associate Dean for Research
iii
ABSTRACT
This investigation examines the fundamental processes that determine the distribution of cooling
ages observed in detrital minerals eroded from orogenic belts. A detrital cooling-age sample
collected from a riverbed represents an integration of information from the upstream area. Within
orogenic belts that contain glacial cover and high relief, detrital minerals provide an easy method to
sample the range of cooling ages found within a basin. In addition, detrital-mineral
thermochronology can be used to extract information from the foreland stratigraphic record, which
extends the temporal applicability of the technique beyond traditional bedrock thermochronology.
For example, individual mineral grains can be extracted from a stratigraphic horizon and dated.
Following correction for the stratigraphic age of the horizon, the detrital mineral ages provide a
proxy for the erosion rates contained within the catchment area at the time the rock was deposited.
However, before reliable interpretations of the stratigraphic record are made, a modern calibration
of the technique was needed.
We investigated the spatial development of a modern cooling-age signal in the Marsyandi valley
of central Nepal with muscovite grains dated using 40Ar/39Ar thermochronology. Over 500
individual grains were dated from both the trunk stream and tributaries over a ~100-km transect
along the Marsyandi. These provide a database that displays striking contrasts along the length of
the Marsyandi River. The first stage of the investigation focused on the interaction of geological
parameters that control the distribution of detrital cooling ages from an individual basin. The range
of bedrock cooling ages contained within a catchment is determined by the erosion rate and the
depth of the closure isotherm (~350°C for muscovite). With a 2-D thermal model, we investigated
the effects of the vertical erosion rate and topography on the depth of the closure isotherm.
Increasing the erosion rate and/or topographic relief decreased the depth of the closure isotherms
below valley floors, and re-equilibration following sustained changes in the erosion rate took ~10
My. Once the range in cooling ages had been determined for a basin, the distribution of detrital
cooling ages in sediment at the basin mouth was calculated as a function of catchment hypsometry.
iv
This approach was applied to two sub-catchments of the Marsyandi River. The predicted probability
distribution of cooling-ages matched the observed data better in the more slowly eroding basin, than
in the more rapidly eroding basin.
To understand the more complex distribution of cooling ages from the mouth of the Marsyandi
River, the basin was divided into smaller sub-basins that were modeled individually. To predict the
trunk-stream signal, individual tributaries were mixed as a function of their area, erosion rate, and
the percentage of muscovite in their sediment, which was determined from point counting.
Comparison of the model results with observed data illustrated that the detrital-cooling age signal
evolved downstream in an understandable manner, and suggested that the mechanical comminution
of muscovite was not significant over the length-scale of the basin. The pattern of spatial erosion
seen in the thermochronology – low erosion rates in the Tibetan zone, high erosion rates in the
Greater Himalaya zone, and intermediate erosion rates in the Lesser Himalayan zone – was broadly
similar to calculations of erosion rate based upon the point-counting results. Sample pairs were
dated to assess the temporal and spatial variability of the cooling-age signal within the fluvial
system. Results indicated that the samples were undistinguishable at the 95% confidence level, once
the effects of random selection and the number of grains dated had been accounted for.
A more integrated approach was used to predict the spatial distribution of bedrock cooling ages
within the 3-D landscape, and the distribution of detrital cooling ages resulting from the erosion of
that landscape. A 2-D kinematic-and-thermal model, using the assumption of a single orogen-scale
decollement, was developed to predict the depth of the closure isotherm as a function of the ramp
geometry and the relative partitioning of convergence between the Indian Plate underthrusting and
southern Tibet overthrusting. The thermal result was extrapolated laterally and combined with a
digital elevation model to predict the distribution of bedrock cooling ages. At any site in the
landscape, the cooling age is a function of the distance each rock particle travels after passing
through the closure isotherm and its speed along the trajectory predefined by the underlying
decollement geometry. Once the contribution of each site had been corrected for lithological factors
and the volume of sediment eroded, a theoretical cooling-age probability distribution was calculated
for the Marsyandi by the summation of age-probability for all sites within in the basin. The volume
of sediment was calculated as a function of the regional slope and the angle of the underlying ramp.
Comparison of various model runs with the observed data indicates that the best solution is obtained
v
by partitioning the total of ~20 mm/yr of convergence between India and southern Tibet into 15
km/my of India underthrusting, and 5 km/yr of Asian overthrusting and subsequent erosion.
However, the exact partitioning is dependent upon the geometry of the decollement. A variant of the
model that assumed the modern Main Central Thrust represented the approximate surface trace of
the orogen-scale decollement produced better results than those runs that assumed the Main
Boundary Thrust represented the surface trace of the orogen-scale decollement. This provides
additional evidence that the MCT has been active recently. The new methodology of integrating
complex kinematic-and-thermal models with digital elevation models can be applied to any
orogenic belt, and it may be used to compare theoretical predictions against easily collected and
analyzed detrital-mineral data.
TABLE OF CONTENTS
LIST OF FIGURES......................................................................................................ix
LIST OF TABLES .......................................................................................................xiii
ACKNOWLEDGMENTS............................................................................................xiv
INTRODUCTION........................................................................................................1
CHAPTER 1.................................................................................................................5
AN INTEGRATED APPROACH TO MODELING DETRITAL COOLING-AGE POPULATIONS: INSIGHTS FROM TWO HIMALAYAN DRAINAGE BASINS.
Abstract. .........................................................................................................5 1.0 Introduction..............................................................................................6 2.0 Review of Previous work.........................................................................9 3.0 Predicting the distribution of bedrock cooling ages ................................11 3.1 Thermochronology...................................................................................11 3.2 Determination of bedrock cooling ages ...................................................11 3.3 Thermal structure during active erosion ..................................................12 3.4 Steady-state landscapes............................................................................16 3.5 Spatial resolution .....................................................................................17 3.6 Vertical age distribution for a theoretical basin.......................................18 3.7 Distribution in ages at the basin mouth. ..................................................19 3.8 Examining the control of relief and erosion controls on the theoretical PDF of a
single drainage basin ..............................................................................21 4.0 Application to two Himalayan basins..................................................................22
4.1 Geological Background and sample sites ................................................22 4.2 40Ar/39Ar Analytical Protocols.................................................................24 4.3 Detrital cooling-age results and modeling theoretical PDFs ...................25
5.0 The construction of a grab-sample PDF. .............................................................27 5.1 PDF comparison and statistics. ................................................................27 5.2 Resolution of the detrital dating...............................................................28 5.3 Himalayan catchments – synthesis of theoretical PDFs and random sampling.
................................................................................................................30 5.4 Discussion of modeling results ................................................................31
vii
6.0 Discussion............................................................................................................32 7.0 Conclusions..........................................................................................................35
CHAPTER 2.................................................................................................................49
THE DOWNSTREAM DEVELOPMENT OF A DETRITAL COOLING-AGE SIGNAL, INSIGHTS FROM 40AR/39AR MUSCOVITE THERMOCHRONOLOGY IN THE MARSYANDI VALLEY OF NEPAL.
Abstract......................................................................................................................49 1.0 Introduction..........................................................................................................50 2.0 Previous investigations of detrital thermochronology.........................................52 3.0 Geological Background .......................................................................................54 4.0 Methodology........................................................................................................55
4.1 Sampling strategy ....................................................................................55 4.2 40Ar/39Ar Analytical Protocols.................................................................57 4.3 Point Counting. ........................................................................................58
5.0 40Ar/39Ar results. ..................................................................................................59 6.0 Modeling..............................................................................................................60
6.1 Modeling the detrital cooling age signal .................................................61 6.2 PDF modeling results...............................................................................63
7.0 Discussion............................................................................................................65 7.1 Resilience of the detrital signal................................................................65 7.2 The reliability of the fluvial signal ..........................................................67 7.3 Spatial variations of erosion rate .............................................................69 7.4 Point-counting results ..............................................................................70
8.0 Conclusions..........................................................................................................72
CHAPTER 3.................................................................................................................90
THE APPLICATION OF THERMAL-AND-KINEMATIC MODELING TO CONSTRAINING ROCK-PARTICLE TRAJECTORIES, COOLING AGES OF DETRITAL MINERALS, AND THE TECTONICS OF THE CENTRAL HIMALAYA.
Abstract......................................................................................................................90 1.0 Introduction..........................................................................................................912.0 Geological background........................................................................................933.0 Thermal and Kinematic modeling .......................................................................95
3.1. Constraints on thrust geometry ...............................................................95 3.2. Thermal model ........................................................................................99 3.3. Particle trajectories and detrital cooling-age signals ..............................101
4.0 Modeling Results .................................................................................................106 4.1 Kinematics ...............................................................................................107
viii
4.1.1 Convergence rates..........................................................................107 4.1.2 Angle of Main Himalayan Thrust ramp.........................................109
4.2 The modeled Marsyandi valley detrital cooling age signal .....................111 4.4 The effects of lithology............................................................................112
5.0 Discussion............................................................................................................113 5.1 Modeling..................................................................................................113 5.2 The single-decollement model.................................................................116 5.3 The stratigraphic record ...........................................................................118
6.0 Tectonic implications for the Himalaya ..............................................................119 7.0 Conclusions..........................................................................................................122
REFERENCES ............................................................................................................143
APPENDIX 1 ...............................................................................................................154
1.0 Thermochronology ..............................................................................................154 1.1 The decay equation ..................................................................................154 1.2 The potassium/argon decay scheme.........................................................156 1.3 The 40Ar/39Ar analytical method..............................................................157 1.4 Closure temperatures ...............................................................................158
APPENDIX 2 ...............................................................................................................161
1.0 40Ar/39Ar results and protocols.............................................................................161
APPENDIX 3 ...............................................................................................................180
1.0 Comparing PDF curves........................................................................................180
ix
LIST OF FIGURES
CHAPTER 1
Fig. 1. Thermal structure of continental crust with erosion rates of (a) 1.0 km/My (b) 3.0 km/My after 20 My in a landscape with 4 km of relief. In scenario (c) and (d) relief is increased to 6 km with an erosion rate of 1.0 km/My and 3.0 km/My, respectively…………………………………....36
Fig. 2. Average depth of the 350°C isotherm below the valley floors as a function of varying relief and erosion rates after 20 My.……………………………………………………………………....37
Fig. 3. The temporal response of the depth of the 350°C isotherm for a system with 4 km of topographic relief. ……………………….…………….....38
Fig. 4. Construction of a “theoretical” PDF for an individual basin. …………………….………………………………………………….....39
Fig. 5. Relationship between summit ages and valley ages for topographic relief of 2, 4, and 6 km undergoing erosion rates of 0.5 to 3.0 km/My.………………………………………………………………….40
Fig. 6. Effects of uplift rate and relief on theoretical PDFs for a basin with a Gaussian distribution of land area with elevation..……………………..41
Fig. 7. Effects of hypsometry on theoretical PDFs………………………….....42 Fig. 8. Map of the upper Marsyandi drainage basin showing the detrital sample
locations.………..……….………………………………………..…......43 Fig. 9. SPDFs generated from the results of 40Ar/39Ar dating samples from the
upper Marsyandi (Sample 1) and Dordi basin (Sample 2). …………………………………………………………………………..44
Fig. 10. Plot of grain age versus age uncertainty for the 40Ar/39Ar analysis.……………..…………………………………………………..45
Fig. 11. Error calculation for a basin of 4-km relief eroding at 1 km/My.……………….…………………………………………………46
Fig. 12. Number of grains versus the mismatch error from 1000 iterations. …………….…………………………………………………………….47
Fig. 13. A selected range of outcomes from sampling 50 grains from the theoretical PDF (shaded gray) of a basin with 4 km of relief eroding at 1.0 km/My.……………………………………………………………...48
x
CHAPTER 2
Fig. 1. Simplified geological map of the Marsyadi region.……………………..76 Fig. 2. Map of Marsyandi drainage system based on a 90-m
DEM…………………………………………………………………….77 Fig. 3. Detrital cooling-age PDFs for samples from the Marsyandi drainage.
.…………..……………………………………………………………...78 Fig. 4. Parameters controlling the contribution of an individual tributary to a
trunk-stream cooling-age signal. ……………………………………….79 Fig. 5. Model results compared to 40Ar/39Ar analyses. ………………………...80 Fig. 6. Predicted ages for specified erosion rates.………………...…………….81 Fig. 7. (a) Age versus error (1-σ) for analyses with greater than 40% radiogenic
40Ar. No clear relationship between age and error can be seen. Inset (b) shows a PDF generated from the 1-σ errors..…………………...………82
Fig. 8. Results of repeat sampling to test: a) the spatial variability of the detrital cooling age signal, and; b) the temporal variation of the signal. …………………………….…………………………………………….83
Fig. 9. Spatial variation in erosion rates at the drainage-basin scale. Erosion rates are taken from the results of modeling the detrital cooling age PDFs for individual tributaries. .………………………………………………......84
Fig. 10. The procedure used to convert point-counting results into relative erosion rates..……………………………………………………………85
Fig. 11. Spatial variation in erosion rates at the drainage-basin scale. Erosion rates are calculated from the point-counting data using the methodology illustrated in figure 9.……………….…………………………………...86
CHAPTER 3
Fig. 1. Location of the Marsyandi drainage basin and the study area……….....125 Fig. 2. Conceptual basis for the combined thermal, kinematic, and detrital
model.……………………………………………………………………126 Fig. 3. Constraints used for the kinematic-and-thermal model. ……………......127 Fig. 4. The three components needed to construct cooling ages for the
landscape. ……………………………………………………………….128 Fig. 5. Volume of material eroded in a time increment (dt) depends upon the
aspect of the topography in relation to the particle velocity (V). The gray line mirroring the present topography illustrates the volume of rock eroded in dt with an assumption of complete steady-state conditions.….129
Fig. 6. Calculation of volume of rock eroded in time increment (dt) for one digital-elevation model (DEM) grid cell, assuming a steady-state landscape. ……………………………………………………………….130
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Fig. 7. Relationship between the topographic slope and particle trajectory angle in determining the volume of material eroded from a DEM cell.………….…………………………………………………………...131
Fig. 8. The three linear segments used as a proxy for the regional slope, taken from a transect normal to the strike of the orogen.……………………...132
Fig. 9. Three scenarios for partitioning convergence rate between India and south Tibet. ……………………………...………….………….………..133
Fig. 10. Effects of partitioning the relative convergence rate between India and Asia.………………………………………………………………….......134
Fig. 11. (a) The detrital cooling age signal from the entire mountain front compared against the sample from the mouth of the Marsyandi. (b) Corrected for the age-signal generated specifically from the Marsyandi basin. ……….………….………………………………………………..135
Fig. 12. The steady-state thermal structure with 20 mm/yr of total convergence with (a) 4 mm/yr of total convergence partitioned into Asia, and (b) 8 mm/yr of convergence partitioned into Asia.……….………….………………….………….…………………..136
Fig. 13. The distribution of cooling ages derived from different ramp geometries. ……..……………………………………………………….137
Fig. 14. A comparison of the distribution of detrital cooling ages using (i) a lithological correction and (ii) no lithological-correction factor…...…...138
Fig. 15. Transects…………...……….………………………...……….……….139 Fig. 16. Variation of “apparent” relief as a function of particle trajectory. ……140 Fig. 17. A comparison of the distribution of detrital ages from an orogenic
swath in the study area with: (i) the MHT represented by the MBT being the active fault, and; (ii) the MHT represented by activity on solely the MCT……….…………………………………………………………….141
Fig. 18. A cartoon showing three end-member models for Himalayan evolution. ……………….………………………………………………...………...142
APPENDIX 1
Fig. 1 Diagram illustrating the T-t path of a rock undergoing burial metamorphism and subsequent exhumation.…….…………..………….160
xii
APPENDIX 2
Fig. 1. Age versus percentage of radiogenic 40Ar for the geochronological analyses presented in this paper.…….………….…….….……………...163
APPENDIX
xiii
LIST OF TABLES
CHAPTER 1
CHAPTER 2
Table 1. Point-count data……………...………………………………………..87 Table 2. Drainage basin characteristics.………………………………………..89
CHAPTER 3
APPENDIX 1
APPENDIX 2
Table 1. Thermochronology isotopic data.…….…………...…………………..164
APPENDIX
ACKNOWLEDGMENTS
This work was funded by National Science Foundation grants EAR-9627865, EAR-9896048, and
EAR-9909647. The Chevron Corporation provided a scholarship and the Krynine Funds from the
Department of Geosciences provided travel support. I would like to thank my advisor, Douglas
Burbank, who has given me much support and advice. Kip Hodges provided his scientific approach
and reviews, which helped improve our approach to the problems herein. My committee, Rudy
Slingerland, Peter Flemings, and Derick Elsworth have provided help full guidance and scientific
insight. Kevin Furlong, Rocco Malserversi and Chris Guzofski provided helpful discussions about
the thermal modeling. I would like to thank Kevin in particular for his excellent insights. Peter
Deines helped further my understanding of isotopic dating. Bill Olszewski, Jose Hurtado, and
Michael Krol provided invaluable help at the MIT laboratory and I would like to thank other
students for making my time in Boston enjoyable. Collaboration with John Garver was rewarding
and enjoyable, and a statistics discussion with Mark Brandon was useful. During my
Undergraduate degree at Oxford University, Mike Searle, Steven Hesselbo, John Dewey and Phillip
Allen passed on much of their enthusiasm. I would like to thank Mike in particular for the great
time we spent mapping in Khumbu. Thanks to friends and faculty at USC who helped me during
my first year in the USA. In Nepal, Dorjee Llama and Chandra Bdr. Niraula provided logistical
support and Pasang Kaji Sherpa and Dawa Tshering Sherpa managed to cope admirably with me in
the field. Dina Bandhu Baral helped prevent my arrest! Thanks to my office mates, Ann Blythe,
Mike Bullen, and Merri Lisa Formento-Trigilio for keeping me sane, and I would lastly like to
acknowledge all my friends here at PSU who have made my life very enjoyable during the course of
this work.
xv
Little drops of water,
Little grains of sand,
Make the mighty ocean
And the beauteous land.
J.A..Carney (1845)
1
INTRODUCTION
In 1895 the renowned French physicist Henri Baecquerel discovered radioactive decay, which
revolutionized the science of geology. Not only did radioactive decay provide an additional heat
source for the interior of the earth, supporting theories that the Earth was indeed very ancient, but
when Ernest Rutherford dated the first mineral in Montreal in 1905 geologists could begin to
quantify this antiquity. For the first time, events in Earth history could be placed within a calibrated
temporal framework. From this foundation less than 100 years ago the study of dating rocks,
“thermochronology,” has evolved into a major sub-discipline of Earth Sciences. Many different
radioactive systems are now employed, and a wide range of applications have been developed.
Despite this, the same basic methodology underlies all studies using radioactive isotopes, and
readers unfamiliar with the basics of thermochronology should refer to the overview in Appendix 1.
The initial motivation of thermochronology was to measure the formation age of a rock.
Thermochronometers with high closure temperatures, such as those using the U-Pb decay scheme,
for example, are typically used for such applications because of the similarity between closure and
magma crystallization temperatures. Low-temperature thermochronometry, however, has more
recently developed into an extremely useful tool. The 40K/40Ar series, for example, once primarily
used to date the effectively instantaneous cooling of extrusive igneous rocks, is now used to
constrain erosion and deformation during orogenesis. In active collisional belts, the rate of cooling
is driven by the rate at which a rock particle moves towards the surface. Thus, if the depth of
closure is known, a cooling-age taken from the surface today can be used as a proxy for the erosion
rate.
A limitation of bedrock thermochronology is that the temporal record is limited; only the rocks
found at the surface today can be dated. Detrital-mineral thermochronology is one way to overcome
this problem because sand grains can be preserved in basins. With increasingly accurate mass-
spectrometers, single crystals from the stratigraphic record can now be dated using laser
microprobes. If the cooling age of a grain extracted from the geological record is corrected for the
2
stratigraphic age of the rock that contained it, it can provide a proxy for erosion rates at the time the
rock was deposited [e.g. Cerveny et al., 1988].
If we can illustrate that detrital-mineral ages produce a reliable indication of the rock uplift and
erosion variability within the contributing area, key questions concerning the tectonic and
physiographic evolution of mountain belts can be answered. “When did structural deformation
initiate in a given range? How rapidly did rock exhumation occur, and was there temporal
variability in the rate or erosion?” Previous studies using detrital thermochronology in the Himalaya
have either focused on constraining the stratigraphic age [Najman et al., 2001; Najman et al., 1997]
or, in an effort to gain insights into the temporal exhumation of the mountain range, have sampled
the stratigraphic record of cooling ages preserved in the Bengal Fan [Copeland and Harrison, 1990]
and the Pakistan Siwaliks [e.g. Cerveny et al., 1988]. The limitation of both the Bengal Fan and the
Pakistan Siwalik investigations is that the sampled sites have such vast upstream areas that only
very general inferences about erosion within the Himalaya can be drawn from these data.
The thrust of this investigation has been to understand modern detrital systems and to provide a
solid foundation for future applications in the stratigraphic record. In doing this we have had to
address some fundamental questions, the most basic being, “What is controlling the detrital cooling-
age signal?” This is a complex question because of the effects of the regional tectonics, distribution
of bedrock cooling ages, lithology, the fluvial system, and the fidelity of our sampling and dating
procedures. We focus on intermediate scale rivers that transect the width of the orogen, with
drainage basins on the order of 10,000 km2. These potentially produce detrital records that are
characterized by high spatial resolution, and are readily preserved in foreland basins within close
proximity to the mountain front. To date, studies of such rivers have neither been widely used to
constrain the modern pattern of erosion, nor to investigate the information preserved within the
stratigraphic record. The latter is because of the uncertainty in interpreting the results, whereas the
former is because bedrock thermochronology has traditionally been used.
In our investigation we examine the modern Himalaya, the preeminent collisional belt of the
Cenozoic. The combination of extreme relief, relative structural simplicity, and high erosion rates
make the Himalaya an excellent natural laboratory for our work. We focus on the Marsyandi valley,
which is located in central Nepal and divides the two 8000-m massifs of Annapurna and Manaslu.
Our thermochronometer of choice is muscovite, dated using 40Ar/39Ar procedures, because it has
3
been widely used in the Himalaya, is resistant to weathering [Najman et al., 1997], and appears not
to have the same problems of inherited argon as biotite [Clauer, 1981]. In this study, we dated over
500 single crystals of muscovite. These were collected from sites on the main stem of the
Marsyandi River, as well as from many tributaries on either flank of the river. These data show
striking downstream changes in the distribution of ages, as well as clearly contrasting patterns
among tributaries in different parts of the range.
The work here is presented as three separate chapters, which to some extent represents a
progression of thought and complexity, although each chapter addresses different problems. The
first chapter focuses on two individual tributary basins and examines the most basic parameters
controlling the detrital cooling-age signal: the thermal system, erosion rate, and the distribution of
land area with elevation. “How does the closure isotherm respond to changes in erosion rate and
topography? How long does it take the thermal system to respond to changes in these parameters?”
These are key questions we have answered with a thermal model that examines the effects of
erosion rate and topography on the depth of the closure isotherm for muscovite (~350°C). Assuming
that vertical erosion dominates, we can use the results of the thermal model to predict the range of
bedrock cooling ages in a basin. The chance of dating a grain of a particular age from the sediment
at the basin mouth will be dependent upon the amount of land contributing that age. Thus the
probability of land area with elevation (hypsometry) can be used as a proxy for the probability of
dating a grain of a particular age.
One assumption to this basic methodology is that individual basins have uniform erosion rate
across them. Comparing the results to the full range of data collected from the Himalaya during
fieldwork in 1997 and 1998, it became apparent that further elements were needed to extend this
approach from models of individual tributaries, to investigating the complex detrital signal seen in
the trunk-stream entering the foreland basin. Thus, the subsequent chapter addresses key questions
that need to be answered in order to understand the evolution of a detrital signal within a much large
and complex drainage. “What factors control the volumetric contribution of a thermochronometer to
the trunk stream from individual tributaries? How is the spatial variation in denudation rate at the
tributary scale manifest in the trunk-stream signal? Does the downstream comminution of the
thermochronometer play an important role? How does variation in lithology affect the signal?” To
address these questions, a network approach was used, whereby the volumetric contribution of a
4
predicted detrital cooling-age signal from an individual tributary, was modeled as a function of the
basin erosion rate, area, and percentage of thermochronometer. We found that our models of the
downstream evolution of the trunk-stream signal were broadly consistent with the data. The results
illustrate that erosion rates vary by a factor of at least two across the range and that there is little
evidence for the downstream comminution of muscovite.
Despite the success of these investigations, the differences between observed data and model
predictions focused our thoughts on further questions. “How can the pattern of bedrock-cooling
ages be explained in the context of regional tectonics? Given that the dominant style of Himalayan
deformation is thrusting along low-angle decollements, how does this affect the thermal structure?”
The final chapter represents a large step forward in answering these questions by defining a
methodology for combining complex geodynamic models with digital elevation models to predict
the distribution of detrital cooling ages. We constructed a 2-D kinematic-and-thermal model for the
Himalaya that answers questions such as: “How does the partitioning of underthrusting affect the
thermal conditions in the overthrusting plate, and to what extent does the geometry of the collision
zone manifest itself in the distribution of bedrock cooling ages?” With additional procedures, we
can predict how the distribution of bedrock cooling ages is manifest in the detrital record as a
function of differences in lithology, and how the erosion rate is controlled by the geometry of the
orogen.
Thus this modern calibration has explored and examined many of the assumptions that are needed
for the reliable interpretation of detrital cooling ages. The first two chapters provide a first-order
approach to understanding variations in the detrital-cooling age signals derived from an orogen,
which may be especially useful in regions where the geology is poorly constrained, or to focus
research on a specific geological parameter. The final chapter provides a more complex and
integrated approach that may be applicable to more detailed investigations of regional tectonics.
However, whether investigating the modern detrital signal, or examining the stratigraphic detrital
record, the insights gained from this investigation provide a considerably more solid foundation for
the future geological interpretation of cooling ages.
5
Chapter 1
An integrated approach to modeling detrital cooling-age populations: insights from two Himalayan drainage basins.
I.D. Brewer and D.W. Burbank
Pennsylvania State University, Department of Geosciences, University Park, Pennsylvania
K.V. Hodges
Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology,
Cambridge, Massachusetts
Abstract.
The distribution of detrital mineral cooling ages in stream sediment can be used to investigate the
erosional history of mountain ranges. We have developed a numerical model that predicts detrital
mineral age distributions for individual basins undergoing vertical erosion. Although this model
requires a restrictive set of assumptions, its judicious application provides an opportunity to explore
the effects of thermal structure, erosion rate, relief, and basin hypsometry on cooling-age
distributions. We illustrate this approach by generating synthetic 40Ar/39Ar muscovite age
distributions for two basins with contrasting erosion rates in central Nepal. We then compare actual
measured cooling-age distributions for stream sediment samples with those predicted by the model.
Monte Carlo sampling is used to assess the mismatch that can be attributed to the number of grains
dated, how well a finite number of grain analyses reproduce the age distribution of the basin. A
6
good match is produced between observed and predicted detrital cooling ages for a slowly eroding
Himalayan basin. The poorer match for a rapidly eroding basin may result from the wide range in
age uncertainties displayed by the real analyses, or inhomogeneous erosion rates within the basin.
Such mismatches emphasize the need for more accurate thermal and kinematic models to improve
geochronological data interpretations.
1.0 Introduction.
Thermochronology is a technique that allows scientists to place geological events into a quantitative
temporal framework. Although the initial motivation was to date the formation, or crystallization,
age of rocks and minerals, increasing interest has focused on applying low-temperature
geochronometers to investigations of sample cooling history. In active tectonic terrains, cooling
rates obtained through the application of isotope geochronometers are frequently used as proxies for
the unroofing rate of samples (the rate at which the sample moves towards the surface of the Earth).
As a consequence, the goal of many thermochronological investigations is not to strictly examine
the cooling history of a sample, but rather to constrain the rate of erosion that has exhumed it.
It is important to realize, however, that it is necessary to make a number of assumptions to convert a
cooling age into an erosion rate. Calculations typically contain, either explicitly or implicitly,
assumptions of: a) a specified geothermal gradient; b) constant erosion rate through time; and c)
vertical erosion and vertical rock-particle trajectories. This simplistic approach often does not
account for the many complex interactions that occur in nature. The local geothermal gradient, for
example, is a function of topographic relief, erosion rate, and the pattern of deformation in an area
[Henry et al., 1997; Mancktelow and Grasemann, 1997; Stüwe et al., 1994]. In this paper we
examine some of the basic assumptions required to calculate erosion rates, explore the extent to
which they are broadly reasonable, and investigate the interplay of parameters that control the
distribution of bedrock cooling ages.
The most rigorous thermochronological approach to quantifying the erosion history of bedrock is to
employ multiple dating systems to reconstruct detailed temperature-through-time cooling paths [for
7
review of t-T and P-t-T investigations in the Himalaya see Searle (1996)]. Although excellent
insights are derived from such investigations, there are important limitations imposed on the utility
of such studies. Samples are limited to individual rock samples collected from the surface today,
and in modern orogenic belts that typically experience high vertical erosion rates, the low
temperature thermochronological record may only extend back a few million years. In addition,
detailed temperature-through-time paths from a bedrock sample provide information on the cooling
history of a single point that often has to be extrapolated to a much wider region.
It is a striking fact that a single handful of sand contains approximately half a million grains, each
derived from a slightly different source within the catchment. Detrital mineral geochronology
produces a spatially averaged erosion rate because a sample of sand taken from the mouth of a basin
provides an encapsulation of the spectrum of cooling ages upstream. A modern sand sample can be
rapidly collected from the river system and provides a means to sample the entire range of cooling
ages within the drainage basin. This may be especially useful within basins of extreme relief, or
containing significant glacial cover – areas in which bedrock thermochronology can be impractical.
Detrital geochronology further allows us to exploit the extensive temporal record of detritus shed
from mountain belts and preserved in sedimentary basins. Thus, the temporal applicability of
detrital dating may be extended far beyond traditional bedrock thermochronology to provide critical
information needed for reconstructing orogenic development [e.g. Cerveny et al., 1988; Copeland
and Harrison, 1990]. Precise spatial and temporal variations in tectonics, erosion rates, and the
resulting development of topography are necessary to understand global interactions of mountain
belts with global geochemical cycles [Derry and France-Lanord, 1996; Raymo et al., 1988], and
climate change [Kutzbach et al., 1993; Ruddiman and Kutzbach, 1989].
Detrital thermochronology is a technique, however, that arguably has not been employed to its full
potential because of issues concerning the interpretation, reliability, and significance of results. For
example, the unique, but unknown, specific source of each grain provides both opportunities and
limitations. Whereas it is possible to obtain a full representation of the cooling ages within a basin,
the generation of a detailed cooling history at a single point is precluded. Additionally, before we
can begin to interpret variations in denudation rate, a series of assumptions have to be made to
8
convert the cooling-age record into erosion rates. Many of these assumptions underlie investigations
of bedrock geochronology, whereas some are specific to the technique of dating detrital minerals.
In this paper we introduce a numerical model that explores the detrital cooling-age signal of a basin.
The model description is divided into two parts to allow a systematic investigation of the controlling
parameters and an assessment of the underlying assumptions. In the first part of the model, we
present a methodology that uses erosion rate and relief to predict thermal structure and the
consequent distribution of ages with elevation. In a new approach, we use the topographic
characteristics of the basin to predict the relative abundance of detrital cooling ages in sediment at
the basin mouth; the theoretical distribution of ages that exactly reproduces the variability of
bedrock cooling ages within the catchment.
The second part of the model evaluates the consequences of the practical fact that we can date only
a finite number of grains and begins to quantify the random nature of detrital grain sampling. It
seems clear that increasing the number of grains produces a more robust analysis, but how can we
quantify this? Apart from initial investigations [e.g. Copeland et al., 1997; Stock and Montgomery,
1996], there have been few tests to determine a) the number of grains required to adequately
represent the entire age signal contained within the river, and b) the nature of the errors associated
with dating different numbers of grains. We use Monte Carlo integration to generate a synthetic
“grab” sample from the known “theoretical” population. This represents the geochronologist
selecting a finite number of grains to date from the millions present at the sample site. Using this
approach, we provide a quantitative measure of how different age distributions, generated from
different individual samples, fit the original cooling-age signal. This is the first methodology that
incorporates the complexity of the detrital signal to determine the uncertainty for a given number of
grains. To compare model results to real data and introduce our Monte Carlo analysis, we present
detrital muscovite ages from two Himalayan catchments. The samples were collected from two sites
within the Marsyandi Valley in central Nepal, and ~35 to 40 grains were dated from each using 40Ar/39Ar thermochronology.
Because our model for generating theoretical age distributions is based on simplifying assumptions,
it is not intended to exactly reproduce the distribution of ages within the data. Instead, if the
assumptions and resulting limitations of the methodology are accepted, we can apply the model to
9
any basin in order to provide a first-order estimate of the parameters that control the detrital
cooling-age signal. The results of the analysis provide a basis to re-examine the initial model and
decide which assumptions are responsible for the mismatches, which are valid for the particular
region, and which may need further constraint and research.
2.0 Review of Previous work.
Detrital mineral geochronology has been used to investigate: (a) the thermal evolution of basins
[e.g. Green et al., 1996]; (b) source area constraints [e.g. Adams et al., 1998; Garver and Brandon,
1994; Hurford and Carter, 1991; Krogh et al., 1987]; (c) stratigraphic age [e.g. McGoldrick and
Gleadow, 1978; Najman et al., 1997] and; (d) the erosion history of orogens [e.g. Cerveny et al.,
1988; Copeland and Harrison, 1990]. The latter two approaches, in particular, are pertinent to the
problem of Himalayan erosion. Najman et al. [1997] used 40Ar/39Ar dating to constrain the
maximum depositional age of the oldest exposed Gangetic foredeep strata as 28 Ma. This
depositional age was interpreted to define the onset of significant exhumation in the Himalaya.
Although the stratigraphic age provides insight into orogenic exhumation, we focus here on the
detailed interpretation of the distribution of ages within the sediment and how to extract from them
information about the erosional history.
At present, 40Ar/39Ar (muscovite, biotite, k-feldspar, and hornblende), fission-track (zircon and
apatite), and (U-Th)/He (apatite and titanite) dating are the major geochronological methods used to
investigate the cooling history of mountain belts because of their relatively low (< 500°C) closure
or annealing temperatures. One of the first investigations of orogenic erosion using detrital sediment
from the stratigraphic record was undertaken by Cerveny et al. [1988]. In the geological record, the
cooling age of detrital minerals within a sedimentary rock can be corrected for the stratigraphic age
of that rock and then used as a proxy for the erosion rate at the time of deposition. Detrital zircons
from Indus River sediments in the Pakistan foreland indicated that a young 1 to 5 My (at the time of
deposition) cooling-age signal had been persistent since 18 Ma. This suggested that the modern
high-cooling rates experienced by the Nanga Parbat region had been a feature of the Indus River
catchment since early Miocene times. Although an analysis of a large catchment such as the Indus
10
provides a good overview of the regional deformation, the analysis of the data is limited by the
uncertainty of the detrital source area. Detrital zircon fission-track analysis has also been employed
to investigate the temporal variations in erosion rate of the Olympic range and the British Columbia
Coastal Ranges [Brandon and Vance, 1992; Garver and Brandon, 1994]. In addition, combined
investigations of detrital-zircon fission-track and U-Pb dating using zircons from the same
stratigraphic horizon were used to distinguish the exhumation of igneous and metamorphic sources
in the Khorat basin, Thailand [Carter and Moss, 1999].
Copeland and Harrison [1990] used 40Ar/39Ar analysis of detrital K-feldspar and muscovite grains
from ODP sites on the southern end of the Bengal fan to interpret Himalayan erosion rates through
time. They show that the youngest cooling age at each stratigraphic level is approximately equal to
the depositional age, suggesting that high erosion rates have persisted for the past 18 My. However,
the temporal and spatial pattern of erosion within the catchment area is impossible to determine
from a sample so far from the orogenic front: we know only that rapid cooling was occurring at
some location within the drainage basin.
Despite the value of the aforementioned studies, they reveal little about the combination of physical
processes that control the detrital signal. Stock and Montgomery [1996] studied the theoretical
effects of relief on the range of ages found in the detrital record. They investigated the potential to
constrain paleotopography using the detrital cooling-age signal with the assumptions that: a) there is
good grain-age precision; b) the grains retain their isotopic ages during transport and deposition; c)
the sediment from the basin is well mixed; and d) there are near-horizontal isotherms. They found
that a sample of 40 grains is required to provide a 90% probability of capturing 90% of the relief of
a basin. We use a similar, but more integrated, approach to try to understand the thermal
framework, basin characteristics, and sampling statistics that control the complete cooling-age
signal from a particular basin.
11
3.0 Predicting the distribution of bedrock cooling ages
We have developed a numerical model that predicts the detrital cooling-age signal from basic basin
characteristics. The model may be divided into two distinct parts and each is addressed separately.
The first part involves constructing a theoretical distribution of cooling ages for a basin, which we
define as the age signal that would be found by dating an infinite number of zero-error detrital
grains that completely sampled every point within the basin. We examine the model results by
comparing them to real data from two Himalayan catchments. In practice, however, only a finite
number of grains can be dated at a given site. Thus, the second part of the numerical model
addresses the uncertainties introduced by the limited number of analyses.
3.1 Thermochronology
This paper is concerned with 40Ar/39Ar dating using muscovite because this has been widely used in
both investigations of both bedrock and detrital-mineral dating. Moreover, there appears to be fewer
problems with excess argon in muscovite than are found with biotite [Roddick et al., 1980]. Our
simplistic treatment assumes that all muscovite samples have the same closure temperature
(~350°C) that is independent of grain size and the rate of cooling through the closure interval [see
Dodson, 1973]. This methodology is typical in geochronology, although when investigating spatial
variation in erosion rates, the latter assumption is clearly violated. In addition, we ignore the
potential effects of inherited radiogenic 40Ar.
3.2 Determination of bedrock cooling ages
In active orogenic belts, cooling ages are determined by the thermal structure and particle velocities
within the crust. The thermal structure of the crust will determine the depth of the mineral closure
temperature. The velocity path that individual rock particles follow to reach the surface will
12
determine how long rocks take to be transported from the closure temperature to the land surface,
i.e. the cooling age.
The majority of geochronological investigations assume a simplified kinematic geometry such that
rocks pursue a vertical trajectory towards the surface, with erosion occurring perpendicular to that
path. Thus calculations based on vertical erosion typically simplify more complex processes
involving lateral advection that are driven by horizontal tectonics and deformation. Lateral
advection usually lengthens the path that a geochronometer takes to the surface. Hence, the particle
travels further than estimated with solely vertical transportation, and cooling ages could
underestimate erosion rates.
Nevertheless, we follow conventional practice in this study by assuming that particle uplift and
erosion are 1-dimensional processes such that an average unroofing rate (dz/dt) may be calculated
from:
=
ct1.
(dT/dz))T-(T
dtdz sc
(1)
Where Tc is the closure temperature of the geochronometer, Ts is the surface temperature, dT/dz is
an assumed geothermal gradient, and tc is the closure age of the mineral.
3.3 Thermal structure during active erosion
Even with a 1D system, estimating the geothermal gradient is of prime importance in determining
erosion rates. Two end-member approaches may be taken to approximate the depth of the closure
isotherm: a) assume an average geothermal gradient to predict the depth of the isotherm, or; b) use
numerical models to predict the depth of the isotherm. A detailed modeling approach might seem to
be the best solution. However, uncertainties in temporal location and rates of fault movement,
distribution of heat-producing radioactive isotopes, the role of fluids, erosion rate, and subsequent
13
topographic development, dictate that this approach is often under-constrained and difficult to apply
to many situations. By default, most geochronological investigations use the first approach,
specifying a linear vertical geothermal gradient below the sampling location. The choice of a
geothermal gradient for an active region is, however, problematic. Most continental heat flow data
are taken from boreholes, commonly in basins, and away from tectonically active mountain belts.
Therefore, an “average” orogenic geothermal gradient is difficult to determine, and constraints
applicable to a particular location are even more elusive.
Because of these problems, we use a widely applicable model-based approach to estimate the depth
of the closure isotherm. Two main thermal effects determine the depth of the closure isotherm and
need to be addressed before we can start to analyse geochronological data. In actively eroding
orogenic belts, the near-surface geothermal gradient will be perturbed by erosion and relief. The
erosion rate controls how rapidly the crustal column moves towards the land surface, and thus the
rate of vertical heat advection by the rock mass. More rapid erosion causes more rapid advection of
heat to shallow depths. Relief controls the surface area of the mountain belt and so will affect the
thermal structure. Increasing the relief produces more efficient cooling because there is more
surface area of rock in contact with the atmosphere.
Previous analytical and numerical investigations [Mancktelow and Grasemann, 1997; Stüwe et al.,
1994] have examined the effects of erosion and relief on the thermal structure of a lithospheric
column, with the basal boundary condition fixed at depths of 50 to 100 km. In these models, the
entire lithosphere is heated by the vertical advection of a rock column (with associated heat) that
has mantle temperatures at its base. The models reach steady-state solutions in ~40 My
[Mancktelow and Grasemann, 1997].
We use a slightly different approach because, in reality, areas that experience rapid uplift rates
typically do not undergo rock and heat translation from mantle depths. Instead, in most mountain
belts, movement of rock occurs from the mid to lower crust to the surface along decollements, and
hence the crustal column experiences less overall heating. We use a model that approximates rock
mass that moves in laterally along a deep crustal decollement before eroding vertically towards the
surface. This limits the kinematic portion of the system to mid-to-lower crustal temperatures (depths
of 35 km), rather than upper mantle temperatures (depths of 50 to 100 km in other models).
14
We investigate the approximate 2-D, steady–state thermal structure using a 2-D combined diffusion
and advection finite-difference scheme [Fletcher, 1991]. Average values for continental crust are
used with surface heat flow of 57x10-3 W/m2 and a uniform radioactive heat production of 1.0x10-6
W/m3 [Fowler, 1990]. The basal boundary condition is fixed at 35-km depth to the temperature at
time t = 0. The sides are zero heat-flow boundaries. Erosion is simulated by the vertical advection of
rock, from the basal boundary, through steady state topography which is generated instantaneously
after t > to. The surface temperature (Ts) is set to 20°C on the valley floor and we assume a lapse rate
(variation of temperature with elevation) of 6.5°C/km [Bloom, 1998]. The topography has straight
hill slopes (in 2D) that are fixed at a 30° angle to model a landslide-dominated landscape, in steady
state, at threshold conditions [Burbank et al., 1996]. The model is run for 20 My because the 350°C
isotherm responds relatively rapidly, and this is a time frame comparable to the longevity of major
structures within many mountain belts. The model output was compared to the basic steady-state
analytical solutions given by Jaeger [1965] and Mancktelow and Grasemann [1997]. We apply the
thermal model to address three classes of problems: 1) the range of erosion rates and relief over
which the assumption of flat isotherms is valid; 2) the depth of the muscovite closure isotherm for
various erosion rates and topographic profiles, and; 3) the temporal response time of the thermal
system to changes in erosion rate.
Stüwe et al. [1994] illustrate that the deflection of isotherms by topography is important in low-
temperature fission-track geochronology. The valleys may have older ages than predicted from
summit ages due to changes in the near-surface geothermal gradient caused by the cooling effect of
valleys and the insulating effect of peaks. In this paper, we argue that the topographically induced
deflection of the 350°C isotherm is negligible for most geologically reasonable erosion rates, given
the errors in the chronological analysis. As an example, we can examine the thermal structure for a
scenario with 4 km of relief undergoing erosion rates of 1.0 and 3.0 km/My (Fig. 1a & 1b). It can be
seen that the depth to the muscovite closure isotherm (considered here to be ~350°C) is very
dependent upon the erosion rate, but the isotherm itself remains effectively horizontal. If the relief is
increased to 6 km and a 3 km/My erosion rate maintained, the isotherms experience only ~400 m of
relief over wavelengths of ~20 km (Fig. 1d). The isotherm deflection from horizontal causes a
maximum discrepancy in the topographic age range of < 0.15 My (calculated using the difference
15
in depth to the closure isotherm in combination with the specified erosion rate). Because this falls
within the typical analytical error of most single-grain 40Ar/39Ar analyses, we ignore this source of
uncertainty.
To investigate the effects of relief and erosion rate on the deflection of the 350°C isotherm, a larger
sensitivity analysis was conducted with the relief ranging from 0 to 6 km and the erosion rates 0.1 to
3.0 km/My (Fig. 2). Increasing the erosion rate causes an exponential decrease in the depth of the
350°C isotherm. Increasing the relief for a given erosion rate decreases the depth of the isotherm
below the valley floor because cooling is enhanced under larger valleys. These rates and
topographic relief span most geologically reasonable circumstances, but due to the exponential
relationship between isotherm depth and uplift rate, the isotherm deflection will increase markedly
with rates over 3.0 km/My in topographic relief of 6 km or more.
An understanding of the temporal response of the thermal system is important to evaluate the
applicability of the model to real situations. Starting from the initial geothermal gradient and 4 km
of relief, the thermal model can be used to examine the time and depth response of the 350°C
isotherm to various erosion rate scenarios (Fig. 3). Compared to the depth of the isotherm at 20 My,
from the initiation of erosion at 0 My approximately 60 to 80% of the depth response has occurred
after 5 My, and approximately 90 to 95% of the depth response has occurred after 10 My (Fig. 3a).
The system generally takes longer to equilibrate for slower erosion rates, whereas with high erosion
rates of > 2 km/My, 95% of the response has occurred after 10 My.
Additional insight comes from examining the response of the 350°C isotherm to instantaneous
change in the erosion rate at time t = 20 My (Fig. 3b). Increasing the erosion rate from 1.0 to 3.0
km/My has a similar response time as before, with ~90% of the total change occurring within 5 to 6
My. The response to a decrease in erosion rate from 3.0 to 1.0 km/My takes longer, with ~90% of
the total change occurring within 10 My. Therefore, the thermal model results are generally
applicable to systems with 0 to 6 km of relief, which have undergone vertical erosion at uniform
rates from 0.1 to 3.0 km/My, for > 10 My
For easy integration into our detrital cooling-age model, we have adopted a simplified approach to
predict the depth of the isotherm for a specified erosion rate (dz/dt) and relief (zs-zv), and limit our
16
analysis to applications where the assumption of a horizontal closure isotherm is valid. To calculate
the depth to the closure isotherm (zc), we use an empirical fit to the model results (Fig. 2). The
equation has two exponential functions that represent: a) the exponential increase of the effects of
topography with increasing erosion rate, and b) the exponentially decreasing depth of the closure
isotherm with increasing erosion rate.
We recognize that constraining the thermal structure is of prime importance for exact interpretations
of geochronological data. Our model uses a simplified topography and is only applicable for those
conditions with approximately horizontal closure isotherms and with erosion rates and relief within
the bounds specified. In reality, each mountain belt and potentially individual particles within a
given orogen will experience a different thermal history. Overestimations of the depth of the closure
isotherm will lead to overestimations in the erosion rate, and vice versa. Given this complexity, our
thermal model is a reasonable solution to generalized applications, and it is important to note that
investigations of relative erosion rates within the same orogen may not be hampered by
uncertainties in the closure-isotherm depth to the same degree as comparisons between regions.
3.4 Steady-state landscapes
A key component of the thermal model is the assumption of a steady-state landscape: average
topographic characteristics remain unchanged over timescales of ~107 years. Although this
assumption is found in many other thermal models [Henry et al., 1997; Mancktelow and
Grasemann, 1997; Stüwe et al., 1994] and is embedded in our thermal model, the concept of a
steady-state mountain belt is poorly defined. The basic assumption of geomorphic steady state is
that regional topographic parameters remain invariant at appropriate timescales. This does not
require erosional output flux from each point in the landscape to exactly balance the tectonic input
of rock flux through each point, but merely requires that regional relief, hypsometry, and drainage
density remains steady at time scales equal to, or greater than, major climatic cycles (> 100 Kyr).
Considered within the time frame of a human life, the assumption of steady state may seem absurd.
In the field we see evidence for striking spatial and temporal variations in erosion: landslides,
17
glacial valleys, and sediment preserved within the mountain belt, all attest to differential denudation
rates. However, at geological timescales, the concept of steady state is necessary, and in the
Himalaya, we can use a simple back-of-the-envelope argument to suggest that a long-term
topographic steady state is likely to exist. If the present convergence rate between southern Tibet
and India (~20 km/My) is representative of the last 10 My, and we assume that half of the total
convergence is due to the Indian plate underthrusting Tibet, then the remaining 100 km of
shortening must be accommodated by the Himalaya. Given that the mean elevation of the Himalaya
is only approximately 2-5 km, a rough balance per unit area is required between rock uplift and
erosion to remove the excess ~9.5 km/My of rock flux. The observations that Himalayan hillslopes
are maintained near the threshold for failure by bedrock landslides [Burbank et al., 1996], and that
major Himalayan drainages appear to predate the main topographic axis [Wager, 1937], also
support the argument that rock uplift is not outpacing the rate of erosion.
Because the response time of the thermal system is longer than short-term fluctuations of elevation
about a mean topography, we can reasonably assume that the closure isotherm does not move
appreciably with respect to the surface during the closure interval of the minerals. The temporal
variations about the average steady-state topography (105 years) are small in comparison to the
cooling ages of most samples. Therefore, it is likely that the minerals will pass though the closure
interval at approximately the same rate and that the resulting cooling ages will provide a good proxy
for the long-term erosion rate, if the other assumptions are valid.
3.5 Spatial resolution
Commonly, geochronologists have interpreted bedrock cooling ages in terms of tectonic zones with
related cooling and erosion histories. The natural division of a landscape into river basins, however,
provides a more readily defined framework within which to consider the detrital cooling-age signal.
For the purposes of this model, we assume that drainage basins are small enough to drain a single
tectonic zone. Therefore, each point in the basin will undergo uniform erosion and share a
genetically common thermal history for the specified relief and erosion rate of the basin. The
18
geological characteristics of the individual drainage basin will control the distribution of cooling
ages found in sediment at the basin mouth
Whereas assumptions of basin uniformity must be correct at some spatial scale, clearly larger
drainages will be more complex. A large basin can be broken down into many sub-basins to
represent spatial variations. If a sub-basin approach is taken to investigate spatial variations in
erosion rate, then each must be considered separately in terms of erosion rate, relief, and thermal
history. This simplification requires that lateral heat flow due to different erosion rates is negligible.
The validity of choosing a particular size of tributary for modeling will depend upon the geological
constraints available: with a larger number of sub-basins and many unconstrained variables, the
model results must be viewed with increasing skepticism.
3.6 Vertical age distribution for a theoretical basin
If we accept that a) the basin is undergoing vertical erosion in a steady-state landscape and thermal
structure, and b) the depth of the closure isotherm for a given basin can be modeled as a function of
a uniform vertical erosion rate and basin relief, then mineral cooling ages will increase linearly with
elevation. The vertical distance from a horizontal 350°C isotherm to valley bottoms, for example, is
less than the distance to mountain summits, and this is reflected in younger bedrock cooling ages at
the base of a mountain (Fig. 4). Thus the cooling age (tc) of a point in the landscape can be
calculated from:
)/( dtdzzz
t cxc
−=
(2)
Where zx is the elevation of the sample location, zc is the elevation of the closure isotherm, and
dz/dt is the erosion rate. We can examine the consequences of varying the erosion rate on the
predicted age range for basins of 2, 4, and 6 km of relief (Fig. 5). As the erosion rate increases, the
summits and valley floors exhibit younger cooling ages, but in addition, the range of cooling ages
between valley and summits decreases as the closure isotherm becomes shallower.
19
3.7 Distribution in ages at the basin mouth.
The distribution of detrital ages in a basin can be presented on a probability density plot, which
displays a probability density function (PDF) representing the probability of finding a grain of a
specified age within the overall age distribution of the basin. Equation 2 can be used to predict the
range of ages found in a basin undergoing a specified erosion rate, but not the distribution of
probability within the age range: the number of grains of each age represented at the basin mouth.
If the system of erosion and transportation is totally efficient, the theoretical detrital cooling-age
signal found in sediment at the basin mouth can be considered to be an exact integration of the
bedrock cooling ages within the basin. For a given relief and erosion rate, the probability of finding
a grain of a certain age (a function of the elevation) will be dependent upon the fraction of land at
the corresponding altitude (see Fig. 4). The probability of dating the maximum-age grain in a
detrital sample, for example, will be low because only a small percentage of the drainage area of an
average basin is at the top of a mountain. Therefore, the probability of land occurring at a specific
elevation (Pz), the hypsometry, can be used as a proxy for the probability of dating a grain of a
particular age (Ptc). Thus the elevation PDF can be combined with the age range between the valley
cooling age (tcv) and the summit cooling age (tcs) to produce the theoretical PDF:
( )xPtP ztc =)(
[3]
where, for tcv < tc(t) < tcs,
[ ]vscvcs
cvccvcsv zz
ttttttt
zx −
−
−−−+= .
)())(()(
[4]
otherwise Ptc(t) = 0. The resulting PDF, with the area normalized to unity, is our “theoretical” PDF
and can be thought of as the hypothetical distribution of ages generated from the zero-error analysis
of grains obtained from all elevations within the basin, in proportion to the frequency of that
elevation.
20
It is illuminating to assess the three assumptions, in comparison to the analytical errors, that are
imbedded in this approach to modeling the distribution of ages: 1) uniform erosion rates across the
basin; 2) homogeneous distribution of the mineral being dated; and 3) insignificant transport and
storage times within the system. The first assumption requires that every point in the modeled basin
be treated as a source that contributes equally to the basin cooling signal, and the erosion rate is
independent of elevation or position within the basin. Although perhaps not intuitive, this is a
necessary consequence of steady state. If average climatic and tectonic factors remained constant,
the relief in a steady-state landscape would neither change substantially through time due to
preferential peak erosion, nor increase substantially through time due to preferential river incision.
In this context, “steady state” means the topography at present has the same statistically averaged
topographic characteristics as the topography at the time that the sediments in the rivers today
eroded. Although it is unlikely that the topography remains exactly the same, perturbations due to
high-frequency small landslides and short-term shielding of areas from erosion should be
insignificant compared to the overall shape of the hypsometry.
Another prerequisite of this approach is the assumption of a uniform distribution of geochronometer
within the basin. The detrital cooling-age PDF will be weighted towards those areas that are
supplying more geochronometer per unit area. The appropriateness of this assumption has to be
assessed in each setting to which this model is applied. If, from bedrock mapping and petrography,
the spatial distribution of the target mineral for dating is known, then appropriate weightings can be
assigned by combining this spatial distribution with the digital topography to yield a weighted “
target mineral hypsometry”, and thus a corrected basin PDF.
The assumption of no significant storage in the basin must be evaluated because, if a significant
fraction of the sediment is stored while in transit to the sampling site, the basin PDF will be skewed
toward older ages. We use two different arguments to contend that, in most active orogens
experiencing rates of erosion > 0.5 mm/yr, storage cannot be significant (over timescales
comparable to the analytical errors of the geochronological technique). First, at such rates, soil-
mantled hillslopes are uncommon, such that most sediment storage would have to occur along the
valley bottoms. Such sediment storage would mantle the valley floor and prevent river incision from
occurring, thereby preventing sustained high erosion rates. Second, from a volumetric perspective,
21
given that valley bottoms only occupy a small percent of the total area, they would have to store a
very large thickness of sediments to have any measurable effect: clearly an uncommonly observed
condition in active mountain belts. We can consider the consequences of storing the sediment in the
basin for 0.5 My, which is a timescale of significance in comparison to the analytical errors of the 40Ar/39Ar dating (note that sediment storage since the last glacial maximum, ~20,000 years ago, is
extremely short compared to the analytical errors). A landscape undergoing erosion rates of 1
mm/yr would experience 0.5 km of erosion over the same interval. It would be possible to store
only a small fraction (probably << 1%) of this volume in the valley floors of rapidly eroding
mountains.
3.8 Examining the control of relief and erosion controls on the theoretical PDF of a single drainage basin
We can use the model to generate a theoretical distribution of detrital ages by defining basin
characteristics (relief, hypsometry, and erosion rate). Before examining actual drainage basins, it is
useful to consider the sensitivity of parameters controlling the cooling-age PDF of a single
catchment. For this purpose, we use a hypothetical drainage basin with a Gaussian distribution of
land area with elevation; in this case most of the land area is contained in the middle elevations of
the drainage network, as might be expected with a steep fluvial basin on a mountain flank.
Various uplift and erosion rate scenarios may be examined (Fig. 6). Increasing the relief of a basin
widens the PDF as the vertical separation between the summit and closure isotherm increases,
whereas the vertical separation between the valley floor and closure isotherm decreases. Increasing
uplift rate generates younger ages and narrows the width of the PDF for a given basin relief (Figs. 5
& 6). The summit-to-valley contrast in ages will be subdued, however, when relief is high and
erosion rates exceed 3 km/My because closure isotherms become increasingly deflected by surface
topography.
Once the thermal structure has been constrained, the distribution in ages in a basin is primarily a
function of relief, erosion rate, and hypsometry. Hence, on the basis of an observed distribution of
detrital ages, we have the potential to invert the relief and erosion rate from the geological record
22
(as suggested for palaeorelief by Stock and Montgomery [1996]). Using the record of detrital
cooling ages from foreland basin sediments, we could in theory test the hypothesis of Molnar and
England [1990] that increased Quaternary incision drove relief production. We would expect the
detrital PDFs from Himalayan basins to move diagonally up and to the right in figure 6, displaying
a younger and narrower range in ages, as relief and erosion rates increased in the Quaternary.
The hypsometry of a basin results from a complex interplay of lithology, erosion rate, tectonics,
climate, surface process, and time [e.g. Keller and Pinter, 1996; Ohmori, 1993]. To explore the
effects of hypsometry, we examine end-member basin morphologies: hypsometries where most of
the basin is situated in the top, base, or middle of the drainage basin. If most of the land area is
concentrated in the lower elevations, the cooling-age signal from the basin will be biased towards
young ages (Fig. 7, case a). If a basin is dissecting the edge of a plateau, land area may be
concentrated in the headwaters, and the age population will be biased towards older ages (Fig. 7,
case e). Basins with land concentrated in the middle reaches (Fig. 7, case d) display normally
distributed cooling-age PDFs like those modeled in figure 6. These might be representative of the
steep fluvial basins experiencing strong tectonic forcing such as those found on the topographic
front of the Himalaya. Alternatively, glacial erosion also appears to concentrate alpine topography
towards the middle elevations of basins with very high relief [Brozovic et al., 1997].
4.0 Application to two Himalayan basins.
4.1 Geological Background and sample sites
In order to illustrate the modeling method outlined above, we consider 40Ar/39Ar detrital muscovite
data for two sediment samples collected in central Nepal from the Marsyandi River and one of its
tributaries, the Dordi Khola (Fig. 8). Along its course, the Marsyandi transects many of the tectono-
stratigraphic zones of the Himalayan-Tibetan orogen [see Hodges, 2000 for review]. Its headwaters
lie within weakly metamorphosed to unmetamorphosed Indian passive margin rocks of the Tibetan
23
zone. As the river cuts south through the Annapurna and Manaslu massifs, it flows across the
Machhapuchhare Detachment Fault, the Chame Detachment fault (the basal structure of the South
Tibetan fault system in this area [Coleman, 1996]) and over high-grade metasedimentary and meta-
igneous rocks of the Greater Himalayan zone that have been intruded by Oligo-Miocene
leucogranites. Finally, as the river passes through the Himalayan foothills, its bedrock includes
deformed metamorphic rocks of the Main Central Thrust zone and footwall metasedimentary rocks
of the Lesser Himalayan zone.
Sample 1 was collected from the riverbed of the Marsyandi roughly 40 km downstream from the
trace of the Machhapuchhare detachment (Fig. 8). Potential source regions for the muscovite in this
sample include the structurally highest Greater Himalayan gneisses and leucogranites (which yield 40Ar/39Ar muscovite plateau dates of ~17 to 18 Ma in this area [Coleman and Hodges, 1995;
Copeland et al., 1990]) and rare hydrothermal veins in Tibetan zone sedimentary rocks (with 40Ar/39Ar muscovite plateau dates of ~14 Ma [Coleman and Hodges, 1995]). Sample 2 was
collected in the Dordi Khola, roughly 400 m upstream of its confluence with the Marsyandi. Its
drainage basin includes the structurally middle and lower parts of the Greater Himalayan zone, the
Main Central thrust zone, and the uppermost Lesser Himalayan zone rocks. Although bedrock 40Ar/39Ar muscovite data are not available for the middle and lower Greater Himalayan rocks in the
Marsyandi drainage area, samples from equivalent structural levels in the Kali Gandaki drainage
(roughly 80 km to the west) yield ~15 Ma plateau dates [Vannay and Hodges, 1996]. Muscovites in
Sample 2 with a provenance in the Main Central thrust zone or the uppermost Lesser Himalayan
zone should yield considerably younger 40Ar/39Ar dates. Edwards [1995] reported dates of 6.2 ± 0.2
Ma and 2.6 ± 0.1 Ma for muscovites collected from the Main Central Thrust zone in the Marsyandi
valley. Such young cooling ages support other thermochronological evidence for widespread Late
Miocene-Pliocene metamorphism of the Main Central thrust zone and its footwall in the central
Nepalese Himalaya [Copeland et al., 1991; Harrison et al., 1997; MacFarlane et al., 1992;
Macfarlane, 1993].
The catchment areas, topographic parameters, and hypsometric curves for the sampled basins (Fig.
8) were extracted from a 90-m digital elevation model (DEM) of the region using ARCINFO
software. The upper Marsyandi basin (Fig. 8, (i)) contains 6500 m of relief and is 2270 km2 in size,
24
of which 1230 km2 comprises Tethyan sediments according to the map of Colchen et al. [1986]. For
this investigation, we consider only the remaining 1140 km2 of basin that drains the top of the
Greater Himalaya sequence because the rare hydrothermal muscovites in the Tibetan Zone as well
as the Tethyan carbonate and mudstone lithologies, make a negligible contribution to the detrital
muscovite signal. This assumption is supported by examination of the fluvial detritus from these
areas, which is dominated by rock fragments of fine-grained sediments. Ignoring the Tibetan zone
in the drainage area does not affect the range in ages of the basin as the maximum basin relief is
contained within the Greater Himalayan zone. The hypsometry changes, however, and mean relief
decreases from 4800 m to 4400 m. In addition, limiting the investigation to the area south of the
Machhapuchhare Detachment Fault means that assumptions of uniform erosion rate are more likely
to be valid. The Dordi Khola drains the southern front of the Himalayan topographic axis and is
351 km2 in extent, with 7200 m of relief, and an average elevation of 2900 m (Fig. 8, (ii)).
4.2 40Ar/39Ar Analytical Protocols
The two samples were washed and sieved to a range of grain sizes between 500 and 2000 µm prior
to the commencement of muscovite separation. Individual muscovite grains were isolated by
applying standard gravimetric and magnetic separation techniques, followed by hand-picking under
a binocular microscope. The mineral separates were washed sequentially in distilled water, acetone,
and ethanol before irradiation at the McMaster University research reactor. The irradiation package
included aliquots of the neutron-fluence monitor Fish Canyon sanidine (28.02 Ma, Renne et al.
[1998]), as well as a variety of salts that served as monitors for interfering nuclear reactions.
After irradiation, the muscovites and monitors were analyzed at the 40Ar/39Ar laser microprobe
facility at the Massachusetts Institute of Technology [Hodges, 1998]. Gas was extracted from
individual mica crystals by fusion in the defocused beam of an Argon laser operating at 18 W for a
period of approximately 10 seconds. After purification to remove reactive species, the extracted gas
was analyzed on an MAP 215-50 mass spectrometer using a Johnston electron multiplier. Total
system blanks were measured at the beginning of each analytical session and after every tenth
analysis of an unknown.
25
Apparent ages (dates) calculated for each muscovite are reported in Appendix2, Table 1, with an
estimated 2-σ uncertainty obtained by propagating all analytical uncertainties. (In order to illustrate
the proportion of this uncertainty that is attributable to uncertainties in the neutron flux during
sample irradiation Appendix2, Table 1, shows uncertainties in apparent ages calculated with and
without the contribution from the irradiation parameter J). Further details on analytical techniques
may be found in Hodges and Bowring [1995].
Given a date (tc), and an analytical uncertainty for that date (σ), a probability density function can
be calculated for each grain assuming that a Gaussian kernel represents the distribution of error [e.g.
Bevington and Robinson, 1992; Deino and Potts, 1992]]. For a sample of N grains collected from a
specific locality, the PDF of the age of each grain (n) can be combined:
∑=
=
−−
=Nn
n
nntt c
en
tP1
))(.2))((
( 2
2
..2).(
1)( σ
πσ
(5)
Once the area of the resulting curve is normalized to unity, a summed probability density function
(SPDF) is generated that represents the distribution of age probability within the sample.
4.3 Detrital cooling-age results and modeling theoretical PDFs
The 40Ar/39Ar results display distinctly different detrital signals originating from each catchment
area (Fig. 9). The upper Marsyandi basin SPDF contains 35 grains that range in age from 11.2 ± 1.4
My to 18.7 ± 1.3 My and is characterized by a sharp peak at ~ 17 My and a “tail” of younger grains
from 10 to 14 My. The peak is comparable to bedrock muscovite 40Ar/39Ar ages from the upper
Greater Himalaya sequence [Coleman and Hodges, 1995; Copeland et al., 1990]. The Dordi Khola
contains 39 grains that range from 2.6 ± 1.2 My to 12.7 ± 0.5 My. The SPDF is characterized by
multiple peaks between 3 and 8 My, and a single peak at ~13 My.
Given the measured hypsometry for the sampled basins, our model can be used to predict the forms
of PDFs that would be expected to be observed for a given vertical erosion rate under steady-state
26
conditions. By matching the predicted curve to the actual SPDF we determine the solution that
results in the lowest mismatch (as defined below) by varying the erosion rate. With this
methodology, we estimate the approximate erosion rate for the upper Marsyandi basin (Sample 1)
as 0.95 km/My and for the Dordi Khola basin (Sample 2) as 2.15 km/My (Fig. 9). Although the
distribution of ages within the two samples is about what we would expect if the erosion rates were
a factor of two higher in the Dordi Khola basin than the upper Marsyandi basin (cf., Fig. 5), our
ability to reproduce the simple SPDF of Sample 1 is much greater than our ability to match the
more complex function of Sample 2. There are several possible reasons for this. One is that the
riverbed sediments at the Sample 2 locality do not represent the distribution of bedrock cooling ages
in the Dordi Khola basin. This possibility could be examined through additional detrital mineral age
determinations for samples from the Dordi Khola. A second reason is that one or more of the initial
assumptions behind our model is incorrect. For example, the assumptions of uniform uplift rates
and steady-state behavior may be erroneous if the Late Miocene-Pliocene cooling ages in Sample 2
and the lower Marsyandi bedrock reflect episodic reactivation of the Main Central thrust in the
Marsyandi drainage [Edwards, 1995]. Under such circumstances, the pattern of bedrock cooling
ages through the Main Central thrust zone might reflect local complexities in thermal structure and
not the simple, depth-dependent distribution of isotherms required by our modeling scheme. Better
resolution of the bedrock cooling-age distribution would help us test this hypothesis.
For now, we focus on a third reason why the Sample 2 SPDF might be so complex and, moreover,
why even the simpler SPDF for Sample 1 should be viewed with caution: in each case, the
relatively small number of grains we analyzed at each locality might be insufficient to adequately
characterize the true population of detrital muscovite ages. Given the fact that any reasonable
detrital mineral geochronological study involves a random sampling of only a tiny fraction of the
total muscovite grains at a particular site, how confident can we be that such a sample is
representative? Our approach to this problem is to explore the fidelity with which random picks of
grains (which we refer to as a "grab sample") from a synthetic population reproduce the population
PDF as a function of the number of grains in the sample.
27
5.0 The construction of a grab-sample PDF.
To simulate the random dating of grains from a grab sample of sand containing millions of particles,
Monte Carlo integration [Press et al., 1992] is performed on the theoretical PDF (see Fig. 10). In
this paper we use the random-number generator of MATLAB 5.3. The initial conditions for the
random-number generator are determined by the computer clock at the start of each run. The
integration, with the number of points limited to represent the number of grains dated, represents the
random selection of grains in the grab sample from the river, and the random choice of which
particular grains are used for dating. In practice, micas from rapidly cooling areas require a size
fraction of approximately 500 to 2000 µm (lower-coarse to upper-very-coarse sand) in order to
select grains with enough radiogenic 40Ar for reliable analysis. In this situation, Monte Carlo
integration represents the random picking of muscovite grains within this specified size and mineral
fraction. To construct a synthetic SPDF for each Monte Carlo age pick, a standard deviation
representing the expected analytical error in the apparent age of the pick has to be specified. For the
purposes of this model, we use an estimated standard deviation of 0.64 My (Fig. 10), taken from the
mean uncertainty of our data in Appendix2, Table 1.
5.1 PDF comparison and statistics.
Given a grab-sample SPDF, some quantitative measure is required to compare it to the theoretical
PDF: we want to know how well the grab-sample SPDF reproduces the theoretical PDF. In
particular, if a finite number of grains (20-100) are dated, how well can we expect to reproduce the
characteristics of the theoretical PDF? To quantify the match (or mismatch), the sum of the
difference in the distribution of probability (Pdiff) between the theoretical probability (Ptheoretical) and
grab-sample probability (Pgrab) is computed over each age increment (t), and expressed in terms of a
percentage of total probability:
100*2
)()(0
tPtPP
grabltheoretica
t
tdiff
−=
∑∞=
=
28
(6)
This provides the percentage mismatch of the entire probability signal in the units of percentage
probability (Fig. 11). For illustration, if the two PDF curves are identical then the error is zero
percent. Alternatively, if we consider an error of 100 % then the two curves would have completely
different age ranges, with no overlap in probability-age space. To investigate the range of SPDFs
that a single theoretical PDF can generate, successive iterations produce many individual synthetic
“grab-sample” curves. Each iteration contains the same number of grains and the misfit between
each iteration and the theoretical curve is recorded. The 95% confidence interval of these errors is
taken as the measure of how well the specified number of grains represents the theoretical PDF for
95% of the time.
5.2 Resolution of the detrital dating
Before examining the observed data, the resolution of the detrital dating methodology can be
investigated. How small a change in the age distribution from a catchment can we detect using a
given number of dates, and how can we be sure that detrital signals are statistically similar or
different? The model can be used to help address the problem of whether SPDF ‘A’ can be
explained by the statistical variability of ‘B’ due to random grain selection. To do this we generate
an theoretical curve that best matches B. A number of iterations are performed (with the number of
grains in each iteration equal to that contained in A) to determine the most likely range of outcomes.
If the misfit between A and B is less than the 2-σ errors on the modeled range of outcomes, we can
be 95% certain that A and B are statistically indistinguishable.
As an example, we use a basin with 4 km of relief eroding at 1.0 km/My to investigate how well
different numbers of grains match the theoretical sample. For each specified number of grains, 1000
iterations produce 1000 grab-sample SPDFs, and the 95% confidence limits are taken from the
range in these (as described in 5.2.). In this example, (Fig. 12, scenario a) increasing the number of
grains decreases the average mismatch of the grab-sample SPDFs from the real PDF. In addition,
increasing the number of grains leads to more certainty in the result as the width of the 95%
29
confidence window decreases. The reduction in mismatch drops rapidly at first with increasing
numbers of grains, indicating that there is much to be gained from performing additional analyses.
However the rate of improvement declines rapidly after ~50 grains; increasing the number of grains
dated does a better job of constraining the theoretical cooling-age signal, but with diminishing
returns. With expensive dating techniques, there is clearly a trade-off between the cost of dating and
the extra confidence that large numbers of grains provide.
Unfortunately the same result is not applicable to all tributaries; the mismatch of SPDFs will be
related to the shape of the theoretical PDF. Consider, for example, the results of an age PDF
combined from a basin of 4.0-km relief eroding at 1.0 km/My and a basin of 4.5-km relief eroding
at 1.3 km/My (Fig. 12, scenario b). The more complex two-basin PDF (see figure insert) is more
difficult to match than the simple one-basin PDF. For any given number of dated grains, the mean
mismatch of SPDFs is ~3-8% larger for the more complex PDF than the individual basins shown.
The method of representing individual grain errors with Gaussian distributions means that the
precision of the geochronometer, in relation to the shape of the real PDF, will also affect the
mismatch. Low-relief basins with high erosion rates will have a narrow age PDF (Fig. 6) that high-
precision geochronometers will fit well. These geochronometers will have more trouble fitting the
broader peaks characteristic of basins with low erosion rates and high relief. It is therefore easier to
fit the “peaks” of a narrow PDF than the “tails” of broad peaks.
In these scenarios, the statistical analysis illustrates that ~60+ grains (scenario a) and ~90+ grains
(scenario b) are needed to achieve a mismatch of ≤ 15% at the 95% confidence level. Although a
15% mismatch may seem large, in practice it produces a reasonable fit visually (Fig. 13). This is
because error is only calculated where ages are present (if the error is < 100% then two curves have
some ages in common), and because most of the error generally represents misfits with the tails of
the theoretical PDF.
30
5.3 Himalayan catchments – synthesis of theoretical PDFs and random sampling.
We can also use this approach to explore the differences between the theoretical PDF and observed
data. The Dordi theoretical PDF is generated using an erosion rate of 2.15 km/My that produces a
mismatch error (calculated with equation 6) of 41% of total probability with the observed data . The
upper Marsyandi theoretical PDF has an erosion rate of 0.95 km/My and an error of 10% compared
to the observed data. From the theoretical PDFs of the two basins, 1000 grab samples were
generated that each contained N age selections (where N was the number of grains actually dated in
each basin). The dashed lines in figure 9 indicate the grab-sample SPDF that was the best fit to the
data SPDF from the first 30 iterations of Monte Carlo picks. They are shown to illustrate how the
grab-sample SPDF differs from the theoretical PDF. The best-fit grab-sample SPDF from the Dordi
has an error of 22% when compared to the observed data SPDF, while the best-fit grab-sample
SPDF from the upper Marsyandi has an error of 6%.
The model allows us to examine how well the theoretical PDFs represent the data SPDFs when we
start sampling the sediment. We can find the 95% confidence interval that N grains produce, and
test whether the theoretical curve falls within these limits. A confidence interval of 4% to 19% was
generated from the upper Marsyandi with 1000 iterations of picking 35 grains. The theoretical PDF
of the upper Marsyandi fits the data SPDF well, falling well within confidence limits and indicating
that the two curves are statistically indistinguishable. However, the fit is sensitive to the choice of
the erosion rate because small shifts in the peak probability of the theoretical PDF, away from the
peak probability of the data SPDF, produce larger errors.
The theoretical PDF from the Dordi fits less well, falling outside of the 18% to 26% confidence
interval, and the error is less sensitive to changes in the erosion rate. The very spiked SPDF from
the dated grains is due to ages with low errors (e.g. 5.7 ± 0.2 My), whereas the wide tails are caused
by ages with large associated errors (e.g. 2.8 ± 4.5 My). This makes it difficult for the mean 1-σ
error (0.64 My), used in the production of the theoretical PDF, to fit the curve very closely. The
effects of grain error can be seen as the grab-sample SPDFs fit the observed SPDFs more closely:
the errors associated with individual grains increase the range of ages found in the grab-sample
curve in comparison to the theoretical curve.
31
5.4 Discussion of modeling results
Although the model does a good job of matching the peak probabilities, both basins show minor age
populations that are problematic to replicate. The upper Marsyandi contains a young age population
(10 to 14 My), and the Dordi shows a minor older age population (9 to 13 My) that the model does
a poor job of representing. These are most likely due to invalid assumptions within the model. The
most likely cause is that erosion rates are not uniform across the basins and hence there are cooling-
age variations.
Differential erosion rates in the Dordi Basin would be geologically reasonable. There is a growing
body of evidence from geomorphology [Lave and Avouac, in review; Seeber and Gornitz, 1983],
structural (ref), and geochronology [Catlos et al., 1999; Catlos et al., 1997; Harrison et al., 1997;
MacFarlane et al., 1992], that the MCT has been active during the past 5-6 million years, or that
subsurface deformation associated with a ramp structure on the Himalayan sole thrust has led to
differential uplift across the Himalayan topographic front. To examine a basic scenario of
differential erosion, the Dordi basin can be divided into two regions, in which the MCT separates
the Greater Himalaya and Lesser Himalaya (see Fig. 8). For example, with erosion rates of ~2.2
km/My in the physiographically high Greater Himalaya and ~1.8 km/My in the Lesser Himalaya
foothills, together with an assumption that the latter is contributing half the amount of muscovite
per unit area, the mismatch may be reduced from 41% to 34%. This still falls outside the confidence
interval and the very young ages are still difficult to represent, perhaps due to hydrothermal
alteration in the MCT zone [i.e. Copeland et al., 1991].
Other potential sources of mismatch include sediment storage in the system, and short-term
imbalances in sediment supplied to the fluvial system. As discussed earlier, the first can be
effectively discounted due to the high erosion rates. In particular, with erosion rates of 1.7 km/My
in the Dordi, long-term sediment storage is unlikely. Short-term imbalances in sediment supply,
however, are more difficult to discount. Large landslides and debris flows have been reported from
the Marsyandi valley [Yamanaka and Iwata, 1982] and may cause an influx of grains of a certain
age (i.e. causing the characteristic 6-My peak in the data from the Dordi that is not seen in the
32
theoretical curve). However, these landslide fills are mainly concentrated in the lower reaches of the
Marsyandi.
The thermal modeling is an additional source for error as we employed a highly simplified model.
The model is restricted to the vertical erosion of a 35-km-thick crustal block. This matches the
depth of the Himalayan sole thrust that has been seismically imaged at approximately 30 to 40 km
depth beneath South Tibet [the MHT in Nelson et al., 1996]. However, in the Himalaya, erosion
occurs as the column is uplifted along the fault plane, and rocks therefore have a complex thermal
history. Cooling by the underthrusting slab, accretion of material to the hanging wall, shear heating,
and time, will all affect the thermal structure and resulting cooling history. Hence, it is clear that
improving thermal models and the subsequent calculations of the depth to the closure isotherm will
produce better insights into the tectonics.
6.0 Discussion
In this paper we have presented a numerical model that investigates the parameters that control the
detrital cooling-age signal from an individual basin. Numerous assumptions, many of which are
impossible to evaluate in the Himalaya at this time, underpin our treatment, but we believe that it is
an improvement on the simple assumption of a geothermal gradient, as used in many investigations,
because it accounts for the effects of erosion rate and topographic relief when predicting the depth
of the closure isotherm. Another improvement in the calculation of the position of the 350°C
isotherm is that erosion of the crustal column occurs from a depth limited to 35 km. This seems
more reasonable than eroding the entire lithospheric column, given that rock flux into mountain
belts commonly occurs along detachments at such depths. From examination of the temporal
effects, we have seen that for most scenarios the 350°C isotherm has achieved > 90% of its total
response within 10 My.
Despite these insights, the thermal and kinematic structure is typically the most difficult parameter
to constrain when trying to extract erosion rates from geochronology, especially from the geological
record. Although we realize that many the assumptions made are not strictly valid for many areas,
33
more accurate constraints may be, at best, difficult to determine. Our assumption of uniform and
vertical erosion over large areas is probably the largest simplification for most orogenic systems.
The lateral advection of heat and rock mass into mountain belts [i.e. Beaumont et al., 1994; Willet,
1999] along underlying thrust faults are important processes and will determine the exact pattern of
bedrock cooling ages.
For a predetermined thermal structure, our simplified model predicts the variation of cooling age,
given a uniform post-closure history, as a function of elevation. In a situation with horizontal
isotherms and a uniform distribution of geochronometer, we have shown that the hypsometry may
be used as a proxy for determining the detrital cooling-age signal that results from uniformly
eroding that topography. Assumptions of uniform distribution of geochronometer can be readily
assessed for modern applications in the field, and differences accounted for using GIS applications.
Extrapolation back into the stratigraphic record, however, requires more caution.
If the constraints and assumptions of the model are accepted, the methodology may be used to
predict the detrital cooling-age signal of an individual tributary. If the tributary is now sampled in
the field, and N grains dated, we can use our statistical method to: 1) assess how well N grains can
define the real cooling-age signal; 2) test whether the real data is statistically identical to the model
results (are we able to disprove the assumptions?); 3) decide whether dating 10 more grains, for
example, would produce a more conclusive result, and; 4) discern whether tributary A is eroding
faster than tributary B, given differences in basin characteristics and sampling uncertainty. We use
Monte Carlo techniques to assess this intrinsic variability of grain sampling, and have introduced a
way to measure the difference in two cooling-age distributions.
Our statistical analysis (Fig. 12) shows that, while the exact values of the error are not known when
using forward modeling, the relative increase in accuracy of dating of dating 70 grains, rather than
30, may be considered important, but the increase from 70 to 150 grains may not justify the extra
time and expense. It seems that as a general approximation 50-70 grains provide a good match of
the “grab-sample” SPDF to the theoretical PDF for a simple basin, with mismatch approaching
15%.
Given a series of detrital SPDFs from the stratigraphic record, we can now test if they are
statistically differentiable from one another. For example, if a modelled theoretical curve typically
34
generates 5-25% error at the 95% confidence level using 40 grains, then SPDFs generated from 40
grains in different stratigraphic horizons cannot be statistically differentiable until the mismatch
errors increase above 25%. As we have seen, (Fig. 12) the 95% confidence interval will be
dependent upon the shape and complexity of the SPDF, the analytical age error, and the number of
grains dated.
One caveat using this technique, however, is that the exact error remains ambiguous because the
true age signal is unknown. Unless the drainage area can be sampled uniformly, at regular sites
throughout the entire altitudinal and spatial range, the exact distribution of bedrock cooling ages
cannot be constrained. Furthermore, the detrital age signal can only be defined once the contribution
of each point within the basin has been corrected for local short-term variations in the erosion rate.
Clearly such an undertaking would be unrealistic for most applications of detrital mineral
thermochronology. Some method of approximating the theoretical signal is, therefore, needed to
assess the uncertainties associated with sampling. As a consequence, however, uncertainty
calculations using forward modeling are not strictly robust for real data.
The theoretical-PDF model is envisioned to be a tool for evaluating the relative influence of
parameters controlling the detrital cooling-age signal. It provides a good first-order approximation
for areas that have limited constraints and focuses the user on assumptions that may not be
applicable. With this approach in mind, we have presented 40Ar/39Ar analysis from two modern
Himalayan catchments. In one instance (the upper Marsyandi sample), the model provides a
reasonable fit to the observed data; in the other, it does not. In the latter case, further analysis
suggests that the mismatch is not the product of sampling bias alone, but instead indicates that one
or more of our assumptions is incorrect. Nevertheless, it is evident that, despite modeling
mismatches, we can confidently state that the average erosion rate varies significantly between the
two basins. Even if the erosion rate is not uniform across each basin, a spatial variation of 10-20%
is insignificant compared to the difference between the two basins considering the uncertainties on
the dates and random sampling. Furthermore, an estimation of the average erosion rate using an
integration of data from the entire basin will probably represent a more accurate value than a single
bedrock cooling age that is then extrapolated to a wider region.
35
7.0 Conclusions
We have presented an integrated approach to investigate how drainage-basin parameters interact to
produce the distribution of cooling ages found at the basin mouth. Understanding these factors must
underpin a thorough analysis of detrital cooling ages in the modern and stratigraphic record. A
thermal model is used to predict how the interaction of topography and erosion rate control the
depth of the 350°C closure isotherm. Increasing the erosion rate causes an exponential decrease in
the isotherm depth, and increasing the relief compresses the isotherms beneath valley floors. With
respect to the depth of a steady-state isotherm in our model, > 90% of the total depth response to an
increase in erosion has occurred within 10 My.
Monte Carlo analysis provides a useful tool for examining the processes of random selection that
control the detrital age signal. We have provided a new method to constrain the errors of detrital
cooling-age signals and to compare PDFs. The mismatch associated with a grab sample is
dependent upon the precision of the geochronometer, the shape of the SPDF or theoretical PDF, and
the number of grains dated. Therefore, the statistics of each sample need to be assessed separately,
with the caveat that forward modeling is not an exact predictor of the uncertainty.
Application of the model to real data provides a basis for examining the parameters that control the
theoretical cooling-age signal and may emphasize parameters that need further research and
constraint. Our Himalayan data highlights the need for a greater understanding of the kinematic and
thermal structure of an orogen in order to accurately interpret geochronological information. In
addition, further investigation is needed into how individual hinterland drainages interact and
combine to produce the cooling-age signals found in the foreland basin. Only then can we use
detrital mineral geochronological data to investigate the complexities of modern orogenic
deformation, and to extrapolate the results back into the stratigraphic record with confidence.
0
4
8
12
16
20
24
3.0 km/Myr1.0 km/Myrde
pth
belo
w v
alle
y flo
or (
km)
distance (km)
350oC
350oC
a) b)
403020 100
c)
3.0 km/Myr
403020 100
350oC
d)
403020 100
350oC
403020 100
c)
0
4
8
12
16
20
24
dept
h be
low
val
ley
floor
(km
)
1.0 km/Myr
36
Figure 1. Thermal structure of continental crust with erosion rates of (a) 1.0 km/My (b) 3.0 km/My after 20 My in a landscape with 4 km of relief. In scenario (c) and (d) relief is increased to 6 km with an erosion rate of 1.0 km/My and 3.0 km/My, respectively. Relief production in all models is instantaneous, with a steady-state landscape that contains 30o slopes, which simulate threshold conditions for landsliding. Note that the 350°C closure isotherm for 40Ar/39Ar in muscovite is essentially flat for scenarios (a), (b), and (c), and has only ~200 m amplitude of deflection for (d).
Figure 2. Average depth (y-axis) of the 350oC isotherm (zc) below the valley floors as a function of varying relief (x-axis) and erosion rates (labeled on the lines representing equal erosion rate) after 20 My. Each point represents the results of one model run. In the model, relief production is instantaneous, with a steady-state landscape that has slopes of 30o to simulate threshold conditions for landsliding. Range bars on the points indicate the vertical deflection of the 350oC isotherm, about the mean, due to topographic influence. The equation is our empirical fit to the modeled depth of 350oC isotherm as a function of the relief and erosion rate. The relief (R) is the difference between summit and valley elevations[zs - zv]
0
2000
4000
6000
8000
10000
12000
14000
16000
18000
20000
0 1000 2000 3000 4000 5000 6000
Relief, R (m)
0.1 km/My
2.5 km/My
2.0 km/My
1.5 km/My
1.0 km/My
0.5 km/My
3.0 km/My
dept
h, z
(m
)
depth of 350oC closure isotherm (zc). Range bars indicate maximum and minimum depths due to topographic deflection.
zc(dz/dt, R) = (0.18exp(-0.67.dz/dt)-0.34)*R + (19600*exp(-0.28.dz/dt))
37
0
2000
4000
6000
8000
10000
12000
14000
16000
18000
20000
0 5 10 15 20 25 30 35 40
3.0 km/My
2.0 km/My
1.5 km/My
0.5 km/My
1.0 km/My
2.5 km/My
0.1 km/My
1.0 km/My
3.0 km/MyDECREASE
INCREASE
0 to 20 My 20 to 40 My
(b)(a)
(i)
(iii)
(ii)
Time (My)
Dep
th b
elow
val
ley
floor
s (m
)
Figure 3. The temporal response of the depth of the 350oC isotherm for a system with 4 km of topographic relief. (a) Starting from a thermal steady state in the absence of topography and erosion, the lines represent the depth of the 350oC isotherm, at each point in time, for scenarios undergoing uniform erosion rates of 0.1 to 3.0 km/My (labeled). (b) After 20 My, three scenarios show the response to: (i) a decrease in erosion from 3.0 to 1.0 km/My; (ii) an increase in erosion from 1.0 to 3.0 km/My, and (iii) an increase in erosion from 0.5 to 3.0 km/My.
38
Sum
mit
age
Val
ley
age
cooling age (tc)
0 My
Tc
erosion rate (dz/dt)
geothermal gradient (dT/dz)
(zs-zv)
zs
closure
temperature
zx
zv
elev
atio
n (
z)
zc
tcv tcs
z w
ith t
path
tcx(z) = (zx-zc) (dz/dt)
frac
tion
of a
rea
elevation
elev
atio
n
age age
prob
abili
ty
zv zs tcv tcs
zs
zv tcv tcs
HYPSOMETRY x AGE RANGE AGE DISTRIBUTION
(i) (ii) (iii)
Figure 4. Construction of a "theoretical" PDF for an individual basin. A cooling age (tc) is calculated from the depth (zc) of the closure temperature (Tc), which is a result of the thermal modeling, and the erosion rate (dz/dt). The difference between summit elevation (zs) and valley elevation (zv) results in a difference between summit cooling ages (tcs) and valley cooling ages (tcv). The cooling age (tcx) of a sample 'x' collected derived from elevation zx can be calculated using the equation shown. The inset illustrates how the age distribution is governed by the combination of the age range (tcv to tcs), and relationship of land area to elevation, which is shown as a normal distribution here.
39
6km of relief
4km of relief
2km of relief
erosion rate (km/Myr)
age
(Myr
)
SUMMITS
}summit-to-valley
age ranges
0.5 1 1.5 2 2.5 30
5
10
15
20
25
30
35
40
45
VALLEY FLOORS
6km4km2kmAge ranges for basins of specified relief.
Figure 5. Relationship between summit ages (solid lines) and valley ages (dashed lines) for topographic relief of 2, 4, and 6 km undergoing erosion rates of 0.5 to 3.0 km/Myr. The vertical bars illustrate the age range with elevation for erosion rates of 1.0 and 2.0 km/Myr. The range in ages is a function of erosion rate and the relief. The range narrows as erosion rate increases, and 2 km of relief (black lines) contains a smaller range of ages than 4 km of relief (dark gray lines), which in turn is smaller than 6 km of relief (light gray lines).
40
0.5 1.0 1.5 2.0
2.0
4.0
6.0
increasing erosion rate (Km/My)
incr
easi
ng r
elie
f (K
m)
age
prob
abili
ty
0 50
0 4frac
tion
of la
nd
area
elevation (km)
cumulative fraction
of land area
0 4elevation (km)
Figure 6. Effects of uplift rate and relief on theoretical PDFs for a basin with a Gaussian distribution of land area with elevation (illustrated in the bottom two plots). In the calculations, the depth to the 350oC isotherm is taken from our thermal modeling. The scale on each inset theoretical-PDF plot is the same with the x-axis ranging from 0 to 50 My, and probability on the y-axis.
41
prob
abili
ty
"time since closure" (tc)
0
1
10 cumulative fractionof elevation
cum
ulat
ive
frac
tion
of a
rea
a
a
b
b
c
c d
d
e
e
a
b
c
d
e
elevation (z)
Fra
ctio
n of
land
are
aat
spe
cifie
d el
evat
ion
0zv
00
tcstcv
zs
cooling age
Figure 7. Effects of hypsometry on theoretical PDFs. The upper-left panel shows the relationship between a specific elevation and the land area at that elevation for 5 basins. The cumulative hypsometric curves are shown in the lower-left panel. The right panel shows the resulting theoretical PDF for the basin. The range in ages (tcv to tcs) is dependant upon the specified erosion rate. Basin (a) contains most land at lower elevations, whereas (e) contains most land at higher elevations. Basin (b) has a uniform distribution of land with elevation, and (c) is biased towards concentration in the middle elevations. Basin (d) has a normal distribution of land with elevation that was used as an approximation in the sensitivity analyses (Fig. 6).
42
MDF
Manang
TibetN
scaled 45%
% a
rea
0 2000 4000 6000 80000
0.2
0.4
0.6
0.8
1.0
frac
tion
of a
rea
0.5
1
1.5
2
frac
tion
of a
rea
% a
rea
U.MARSYANDI
DORDI
elevation (m)
0
0.2
0.4
0.6
0.8
1.0
0 2000 4000 6000 8000
MCT
Nepal
0.4
0.8
1.2
1.6
Tethyan strata
Greater Himalaya
Lesser Himalaya
0 20km
(i)
(ii)
Figure 8. Map of the upper Marsyandi drainage basin showing the detrital sample locations (black markers). The thick white lines represent the catchment areas upstream of the sample sites within the larger Marsyandi Basin. The Macchupuchare Detachment fault (MDF) is shown with fine dashes, and the Main Central Thrust (MCT) is shown with longer dashes. The inserts depict the hypsometry for (i) the upper Marsyandi (Sample 1) and (ii) the Dordi (Sample 2). The hypsometry is calculated using 50-m elevation bins, and then smoothed over 5 bins. Elevation data for the upper Marsyandi is taken from the area south of the CDF because the area to the north is composed of Tethyan sediments.
43
0 5 10 15 20 25 30N=35N=39
u. Marsyandi data SPDF
Dordi data SPDF
theoretical PDF
best fit synthetic "grab sample" SPDF
theoretical PDF
best fit synthetic "grab sample" SPDF
0
0.005
0.01
0.015
0.02
0.025
0.03
age (Myr)
prob
abili
ty
0.035
Sample 1
Sample 2
Figure 9. Diagram showing SPDFs generated from the results of 40Ar/39Ar dating samples from the upper Marsyandi (Sample 1) and Dordi basin (Sample 2). The black lines are the best-fit theoretical PDFs generated by the model for each basin. The dashed gray lines indicate the best-fit grab-sample SPDFs (to the data) from 30 iterations. The number of grains dated (N) varies for each sample, and this determines the number of Monte Carlo picks used for generating each grab-sample SPDF.
44
0 2 4 6 8 10 12 14 16 18 20
1-si
gma
erro
r (M
yr)
age (Myr)
mean = 0.64 Myr
0
0.5
1
1.5
2
2.5
Figure 10. Plot of grain age versus age uncertainty for the 40Ar/39Ar analysis of muscovite crystals from both samples. We use mean age error of 0.64 Myr (1-s) for the uncertainties in our model. The generally large age uncertainties are a result of the young grains in our study that contain relatively small amounts of 40Ar*.
45
10 15 20
20% mismatch
theoretical PDFgrab-sample
SPDF
age (My)
prob
abili
ty
Figure 11. Error calculation for a basin of 4-km relief eroding at 1 km/My, in conjunction with a normal distribution of land area with elevation. The theoretical PDF is outlined in black and shaded, whereas the grab-sample SPDF, containing 50 grains, is outlined by the gray dashed line. The white stars are a cartoon illustration of the Monte Carlo sampling of grains from the theoretical PDF (note that they all fall inside the black curve). The x-axis values of the stars are used as the reported mean age, and with a specified error, are used to produce Gaussian distributed kernels for each grain. The grab-sample SPDF is the summation of the individual grain kernels normalized to unity. The area with diagonal hatching represents the total mismatch between the theoretical PDF and the grab-sample SPDF, which is 40% of the total probability (area) of the theoretical PDF, or an error of 20%.
46
0 20 40 60 80 100 120 140 160 180 2000
10
20
30
40
50
number of grains dated (N)
erro
r (%
of p
roba
bilit
y)
mean95 percentilemean95 percentile
2- sigma
a) b)
relief 4.0 km 4.0 & 4.5 kmerosion rate 1.0 km/My 1.0 & 1.3 km/My
5 10 15 20 25 5 10 15 20 25
Theoretical PDF
b)
a)
Figure 12. Number of grains versus the mismatch error from 1000 iterations. The mean is shown with thick lines and the 95% confidence envelope in thinner lines. Two scenarios are illustrated: a) a theoretical PDF from a single basin with 4 km of relief eroding at 1 km/My (solid black line as mean) and; b) a more complex theoretical PDF constructed from a basin with 4.0 km of relief eroding at 1 km/My and a basin with 4.5 km of relief eroding at 1.3 km/My (dashed gray line as mean). Note that it is harder to match the more complex theoretical PDF than the individual basin.
47
10 15 200
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
0.018
7.5%2.5%
10%
15%
age (My)
prob
abili
ty
20%
5%
theoretical PDF
mismatch withgrab sample
SPDFs
Figure 13. A selected range of outcomes from sampling 50 grains from the theoretical PDF (shaded gray) of a basin with 4 km of relief eroding at 1.0 km/My (as in Fig. 11). Note that while mismatches up to 20% sound large, in reality the grab-sample SPDF still captures the key attributes of the theoretical PDF: the peak-probability age of each grab-sample SPDF varies less than ± 1 My in comparison to the peak-probability age of the theoretical PDF. The mean mismatch for 1000 runs and 50 grains is 9 ± 7% (see Fig. 12) at the 95% confidence limit.
48
49
Chapter 2
The downstream development of a detrital cooling-age signal, insights from 40Ar/39Ar muscovite thermochronology in the Marsyandi Valley of Nepal.
I.D. Brewer and D.W. Burbank
Pennsylvania State University, Department of Geosciences, University Park, Pennsylvania
K.V. Hodges
Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology,
Cambridge, Massachusetts
Abstract
The nature and variation of the distribution of cooling-ages in modern river sediment may provide
useful constraints on the rates of uplift and erosion within mountainous drainage basins. Such
sediment effectively samples all locations within the catchment area, however remote and
inaccessible, and may be preserved in the foreland basin. We assess the applicability of using
detrital cooling ages to constrain hinterland deformation by examining the modern drainage system
of the Marsyandi valley in central Nepal. Laser fusion 40Ar/39Ar data for detrital muscovite
collected from 12 separate sites illustrates that the downstream development of a detrital signal is
both systematic, and representative of the contributing area. The distribution of bedrock cooling
50
ages in a sub-catchment and the resulting detrital signal at the basin mouth can be modeled a
function of the erosion rate, relief, hypsometry, drainage area, and the distribution
thermochronometer. Given that independent constraints are available for most of these variables,
the detrital age signal is a robust indication of the spatially averaged erosion rate. In the Marsyandi,
our model predicts ~2 fold differences in erosion rates, with the southern topographic front of the
Himalaya experiencing the most rapid rates of exhumation, exceeding ~2 mm/yr. Over the 100 to
200 km length scale of the Marsyandi basin, there is no significant comminution of the muscovite
grains. Comparison sample pairs from: a) opposite ends of the same sandbank; b) from the modern
river and a fill terrace, are not found to be statistically different at the 95% confidence level,
indicating that at short spatial (10’s of m) and temporal (1000’s of years) scales, the detrital cooling-
age signal appears to be stable.
1.0 Introduction
The growth and evolution of an orogenic belt can have global impact through interactions with
geochemical cycles [Derry and France-Lanord, 1996; Raymo et al., 1988] and climate [Kutzbach et
al., 1993; Ruddiman and Kutzbach, 1989]. Constraining the temporal variation in the development
of topography and the rate of erosion is fundamental to understanding the relationship between
orogenesis and these processes. Despite numerous previous studies of actively deforming mountain
belts, understanding the development of an orogen over geological timescales remains problematic
due to a lack of precise timing constraints. For example, bedrock thermochronology restricted to
rocks currently exposed at the surface today and hence provides a limited temporal record due to the
high erosion rates found in active orogens. Conversely, analysis of basinal sediment can yield a
good temporal record, but is commonly difficult to interpret directly in terms of hinterland erosion
and development.
Detrital mineral thermochronology offers the opportunity to combine the stratigraphic record
preserved in the foreland with the quantitative analysis of thermochronology. Sand grains preserved
in foreland-basin stratigraphy represent an integration of information from the contributing
upstream area at the time of deposition. Such a sample contains millions of sand grains, with each
51
particle sampling a slightly different point within the basin. Before detrital thermochronological
data can be reliably interpreted, however, the processes controlling the cooling age signal need to be
understood and key questions need to answered: “How are the pattern of erosion, distribution of
lithology, and landscape characteristics manifest within the distribution of detrital cooling ages
observed in the foreland?” In addition, the effects of mechanical breakdown of the
thermochronometer within the river system, and the temporal and spatial reliability of the age signal
are unknown. For example, if we collect two samples from different locations within the river
sediment, will these produce different age distributions or will they represent one homogeneous age
population? If the age signal varies locally, or if a point source or a sub-catchment within the basin
controls the signal, then only a limited amount of information will be extracted from the sediment
preserved. To answer these questions using the stratigraphy, however, is impossible and so the
basic Principle of Uniformitarianism must be applied; we must understand the processes operating
in the modern environment in order to provide a basis for the interpretation of the geological record.
Our previous work [Brewer et al., Chapter 1] investigated factors controlling the modern detrital
signal in two small Himalayan catchments. The examination of individual catchments enabled the
distribution of bedrock cooling ages to be modeled as a function of topographic relief, erosion rate,
and the subsequent geothermal gradient. If isotherms are horizontal (a reasonable assumption at
depths > 8 km below the valley floors), the detrital cooling-age signal resulting from erosion of
topography is determined by the hypsometry (the distribution of area with elevation) of the basin.
These simple models, however, are applicable to drainage basins that are contained within one
tectonic zone and have homogeneous distribution of thermochronometer. In most active orogens
this constraint limits investigations of this type to catchments within larger, orogenic-scale drainage
systems. For example, Brewer et al. [Chapter 1] examined the cooling age signal of two tributary
basins within the larger Marsyandi River system.
In this paper we investigate the more extensive detrital system of the complete Marsyandi River,
and examine how the cooling-age signal of individual catchments combine to produce a modern
foreland signal. We use 40Ar/39Ar analysis of individual muscovite grains to examine how the
lithology, erosion rate, and hypsometry of individual catchment areas vary, and investigate how
these parameters control the evolution of the trunk stream cooling-age signal from the headwaters to
the foreland basin. This allows us to examine how well the cooling-age signal at the basin mouth
52
represents the contributing area upstream, and hence provides a baseline study for the interpretation
of future detrital investigations.
2.0 Previous investigations of detrital thermochronology
Detrital-mineral thermochronology has been used to investigate: (a) the thermal evolution of
basins; (b) source area constraints; (c) stratigraphic age, and; (d) the erosion history of orogens. The
wide range in closure temperatures for different thermochronometers means that they can be applied
to many types of temperature-dependant geological problems. High-temperature
thermochronometers are typically used to date the crystallization ages of minerals, while low-
temperature thermochronometers are typically used to investigate the late-stage cooling history.
Thermal evolution studies of basins are commonly used to constrain hydrocarbon production
windows. They typically have relied on fission-track dating of detrital apatite [e.g. Green et al.,
1996], although 40Ar/39Ar thermochronology has also been used [Copeland et al., 1996; Mahon et
al., 1998]. The age at which mineral cooling ages are reset by burial metamorphism has been used
to constrain models for the thermal evolution of the basin. Low-temperature thermochronometers
are most commonly used because kerogen breakdown starts to occur at < 400°C [Levorsen, 1967].
Studies of mineral-isotopic systems with high-closure temperatures (e.g. U-Pb zircon or monazite)
are principally aimed at characterizing sediment source areas [i.e. Adams et al., 1998; Krogh et al.,
1993; Krogh et al., 1987; Roddick and van Breemen, 1994]. The low closure or annealing
temperatures of 40Ar/39Ar (hornblende, muscovite, biotite and k-feldspar), (U-Th)/He (titanite and
apatite), and fission-track (zircon and apatite) thermochronometers make them ideal tools to
investigate stratigraphic age and erosion history. When investigating stratigraphic age, the youngest
individual grain age provides a constraint on the maximum depositional age of the sediments. For
example Najman et al. [2001] and Najman et al. [1997] use 40Ar/39Ar analyses from individual
muscovite grains to constrain the age of the oldest exposed foredeep sediments of the Himalaya.
The cooling age of detrital minerals within a sedimentary rock can be corrected for the
stratigraphic age of that rock and used to define cooling rates at the time at which the rock was
deposited. With low-temperature thermochronometers, the corrected cooling rates are typically used
53
as a proxy for the erosion rate within the catchment at that time. The Himalaya has been a focus for
many such studies. Cerveny et al., [1988] were among the first to use this technique; in Pakistan,
detrital zircons from Indus River sediments provided evidence of a young 1-5 Ma cooling-age
signal that had been persistent for the past 18 Ma. Copeland and Harrison [1990] interpreted 40Ar/39Ar analyses of detrital K-feldspar and muscovite grains from the distal Bengal fan to record
Himalayan erosion rates through time. The youngest cooling age at each stratigraphic level was
approximately equal to the depositional age, suggesting that that rapid cooling was occurring at
some location within the catchment area for the past 18 Ma.
Despite the value of the aforementioned studies, the parameters controlling the detrital signal and
the appropriate inferences are poorly known. Stock and Montgomery [1996] investigated the
potential of the detrital cooling-age signal to place limits on the paleotopography in the source area.
They show that the range in ages produced by a particular basin, in combination with a specified
geothermal gradient, allow the relief to be calculated. Brewer et al. [Chapter 1] extended this study
by investigating how the interactions between geothermal gradient, erosion rate, and relief can be
used in conjunction with the basin hypsometry to predict the distribution of detrital cooling ages.
Brewer et al. [Chapter 1] also address the random nature of detrital sampling and statistically assess
how faithfully specified numbers of grain ages will reproduce a defined detrital signal.
The results of Stock and Montgomery [1996] and Brewer et al. [Chapter 1] indicate that the
detrital cooling-age data can provide useful tectonic-geomorphological insights, although the scale
of such investigations needs to be limited to individual drainages contained within zones of uniform
uplift. Studies of catchments and their detrital signals at the orogenic scale, however, require
consideration of many tectonic zones; a large drainage will produce a more complex signal
representing an integration of detrital grains from multiple tributaries. In this paper, we attempt to
build on previous work to understand the parameters controlling the complete cooling-age signal
from an orogenic-scale basin. Field data from the Marsyandi valley in central Nepal are used to
examine the spatial pattern of erosion in the modern Himalaya.
54
3.0 Geological Background
The Himalaya are often described as the quintessential continent-to-continent collision zone, and
represent the discrete chain of extreme topography on the southern edge of the Tibetan Plateau and
the more diffuse deformation to the north [Molnar and Tapponier, 1975]. To the north of the
Himalayan topographic axis, the Indus-Tsangpo suture zone marks the surface boundary between
lithologic units of Eurasian plate affinity to the north and Indian plate affinity to the south. After the
initial collision at ~50 to 54 Ma [Rowley, 1996; Searle et al., 1997], the downgoing Indian plate was
imbricated along a series of south-vergent thrust fault systems, and the Himalaya formed as a result
of the subsequent crustal thickening. Deformation continues today and GPS data [Bilham et al.,
1997] indicate that approximately one third of the current convergence between the Indian Plate and
Eurasian Plate, estimated at 58 ± 4 mm/yr from global plate motions [DeMets et al., 1990],
currently occurs across the Himalaya.
The thrust fault systems mark many of the principal boundaries between tectono-stratigraphic
divisions, and have been used to characterize Himalayan geology for decades. The oldest and most
northerly of these, the Main Central Thrust (MCT) system, juxtaposes high-grade metamorphic
rocks and leucogranites of the Greater Himalayan sequence against lower-grade metasedimentary
rocks of the Lesser Himalayan zone. Farther south, the Lesser Himalayan zone is separated from the
foreland basin of the Himalaya by the Main Boundary Thrust (MBT) system. The most foreland-
wards topographic expression of the collision, the Siwalik Hills, corresponds to the Main Frontal
Thrust (MFT) system. The initiation ages of these major thrust systems are progressively younger
from north (20 to 23 Ma for the MCT system) to south (Pliocene to Holocene for the MFT system),
although ample evidence exists for episodic out-of-sequence thrusting along these and other less
significant fault systems in the Himalayan realm over the Miocene-Recent interval [Hodges, 2000].
The surface trace of the MCT system marks the approximate physiographic transition from the
Lower Himalaya to the Higher Himalaya, representing a large increase in mean elevation and relief.
As a consequence, much of the steep southern front of the Higher Himalaya, where erosion rates are
likely to be the highest, is developed on the metamorphic and igneous rocks of the Greater
Himalaya sequence. A fourth important fault system marks the top of the Greater Himalayan
sequence: the South Tibetan Detachment System (STDS). Carrying essentially unmetamorphosed,
55
Neoproterozoic-Paleaozoic clastic and carbonate sedimentary rocks of the Tibetan zone in its
hanging wall, the STDS incorporates a variety of structures, but chief among them are low-angle,
north-dipping detachments with normal-sense displacement [Burchfiel et al., 1992]. In the study
area, the STDS comprises two splays, the Chame Detachment Fault and Machhapuchhare
Detachment Fault, which are separated by the greenschist-to-amphibolite grade marble of the
Annapurna Yellow Formation [Coleman, 1996; Hodges et al., 1996].
The Marsyandi River system of central Nepal (Fig. 1) has its headwaters north of the trace of the
STDS and drains portions of the Tibetan, Greater Himalayan, and Lesser Himalayan zones over an
area of ~4760 km2. Its major tributaries flow over subsets of these tectonostratigraphic zones and
their streambed sediments thus sample different zones of bedrock in different proportions. As they
flow into the main Marsyandi trunk stream, individual tributary signals are progressively mixed
downstream. The Khansar Khola ("khola" is the Nepali word for river) and Nar Khola
predominately drain Tibetan zone sedimentary bedrock. The Dudh Khola drains Tibetan zone rocks
as well as a major Miocene leucogranite, the Manaslu pluton [Le Fort, 1981]. The Dona Khola
flows over exposures of this pluton as well as a variety of metamorphic rocks of the Greater
Himalayan sequence. The Miyardi, Nyadi, and Khudi rivers have headwaters in the Greater
Himalayan zone and exclusively sample this bedrock before emptying into the Marsyandi. The
Dordi, Chepe, and Darondi rivers flow across the MCT system and thus have sediments with
provenances in both the Greater Himalayan and Lesser Himalayan sequences.
4.0 Methodology
4.1 Sampling strategy
Detritus shed from an evolving mountain belt is primarily transported to the foreland basin by
fluvial systems. The resulting stratigraphy can provide a proximal record of hinterland erosion over
orogenic timescales. As a consequence, detrital cooling-age signals extracted from the foreland
potentially provide one of the highest spatial and temporal resolution records of orogenesis
56
available. One of our goals in studying the detrital cooling-age signal of the Marsyandi river system
is to evaluate how faithfully samples of sediment from major transverse rivers reflect the pattern of
bedrock cooling ages in the source area. Therefore, it is important to examine how faithfully a
foreland-basin sample portrays the pattern of bedrock cooling ages in the orogenic belt, and
understand the limits of the detrital signal.
In order to constrain the modern foreland cooling-age signal, we need to understand the present
distribution of cooling ages within the hinterland, and how these are eroded and transported
downstream. The sampling strategy in this investigation was designed to: a) maximize the statistical
constraints on contributions by tributary cooling-age signals; b) investigate the downstream
development of the trunk-stream cooling-age signal, whilst; c) using small enough catchment areas
to constrain adequately the spatial variation in cooling ages. With a finite number of age analyses,
there will always be unavoidable trade-offs between obtaining the optimal representation of any
given tributary and reliably reconstructing the evolution of the detrital age signal along the course of
a large river. For example, using very small catchments will increase the resolution of spatial
variation in bedrock cooling ages, but leave fewer analyses to constrain the downstream evolution
of the trunk stream. Conversely, using more analyses to constrain the foreland cooling-age signal
will provide a more reliable characterization the individual sample, but limit the spatial resolution of
the study.
Detrital sand samples were collected within the Marsyandi catchment from sites ranging from the
Tibetan zone to the junction with the Trisuli River in the Lesser Himalayan zone (Fig. 2). At each
sample site, large-grained sand was collected from bars within the modern river channel. Care was
taken to collect samples upstream of sediment-mixing zones at river junctions, and to avoid the
influence of small side tributaries and fill deposits, such as terraces.
While 27 samples were collected for point counting (to characterize the mineralogical constitution
of the sediment), only 14 samples from twelve separate locations were selected for 40Ar/39Ar dating.
Six samples were chosen from the Marsyandi River to investigate the trunk stream, and five
samples were taken at the mouth of major tributaries (Fig. 2). One sample (S-40) represents a sub-
catchment within the overall Darondi Khola (S-37), taken to assess the relative input of ages from
the Greater Himalayan sequence portion of the basin in comparison to the entire basin. To examine
the temporal variability of the detrital signal, two samples were collected from the same location;
57
one from the modern river bed (S-8), and one from a fill terrace elevated 2 m above it (S-9). To
examine the natural spatial variability of the signal samples were collected 45 m apart on the
downstream (S-53) and upstream (S-52) ends of the same sandbar.
4.2 40Ar/39Ar Analytical Protocols
Sand samples were washed and grain sizes between 500 and 2000 µm separated by sieving. This
investigation focused on detrital muscovite, which has been widely used in detrital mineral
geochronology and appears to have fewer problems with excess argon than biotite [Roddick et al.,
1980]. Individual muscovite grains were extracted from the sieved fraction by applying standard
gravimetric and magnetic separation techniques, followed by hand-picking under a binocular
microscope. Mineral separates were irradiated at the McMaster University research reactor after
being washed sequentially in distilled water, acetone, and ethanol. Aliquots of the neutron-fluence
monitor Fish Canyon sanidine (28.02 Ma, Renne et al. [1998]), as well as a variety of salts that
served as monitors for interfering nuclear reactions, were included in the irradiation package.
Mineral grains and monitors were analyzed at the 40Ar/39Ar laser microprobe facility at the
Massachusetts Institute of Technology [Hodges, 1998]. Individual muscovite crystals underwent
fusion in the defocused beam of an Argon laser operating at 18 W for a period of approximately 10
seconds. After purification to remove reactive species, the extracted gas was analyzed on an MAP
215-50 mass spectrometer using a Johnston electron multiplier. At the beginning of each analytical
session and after every tenth analysis of an unknown, the total system blanks were measured.
Appendix 2, Table 1, shows the apparent ages calculated for each muscovite with an estimated 2-σ
uncertainty obtained by propagating all analytical uncertainties. Hodges and Bowring [1995]
provide additional details on the analytical techniques.
Detrital cooling-age signals are commonly represented as a probability density function, which
represents the probability of finding a grain of a particular age, as a function of the age [Deino and
Potts, 1992]. Assuming that a Gaussian kernel represents the distribution of error [e.g. Bevington
and Robinson, 1992], a probability density function can be calculated for each grain, given the age (
58
tc) and analytical uncertainty (σ). For a sample of N grains collected from a specific locality, the
PDF of individual grains (n) can be combined:
∑=
=
−−
=Nn
n
nntt c
en
tP1
))(.2))((
( 2
2
..2).(
1)( σ
πσ
(1)
By normalizing the area under the resulting curve to unity, a summed probability density
function (SPDF) is generated. The SPDF represents the distribution of age probability as a function
of all the grains analyzed from the sample.
4.3 Point Counting.
Cooling-age signals can be used to examine how a trunk-stream signal changes downstream, as
successive tributaries contribute varying age populations (as described below). Point counting
provides a complimentary approach to investigating the trunk-stream signal that does not rely on
thermochronology and is less expensive. Detrital minerals can be used as conservative tracers,
whereby the relative abundance of a particular mineral species is used to examine the relative
contribution from an individual tributary. Although this technique has much lower resolution than
the thermochronological approach, it can provide another constraint on the relative erosion rate. In
addition, point counting serves to delineate the relative abundance of the target thermochronometer
within the Marsyandi study area.
The grains used for 40Ar/39Ar analysis are not a complete representation of the fluvial sediment
due to the sample and separation procedure necessary for grain selection. Field sampling restricts
the grain diameter to sand-size particles, and sieving further restricts this to 500 to 2000 µm.
Therefore any analysis of point counting results used in conjunction with cooling-age signals has to
be considered within the context of this range of grain sizes. Hence, in this study, point counting
was used to quantify the distribution of muscovite and other components within the 500-2000 µm
fraction.
59
Sieved sand samples were stained red for plagioclase feldspars and yellow for alkali feldspars
before being thin sectioned and counted using a mechanized stage. Quartz, feldspars, and micas
were the major minerals counted, with additional minerals grouped together and rock fragments
considered to be an additional species. Crystalline carbonate was considered to be a mineral,
whereas granular carbonate was considered a rock fragment. This method produced an approximate
quantification of the major constituents in each sample (Table 1) while not involving large amounts
of time identifying the broad range of other constituents. In each sample 600 to 900 grains were
identified. All reported errors from the point-counting results are taken from the statistical analysis
of Van der Plas and Tobi [1965]. Repeat counts were performed on three samples (S-1, S-2, S-3:
Table 1) to investigate the consistency of individual counts. Overall, the recounts showed that the
results were indistinguishable at the calculated 2-σ confidence level.
5.0 40Ar/39Ar results.
Before we attempt to interpret the 40Ar/39Ar results using a modeling approach, it is useful to
examine the broad trends shown by the data. The most encouraging observation is that the trunk-
stream age signal illustrates a systematic downstream pattern (Fig. 3). The sample furthest upstream
(S-12) drains the headwaters of the Marsyandi from the edge of the Tibetan Plateau to the crest of
the Annapurna massif. The age signal is dominated by an age population concentrated between 12
and 16 Ma. One source of ages may be rare hydrothermal veins with 40Ar/39Ar muscovite plateau
dates of ~14 Ma that have been reported from Tibetan zone sedimentary rocks that dominate the
bedrock lithology in this area [Coleman and Hodges, 1995]. Alternatively, the catchment contains a
small portion of the Annapurna Yellow Formation and the upper Greater Himalayan sequence,
which also contribute muscovite. The next sample downstream (S-8/ S-9) was collected to the
south of the trace of the STDS. This sample is influenced by two additional major tributaries, the
Dudh and Dona Khola, which drain the top of the Greater Himalaya sequence and the Manaslu
Granite. Whereas the population of ages observed in S-12 is still represented, the cooling-age signal
is dominated by a major age population from 15 to 20 Ma. The weak expression of the < 15 Ma age
population in the downstream sample, and the paucity of muscovite in the upper reaches of the
60
drainage basin suggest that the area upstream of sample S-12 makes a minor volumetric
contribution when compared to the additional tributaries found upstream of sample S-8/ S-9.
The next trunk-stream sample (S-6) was collected approximately 20 km downstream. This
displays the same 15 to 20 Ma population seen in the upstream sample, but contains additional 5 to
15 Ma ages. After the Marsyandi has crossed the MCT zone (S-3), the 0 to 10 Ma population
becomes more dominant and the 15 to 20 Ma peak represents less than half the total probability.
The Nyadi Khola (S-5), which drains the lower Greater Himalayan sequence, is partly responsible
for the increase in the younger age population as it comprises exclusively the 0 to 10 Ma age
population. Downstream of S-3 the Khudi Khola (S-2) contributes a young population of ages
between 4 and 12 Ma to the trunk stream. Other tributaries, the Dordi Khola (S-44) and Chepe
Khola (S-54) exhibit asymmetric 3 to 10 Ma and 4 to 13 Ma age populations, respectively. The
main Marsyandi River shows a dominance of the 5 to 10 Ma age population after the influx of these
tributaries (sample S-52/S-53).
Two samples were collected from the Darondi Khola: S-40 was collected from above the base of
the MCT zone, whilst S-37 was collected from the basin mouth. Sample S-40 displays a strong 0 to
12 Ma age population. Sample S-37 is similar, but includes a single older age component. The
trunk-stream signal at the basin mouth (S-24) comprises a prominent 5 to 10 Ma signal, a lesser 10
to 15 Ma signal, and a weak 15 to 20 Ma signal.
6.0 Modeling
Given that the results of the 40Ar/39Ar analysis seem to behave in a systematic way within the
Marysandi drainage system, we can use numerical modeling to further our understanding of the
hinterland geology, and interactions within the drainage system. This allows us to examine the
impact of individual parameters and focus on which characteristics of the detrital signal can be
explained by the model, and which cannot due to the limitations of the initial assumptions. Thus, in
combination with the 40Ar/39Ar data, we want to use a numerical model to: 1) assess the spatial
variation of parameters that control the hinterland geology; 2) understand how these parameters are
61
manifest in the detrital cooling-age signal observed at the basin mouth, and; 3) examine the
reliability and resilience of the cooling-age signal.
To do this we constructed a theoretical tributary PDF for each basin within the Marsyandi
drainage system [Brewer et al., Chapter 1]. This was generated by: 1) putting in the real
topographic characteristics of the basin, and then; 2) finding the optimal match between the
theoretical and observed data PDFs by varying the erosion rate. Once theoretical PDFs had been
generated for each tributary, we modeled the relative contribution from each basin to the trunk
stream. Hence we examined the systematic mixing of age populations in order to understand and
predict the downstream evolution of the cooling-age signal within the Marsyandi Valley.
6.1 Modeling the detrital cooling age signal
Before examining the trunk-stream signal, we need to generate theoretical PDFs for each tributary.
To predict the cooling age of a bedrock sample within a tributary basin the predicted depth of the
closure isotherm, at the time when the mineral passed through the closure temperature, is divided by
the rate of erosion. The depth of the closure temperature, given a crust of predetermined thermal
characteristics, is a function of the topographic relief and the vertical rate of erosion. For virtually
all geologically reasonable erosion rates and topographic relief, this isotherm will experience
negligible deflection due to surface topography [Mancktelow and Grasemann, 1997; Stüwe et al.,
1994]. We use a simplified thermal model [Brewer et al., Chapter 1] to predict the depth of the
350°C closure isotherm as a function of the basin relief and a specified erosion rate. The thermal
model assumes vertical erosion of material containing uniform heat production and conductivity,
from a depth of 35 km, through a steady-state landscape that contains hillslopes at a threshold angle
for landsliding (~30°: Burbank et al. [1996]). These assumptions produce a linear distribution of
cooling-ages with elevation, which forms the basis for calculating the detrital cooling-age signal.
With a uniformly eroding basin, or sub-basin, the PDF is controlled by the distribution of area with
elevation, i.e., the hypsometry. Thus the likelihood of sampling age a particular age at the basin
mouth is a consequence of the fraction of land containing that age.
62
Using this basic model, the larger Marsyandi Valley was broken into individual tributary basins to
represent the area contributing to each of our tributary 40Ar/39Ar age samples. Treating each sample
separately allowed us to model changes in the cooling-age distribution due to spatial variations in
the erosion rate and topographic relief at the tributary scale. The topographic relief and area of each
basin was extracted from a 90-m digital elevation model (DEM) using Arc/Info software. Thus,
with the other parameters constrained, the basin erosion rate was the only unknown parameter.
Hence, the lowest mismatch [Brewer et al., Chapter 1] between our theoretical PDF and the data
PDF was found by varying the erosion rate within an individual basin. Once the optimal theoretical
PDF had been found for a tributary basin, the erosion rate was fixed for any subsequent analysis.
Given the theoretical cooling-age distributions from the tributaries, we now need an additional
model element to predict how individual basins coalesce to produce the trunk-stream signal.
Ultimately, using all the tributaries, we want to predict the whole-basin PDF that serves as a proxy
for the modern foreland-basin deposit that would be produced by the Marsyandi River. The relative
contribution from an individual tributary is a function of the relative amount of muscovite per unit
time eroded from the basin (Fig. 4).
For our model we assume that a long-term steady-state topography exists whereby the regional
mean relief, hypsometry, and drainage density are essentially invariant over timescales exceeding
0.1 My. As a consequence of steady-state, the flux of material out of a basin will balance the
volume of rock moving into a basin. With vertical denudation, the volume of material derived from
a tributary is a function of the basin area and the erosion rate, and the relative contribution to the
trunk stream will reflect this. For illustration, we can consider basin ‘A’ and basin ‘B’ which are
drained by two individual tributaries that converge downstream to produce a trunk-stream signal. If
the basins have equal area, but B is eroding at twice the rate of A, the relative contribution to the
trunk-stream sample will be A:2B.
With the simple relationship of flux being proportional to area for a given erosion rate, there is an
assumption of uniform lithology. In this study our thermochronometer is muscovite, which may be
heterogeneously distributed through the basin: it is common in high-grade metamorphic rocks for
example, but often absent in carbonates. Therefore, even if basin B is eroding twice as fast, its
63
contribution to the downstream sample may be negligible if it is dominated by carbonate lithologies.
We use the percentage of muscovite at the basin mouth, taken from the point counting results (Table
1), to calculate a correction factor for each basin. Note that the point-counting results indicate that
the percentage of muscovite varies over two orders of magnitude within the Marsyandi river system,
indicating that a lithological correction factor can profoundly affect the results.
To model the trunk-stream signal at a particular location, we considered only the predetermined
tributary PDFs upstream of the sample. The individual tributary PDFs were combined after they had
been corrected for lithological variation, erosion rate, and area (Table 2). The resulting PDF curve,
with area normalized to unity, represented the theoretical distribution of cooling ages within the
trunk-steam sediment, at that locality. To examine the evolution of the detrital signal, we worked
systematically downstream by combining the calculated trunk-stream signal upstream of a sample
site with the addition from individual tributaries between the two sample sites. In the case where
tributary addition was unconstrained by ages at the mouth of a tributary (for example, the
inaccessible area represented by the Miyardi Khola: Fig. 2), a geologically reasonable erosion rate,
given the surrounding tributaries, was assigned to the area so as to minimize the mismatch of the
trunk-stream signal in the sample directly below the junction. For the purposes of the modeling, the
observed and data PDFs were smoothed using a 2-My-long scrolling window. This reduced the
“peakiness” of the PDFs caused by individual grains, meaning that the calculated mismatch was less
affected by individual grain peaks, but rather reflected the overall pattern of the entire signal.
6.2 PDF modeling results
With our approach of first modeling the distribution of detrital cooling ages from individual
catchments, and then combining them to model the trunk-stream signal, we can see that the overall
pattern of theoretical PDFs is consistent with the observed data (Fig. 5). The main peaks of the
theoretical PDFs generated for each tributary generally align with those of the data PDFs because
we minimize the mismatch by varying the erosion rate. Generally, the tails on either side of the
younger peaks are harder to match with our approach (i.e. see the Khudi Khola theoretical PDF for
illustration). The trunk stream displays a systematic pattern of change downstream as tributary
64
signals are added. The > 15 My peak that is prominent in the upstream samples becomes diluted
downstream as the 5 to 10 My peak becomes increasingly important, although in comparison to the
data, the predicted basin mouth PDF (represented by S-24) is relatively depleted in the 10 to 15 My
age range.
Some assumptions were made in the modeling in order to find the best solution to the pattern of
observations. Given fixed hypsometries and relief, the erosion rates of the Nar and Khansar were
varied until the best match of the most upstream sample (S-12) was found, yielding an erosion rate
of ~1 mm/yr. However, mixing the contributions from the Dudh and Dona tributaries to the
upstream sample (S-12), according to the initial values, produced a signal that was too dominant in
the 10 to 15 My age range. Therefore, to reproduce the downstream sample S-8/S-9, the relative
contribution from the Nar and Khansar had to be reduced by ~50% of that indicated by the raw data
for the percentage of muscovite. This is geologically reasonable because of the very high proportion
of carbonate rock fragments in the sediment from theses two tributaries. The point counting
indicates that these rock fragments decrease rapidly downstream in the sediment samples below S-
12 and so do not appear to be very resistant. It seems likely, therefore, that significant breakdown of
rock fragments has already occurred within the river before reaching the sample site, S-12. Thus, if
the rock fragments were conservative, we would expect a much higher proportion of them at the
basin mouth, and consequently a much lower percentage of muscovite. In contrast, the percentage
muscovite from the Dudh and Dona tributaries is probably much more representative of the
distribution within the catchment because the large percentage of granitc rock fragments are far
more resistant than carbonate fragments, and thus conservative within the fluvial system.
Furthermore, given that the Tethyan zone contains mostly carbonate rocks and shales, it is likely
that much of the muscovite in sample S-12 is derived from, and representative of, only a small
fraction of the total catchment area situated beneath the Machhapuchhare detachment fault.
Although the model generates a good prediction of the age distribution from tributaries with older
age distributions, it has difficulty reproducing the full range in ages found in many of the tributaries
that yield younger cooling ages. The strong asymmetry observed in the older age tails, in particular,
is difficult to replicate (the 8 to 13 Ma ages observed in the Chepe, for example). Although this
mismatch will be reduced when the model PDF curves are sampled (the analytical errors associate
65
with a grain age will widen the range of ages at each end), this cannot account for all of the
mismatch between the tails of the observed PDF’s and the modeled PDF’s (Fig. 5). Although we
assume that each basin is uniformly eroding, in reality there are probably variations in erosion rate
in the basins to the south of the range crest because uplift rates are locally controlled by the
geometry of the active subsurface structure [e.g. Lave and Avouac, in review; Pandey et al., 1995;
Seeber and Gornitz, 1983]. However, with no detailed sub-tributary data or bedrock ages from these
regions, we have limited the modeling to the same resolution as our data. The under-represented
tails of the observed data certainly account for some of the mismatch seen at the basin mouth (S-
24). Another source of mismatch would be areas not included in the modeling (stippled in Fig. 8),
yet contributing to the detrital cooling age signal seen in sample 24. There were insufficient
geochronological data from these areas to constrain their erosion rate. Most of these areas lie in the
Lesser Himalaya, and if they have intermediate erosion rates, as their low relief and topography
would suggest, then they may be an additional source of 10 to 15 Ma ages not represented in the
model.
7.0 Discussion
7.1 Resilience of the detrital signal.
One of the main concerns with the application of detrital dating is the survivability of the
thermochronometer in the sediment routing system. If the river network causes a rapid comminution
of grains, then there will be a limited sampling window upstream of the sample site. The size of the
window will be controlled by the rate of attrition within the system. Such comminution will
influence the cooling-age signal preserved in the foreland because information becomes
progressively lost downstream from the headwater area. In the best scenario, an ideal
thermochronometer is neither destroyed nor altered during the weathering and transportation history
66
of the sediment. Similarly, post-depositional weathering and diagenesis should not affect the
thermochronometer in the resulting sedimentary rock.
Both chemical and physical processes may cause the break down of minerals. The effects of
chemical weathering was investigated by Najman et al. [1997] for muscovite from the Dagshai and
Kasauli Formations in the Himalayan foreland, with depositional ages of approximately < 25 to 28
Ma and < 22 to 28 Ma respectively. They examined thin sections and conducted electron
microprobe analyses on the micas they dated. Most grains were essentially unaltered, with only
slight modification occurring at the edges of a few grains. Because these sediments are: a) much
older than the modern grains we use; b) from the same depositional basin, and; c) the Himalaya
continue to undergo rapid erosion rates today, we assume that chemical alteration of muscovite does
not significantly affect our results. In addition, in a study of modern tropical weathering, Clauer
[1981] found that biotite is more susceptible to breakdown and loss of argon than muscovite, which
displayed little to no detectable weathering effects. Furthermore, some work suggested that the
chemical weathering of micas may produce a congruent loss of K and Ar such that the apparent
ages of altered minerals may be relatively unaffected by the process [Mitchell and Taka, 1984].
The process of physical attrition of muscovite grains during their passage through the fluvial
system is more difficult to assess. With a hardness of 1 to 2 on Mohs scale and a well-developed
basal cleavage, it seems reasonable to suspect that muscovite may be susceptible to physical
breakdown. However, the work of Copeland and Harrison [1990] suggest that muscovites were
capable of surviving transport from the Himalayan front to a distal site in the Bengal Fan, a distance
of up to 2000 km, with little disturbance of their 40Ar/39Ar systematics. Given that the length scale
of the Marsyandi catchment is an order of magnitude smaller, 100 to 200 km, it seems unlikely that
the physical breakdown of muscovite is significant. The persistence of the 15 to 20 Ma age signal
from the upper Greater Himalaya sequence, through all our trunk-stream samples, to the basin
mouth lends support to this assumption. Rather than being a result of breakdown, we interpret the
downstream decrease in the 15 to 20 Ma age signal to be an effect of dilution. Our modeling
assumes a sediment flux proportional to the erosion rate, basin size, and contains no function for the
downstream loss of cooling age signal with distance. Therefore, if comminution were significant
over this length scale, the model would be expected to over-represent the 15 to 20 My age fraction,
67
particularly in the lower reaches of the river as muscovite grains are progressively destroyed.
Instead, the results approximate the relative proportion of younger to older populations seen in the
data, and indicate that the rate of sediment supply by faster eroding catchments (contributing
younger cooling-age populations) appears to control the downstream signal, as opposed to
significant loss of 15 to 20 My micas.
Given this finding, it is interesting to compare the volume of sediment that our model predicts is
eroded from unit area, for a given aged grain. The results (Fig.6) show that there is significant
differences in the volume of sediment for different cooling ages (representing different erosion
rates). Thus if we consider a basin containing one half eroding at ~2.1 km/My (Fig. 6, i) and the
other half eroding at ~0.8 km/My (Fig. 6, ii), the proportion of sediment contributed by the first half
will be over two-fold greater than that contributed from the second half (indicated by the gray bars).
Thus, if we wish to investigate the relative proportion of a catchment area that is producing a signal
of a specific age, we need to correct for the volumetric contribution of that age. Therefore, although
the 15 to 20 Ma age fraction in sample S-24 is relatively minor, because it comprises older cooling
ages it is areally important in the upstream area. However, note that the relationship between
predicted age and erosion rate (Fig. 6) is not linear in our model because the closure isotherm varies
as a function of denudation rate [Brewer et al., Chapter 1]. Halving the erosion rate from 2 to 1
mm/yr has a large affect, for example, changing the predicted cooling age from 5 to 20 My. The
exponential form of this curve, however, means that when comparing terrains producing cooling
ages of > ~30 Ma, the difference between the volumetric contribution per unit area as a function of
cooling age will be minor. Hence, the probability distribution of age populations in the sediment
will more closely reflect the size of the contributing areas.
7.2 The reliability of the fluvial signal
Two important assumptions in detrital thermochronology studies are: a) that the river is efficiently
mixing the sediment, and; b) that the detrital signal is not prone to point sources causing strong
temporal variations in the age signal. Landslides, rock falls, and localized storms could influence
the latter. If these assumptions are correct, a grab sample should provide a good representation of
68
the entire signal from the river and the upstream catchment. Two pairs of samples were collected to
investigate the validity of these assumptions.
The first pair of samples was used to study the homogeneity of fluvial mixing, in particular
answering the question, “If a modern sand bar is sampled, are there significant differences in the
distribution of ages from one site to another?” Sample S-53 duplicates trunk stream sample S-52,
but was collected approximately 45 m upstream at the other end of the sand bar. To test if these two
curves are statistically differentiable, we applied the Monte-Carlo methodology described by
Brewer et al. [Chapter 1] to generate random grain ages, and resulting synthetic SPDFs. To
represent the large range in errors seen in our single-grain analyses, a more complex method of
specifying the 1-σ analytical uncertainty was used in our model. Because no consistent relationship
of age uncertainty with grain age was observed, a PDF was constructed to represent the probability
of a specified age uncertainty occurring (Fig. 7). The PDF illustrates that while most the 1-σ
analytical uncertainties were less than 1.5 My, there is a significant portion of grains with larger
associated errors. Therefore, for each modeled grain, the uncertainty PDF (Fig. 7b) was randomly
sampled (using the same Monte-Carlo methodology), and the 1-σ error obtained from that PDF
applied to the model-derived grain age.
Using the modeled theoretical PDF for S-52/S-53 (Fig. 5), 500 “grab-sample” curves were
generated using first 15 grains to represent S-52, and then 22 grains to represent S-53. The
mismatch between the grab-sample SPDF and the theoretical PDF was then calculated [Brewer et
al., Chapter 1] and compared against the mismatch calculated between S-52 and S-53. As with the
modeling, a 2-My smoothing window was used before comparing curves to reduce the influence of
individual grains. The mismatch between S-52 and S-53 was calculated to be 32% (Fig. 8), whereas
the modeling indicated that a mismatch of ~20 ± 14% could be expected given a 95% confidence
limit. Thus the mismatch between S-52 and S-53 is just within the expected range of variability due
to random selection, and the two cannot be proven to be statistically different despite originating
from different positions within the river. Furthermore, the actual range of mismatch may be larger
than the value calculated from this modeling because it is based upon the synthetic PDF illustrated
in figure 5. As mentioned in section 6.2, the modeled PDFs are underrepresented in the 10 to 15 My
69
age range (when compared to the data), and thus increasing the range of likely probabilities might
be expected to cause a likewise increase in the variability of sampling.
The second pair of samples was designed to evaluate the temporal consistency of the detrital
cooling-age signal at a particular location. Would samples that are separated by 100’s to 1000’s of
years show the same age distribution? If not, the question of sediment storage and production
becomes important. Large bedrock landslides would be one scenario where the style of sediment
production could affect the detrital cooling-age signal. One can imagine that a landslide might
produce a pulse of sediment containing single ages. To test the short-to-medium-term temporal
persistence of the detrital signal in one location, we collected one sample (S-08) from the modern
riverbed, and another (S-09) from an adjacent fill terrace (Fig. 8b). The terrace formed due to
sediment infilling the Marsyandi Valley behind a bedrock-landslide dam. The Marsyandi is now
beginning to incise through the massive landslide blocks, leaving the fill terrace approximately 2m
above the current river level. The same procedure was applied to these samples, resulting in a 5%
mismatch between S-8 and S-9, and an expected mismatch of 21 ± 15% derived from the modeling.
Thus the two PDFs are very similar and cannot be considered statistically different. One caveat to
this analysis is however, that the almost unimodal cooling signal may mask temporal variability in
sediment supply from the catchment area.
7.3 Spatial variations of erosion rate
The cooling ages derived from low-temperature, bedrock thermochronology in orogenic belts are
primarily used as a proxy for the erosion rate. Likewise, the major parameter that we are trying to
extract from the cooling-age signal is the spatial variation in erosion rate. The results of the PDF
modeling indicate that erosion rates vary by over a factor of two within the Marsyandi drainage
system, from 0.9 to 2.3 km/My (Fig. 9). The highest erosion rates of 1.9 to 2.3 km/My are found in
basins draining the topographic front of the Himalaya. Rates decrease to the north, with the TSS
eroding at rates of 0.9 to 1.1 km/My. Areas to the south of the MCT probably have intermediate
rates, but it is difficult to constrain the signal from solely the Lesser Himalaya as most of the rivers
also drain the Greater Himalaya sequence.
70
Consider the results from the Darondi Khola (Fig. 3). Approximately 40% of the basin area lies
above the MCT zone and is represented by sample S-40. Sample S-37, from the basin mouth, is
very similar to sample S-40. It drains the additional area of the Lesser Himalaya, which is 1.5 times
the size of the Greater Himalaya portion of the basin. The similarity indicates that either: a) the
same erosion rates prevail in both portions of the basin, or; b) the Higher Himalaya sequence is
producing most of the thermochronometer found at the basin mouth. The latter could be explained
either by no effective erosion of the Lesser Himalaya sequence, or low percentages of muscovite in
the Lesser Himalayan lithologies. Point counting indicates that the Greater Himalaya sequence is
probably dominating the signal because Lesser Himalayan catchments have low abundances of
muscovite compared to those draining the Greater Himalayan sequence (Table 1). In addition, lower
rates of erosion in the Lesser Himalaya, compared to higher rates on the topographic front, may be
an explanation for the older PDF “tails” that are difficult to fit with the model, for catchments
draining both regions.
7.4 Point-counting results
The point-counting results (Table 1) indicate that the sediment composition behaves in a
systematic way with the downstream addition of tributary material. Samples from the Khansar and
Nar are very rich in rock fragments, containing up to 80%, mainly limestone, clasts. This is
expected due to the drainage area of predominantly TSS rocks. The percentage of rock fragments
falls rapidly downstream, with some addition of granitic rock fragments, to between 20 and 30%
towards the basin mouth. The Dudh and Dona Khola, draining the Manaslu granite, are quartz- and
feldspar-rich and somewhat under-represented in micas. The percentage of muscovite in the
tributaries increases rapidly southwards and the Nyadi, Khudi and Dordi all contain 5 to 10%
muscovite. The Chepe (S-54) has the largest fraction of muscovite, with over 20% at the basin
mouth. Sample S-41 is taken from the Chepe, at the base of the MCT zone, and shows
approximately 30% muscovite content. This becomes diluted with the addition of quartz and rock
fragments through the lower Himalaya. The two samples in the Darondi show a similar trend of
decreasing muscovite and increasing quartz through the lower Himalaya. However, the percentage
71
of muscovite at the mouth of the Darondi is approximately 5% compared to the much higher value
of 23% in the Chepe. Samples S-51, S-56 and S-38 are from drainages contained within Lesser
Himalayan rocks. All show quartz contents of over 40%, high fractions of rock fragments, and
muscovite abundances of 0 to 3%. The rock fragments may be a function of the immaturity of the
sediment because the basins containing samples S-38 and S-51 are relatively small in size compared
to the larger tributaries.
As defined by the point counting, the proportion of muscovite in the tributaries is used for the PDF
modeling described above. However, the complete mineral proportions of trunk stream and
tributaries may also be used for an additional calculation of erosion rate. Mixing the sediment of
two rivers together should produce a resulting downstream sample that is representative of the
relative proportions of each of the rivers. In reality, the natural variability of the system and point-
counting errors mean that the data are more complex. Because of this uncertainty, we use a basic
model to examine the general pattern of contributions from each of the inputs and the mixing of the
trunk stream.
The model uses point-counting data from each of the upstream samples and mixes them to
produce a resulting downstream signal. The contribution of each upstream sample is varied from 0
to 100%, and the best solution is picked by finding the minimum residual to the downstream
sample. This procedure assumes ideal mixing and no selective deposition, or attrition, of individual
mineral species. We have already suggested that the carbonate rock fragments are susceptible to
comminution, and hence in some areas they bias the ratios. Therefore, we found that instead of
trying to: a) mix all the species at once using the method described above, or; b) drop out individual
mineral species and recalculate the mixing ratio (with or without renormalizing), the best results
were obtained by calculating the mixing ratios for each mineral species individually and taking the
mean. This eliminated instances where individual mineral species controlled the mixing ratio due to
their large volume (e.g. quartz), and weighted each mineral species equally.
Once mixing ratios were determined, relative erosion rates for individual tributaries within the
Marsyandi were calculated using the catchment areas (Fig. 10). Starting at the top of the basin, the
sediment leaving tributary ‘A’ was calculated assuming an erosion rate of 1unit per unit area per
unit time. The area of tributary A can be measured from a DEM, and the volume of eroded sediment
72
per unit time may be calculated. Knowing the mixing ratio of A:B, the relative volume of sediment
leaving tributary ‘B’ can therefore be calculated. The resulting volume of sediment leaving tributary
B, divided by the area of B, produces an erosion rate relative to A. For the next junction
downstream, the trunk-stream sample upstream of the junction is taken to have a combined
sediment volume of A plus B. The erosion rate of the tributary ‘C’ can then be calculated in the
same manner as before, using the mixing ratio to find the sediment volume leaving C and dividing
by the area of C. Using this methodology, we can calculate the relative tributary erosion rates for
the whole basin as we work downstream. To produce numbers that are of the same order of
magnitude as erosion rates calculated by the thermochronology, we normalize the relative erosion
rates of a particular basin with the erosion rate derived from thermochronology (in this case using
the Dordi Khola).
The results (Fig. 11) show that, although there are absolute differences between the erosion rates
calculated from thermochronology and those calculated from the point-counting analysis, the
general pattern of low erosion in the north of the region, high erosion rates in basins on the southern
flank of the main topographic axis, and intermediate erosion rates to the south, is the same. Whereas
the PDF modeling suggested variations in erosion rate of up to 2.5 fold, the point-counting model
yields variations in predicted rates of > 10 fold. These discrepancies are not surprising due to the
expected variability of sediment within the river: a) species such as rock fragments will become
comminuted downstream; b) carbonate rock fragments and minerals will experience chemical, as
well as physical, erosion; c) hydraulic sorting will be important for minerals with different densities.
We have shown that the latter process is not too significant for muscovites in the 500 to 2000 µm
size range, however, at least for samples S-52 and S-53.
8.0 Conclusions
In this study we examine the downstream development of a detrital mineral cooling-age signal.
The investigation provides insights into long-standing questions concerning the interpretation of
detrital-mineral ages. In the past a sample collected from the foreland basin might be used to
interpret rapid erosion rates in the upstream catchment area, but where the erosion was occurring
73
and how much of the basin it represented was unknown. Here, we show that there are systematic
and predictable changes in the detrital cooling-age signal of a large, transverse Himalayan river.
From the analysis of the Marsyandi Valley detrital system, we learn how the inputs from tributary
catchments combine to form the signal at the basin mouth. We can model the cooling-age
distributions from individual tributaries based on observable characteristics of the basin (relief and
hypsometry) to determine a best-fit erosion rate. The numerical modeling indicates that the detrital
cooling-age signal behaves systematically in the trunk stream, whereby the input of an age
population from an individual tributary is a function of the abundance of the thermochronometer per
unit area, the area of the basin, and the rate at which it is eroding. In our analysis, the distribution of
muscovite within the catchment is a critical factor in determining the representation of a particular
area of the basin in the foreland sample. For example, approximately 30% of the Marsyandi
catchment is composed of Tethyan rocks, and yet this represents only a small fraction of the
foreland detrital cooling-age signal because of the paucity of muscovite within the Tibetan zone
lithologies.
Comparison of the detrital-age data versus modeling results indicate that comminution of
muscovite by fluvial processes seems to be insignificant at the 100 to 200 km scale. The 15 to 20
Ma signal derived from the Marsyandi headwaters is persistent downstream, although decreases in
significance. We argue that the calculated volumes of thermochronometer added to the trunk stream
are consistent with the downstream dilution of this signal by younger age populations, rather than
mechanical breakdown of muscovite. This may be attributable to muscovite moving in the
suspended load during the monsoon season, thus encountering less abrasion than during bedload
transportation.
The variability of the cooling-age signal was tested with samples from 1) opposite ends of the
same sandbank, and 2) from the modern river and a fill terrace. Our statistical analysis illustrates
that although there was variability between samples, the sample pairs were not found to be
statistically different at the 95% confidence level: the processes of random selection, from a
common “parent” cooling-age signal, can explain the variation between samples. This indicates
that, for at least these two tests, the detrital cooling-age signal is spatially and temporally reliable in
this area.
74
The results of the thermochronometry indicate that the topographic front of the Himalaya is
eroding faster than the area around it, generating a ~4 to 10 Ma age signal in those basins draining
the Greater Himalayan sequence Areas to the north of the Himalayan topographic axis, on the edge
of the Tibetan Plateau, experience the lowest erosion rates and produce grain ages between 10 and
15 Ma for those basins sourced in the Tibetan zone, and 15 to 20 Ma for those basins draining the
top of the Greater Himalayan sequence. Intermediate rates are probably found in the lower
Himalaya, although the large tributaries draining this zone have headwaters in, and cooling-age
signals dominated by, the Higher Himalaya. The pattern of erosion from thermochronology is
broadly consistent with the erosion rates calculated from point-counting data. The latter predicts a
greater contrast in the erosion rates that should be interpreted cautiously, however, because of the
intrinsic variability of sediments within the river system.
Two explanations for the overall pattern of the erosion rate are plausible. First, if the MCT and
STDS are active, the high erosion rates of the High Himalaya can be explained by the southwards
extrusion of the Greater Himalaya sequence. Alternatively, if the MCT is relatively inactive, then
the spatial variation in erosion rate is probably a function of the angle of the underlying Main
Himalayan Thrust along which Asia overthrusts India. Investigations of seismicity indicate the
presence of a mid-crustal ramp [Pandey et al., 1995], and increased vertical uplift above a steeper
section, below the main topographic axis, would account for the spatial pattern of erosion rates.
Either of these scenarios introduces the complicating factor of lateral advection. In most
investigations to date, cooling ages are converted into rock exhumation rates using an assumption of
1D thermal and kinematic processes. It is increasingly being recognized that the thermal structure of
an orogen is not a simple model of horizontal isotherms, but is subject to the lateral advection of
rock and heat energy into the system [e.g. Batt and Braun, 1997; Jamieson and Beaumont, 1988;
Jamieson et al., 1998; Willet, 1999]. Rock particles move laterally, not solely vertically, during
erosion and although beyond the scope of this paper, this complicating factor needs to be considered
when assessing the results.
This baseline investigation illustrates that, within the Marsyandi Basin, the detrital cooling-age
signal is a reliable representation of the contributing area and that the downstream evolution of the
trunk-stream signal is understandable, and as a result may be numerically modeled. The
75
interpretation of the foreland signal, however, is not necessarily simple because the distribution of
cooling ages within the river system is a complex function of the landscape characteristics, erosion
rate, and distribution of thermochronometer within the catchment. For example, the sample at the
basin mouth is dominated by a 4 to 10 Ma population of grain ages and we might argue that those
drainages downstream of sample 6, representing ~40% of the area sampled, control the signal. On
further investigation, however, it seems that they cannot explain all the intricacies of the older
signal. Thus, the area upstream of samples 8 and 9, representing ~55% of the basin area sampled, is
needed to account for the 15 to 20 Ma age population. In this study we would argue that this signal
is so much less dominant in the foreland, despite a larger contributing area, because of the effects of
lithology and erosion rate.
Therefore, while we argue that the distribution of age within the foreland is a good representation
of the upstream area and provides useful and reliable information about the spatial pattern of
erosion rate in the hinterland, some caution is needed when interpreting the source and importance
of age populations from stratigraphic samples. It is apparent that to extract the maximum amount of
information from the stratigraphic record, understanding the parameters that control the modern
cooling-age signal is vital. In this study, we have dated ~500 muscovite grains from 12 locations
that have provided new insights into how lithology and drainage basin characteristics, both easily
observable in other modern locations, influence the detrital signal of the Marsyandi River. Thus,
with some knowledge of the modern signal it should be possible to extract reliable cooling-rate
information from samples within the stratigraphic record, which can subsequently be used to
constrain the temporal and spatial evolution of the orogenic belt.
Pokhara Basin
Tha
kkho
la G
rabe
n
Annapurna II 7939m
Seti Khola
Marsyandi River
Marsyandi/Trisuli junction
MCT
MCT
MCT
Manaslu granite
Dudh
Dona
Nyadi
Dordi
Chepe
Nar
Khansar
Greater Himalayan sequenceLesser Himalayan sequence
Leucogranite (Manaslu Pluton)Tibetan Sedimentary Series (PCam-Ord)Tibetan Sedimentary Series (Sil-Cret)
N
Miyardi
Khudi
Darondi
CDF Manaslu8156m
MDF
Figure 1. Simplified geological map of the Marsyadi region adapted from Hodges et al, [1996], initially from Colchen [1996]. The south-verging Main Central Thrust (MCT) separates the Greater Himalaya sequence from the Lesser Himalaya sequence. Other south-verging thrust faults, the MBT and MFT, are to the south of this diagram. The South Tibetan Detachment system, with normal displacement, forms two splays in this region: the Chame Detachment Fault (CDF) and the Machhapuchhare Detachment Fault (MDF).
76
POKHARA
N
Tibetan plateau
India
58 mm/yr
17
1612
191021
8/920
6 5
321
4
44
54
41
51
52/5340
56
2437
38
0 20km
MDF
MCT
Sample siteDating site
43a
36
Figure 2. Map of Marsyandi drainage system based on a 90-m DEM. Sample locations are displayed with squares (and gray sample numbers) for point-counting sites and circles (and black sample numbers) for 40Ar/39Ar analysis/point count sites. The Marsyandi drainage (upstream of site 24) is outlined in white. The MCT has triangles indicating south vergence whereas the MDF has half circles indicating down-throw to the north. The MBT/MFT are slightly to the south of this figure. The inset shows the approximate position of the sampling area within Central Asia.
77
12
0 15105 20 25
0 15105 20 25
0 15105 20 25
0 15105 20 25
0 15105 20 25
0 15105 20 25
0 15105 20 25
0 15105 20 25
0 15105 20 250 15105 20 25
0 15105 20 25
0 15105 20 25Age (My)
Age (My)
Age (My)
Age (My)
n=55
n=35
n=25
n=23
n=33
n=37
n=48
n=23
n=25
n=49
n=45
n=37
Darondi
Dordi
Chepe
Khudi
Nyadi
Nar
Khansar
Dudh Dona
Miyardi
Sample Number
Age (My)
Number of grainsP
roba
bilit
y
n=45
Cooling age PDF
Age (My)
KEY
Trun
k
52+53
12
6
3
2
5
37
54
44
40
24
8+900
N
The Trisuli
Figure 3. Detrital cooling-age PDFs for samples from the Marsyandi drainage. All axes range from 0 to 25 My on the x-axis and have probability on the y-axis. Areas under the PDF curves (shaded black) represent a total probability of one in each case. The individual plots have been arranged topologically to indicate their position within the Marsyandi River system: geographic locations are shown in figure 2. Additional grain ages in sample 24 (229 ± 18 Ma) and sample 54 (27 ± 0.9 Ma) are not illustrated.
78
Yield of thermochronometer per unit area per unit time
Denudation rate
Percentage of thermochronometer
Grain size of thermochronometer
Lithological variation
Trun
k st
ream
age
sig
nal
Tributary age signal contribution
Area
Figure 4. Parameters controlling the contribution of an individual tributary to a trunk-stream cooling-age signal. The foreland signal can be modeled as a specified mix of several such tributaries.
79
0 5 10 15 20 25 30
Nar
Khansar
Dudh Dona
Miyardi
0 5 10 15 20 25 30
0 5 10 15 20 25 30
0 5 10 15 20 25 30
0 5 10 15 20 25 30
0 5 10 15 20 25 30
0 5 10 15 20 25 30
0 5 10 15 20 25 30
0 5 10 15 20 25 30
0 5 10 15 20 25 30
0 5 10 15 20 25 30
age (my)
Darondi
Dordi
Chepe
Khudi
Nyadi
Trun
k
Sample Number
Age (My)
Pro
babi
lity
Data PDF KEYModeled
age (my)
age (my)
age (my)
52+53
12
6
3
2
54
44
00
N
The Trisuli
Figure 5. Model results compared to 40Ar/39Ar analyses. Real data PDFs (identical to data used in Fig. 3) are shaded gray and smoothed using a 2-My window. Solid black lines are model PDFs generated using the methodology described in the text, and are also smoothed with a 2-My window. The x-axis of each plot ranges from 0 to 30 My, with probability on the y-axis, and the area under each curve represents a probability of one.
80
8+9
5
37
52+53
24
0
1
2
3
4
5
0 5 10 15 20 25predicted age (My)
eros
ion
rate
(km
/My)
, or u
nit v
olum
eof
sed
imen
t ero
ded
per u
nit t
ime
per u
nit a
rea
Figure 6. Predicted ages from our model for specified erosion rates, Note that changes in the erosion rate between ~0.8 km/My and 2 km/My result in large changes in the predicted ages, which is a function of the isotherm repsonse and the particle speed. Another way to interpret this diagram is to consider the amount of sediment eroded from 1 uinit area of land in one unit time., which is the contribution of each unit land area to a detrital PDF. If we consider a drainage basin containing one half eroding at 2.1 km/My (i), and the other half at ~0.8 km/My (ii), the older grains represent a much smaller signal despite represeting the same amount of land area.
81
(i)
(ii)
0 5 10 15 20 250
2
4
6
8
10
12
14
16
18
0
1
2
3
4
5
6
7
8
1-s
erro
r of
gra
in a
ge (
My)
Probability
1-s
erro
r of
gra
in a
ge (
My)
age of grain (Ma)
a)b)
smoothed error PDF
Figure 7. (a) Age versus error (1-s) for analyses with greater than 40% radiogenic 40Ar. No clear relationship between age and error can be seen. Inset (b) shows a PDF generated from the 1-s errors. This PDF is smoothed (solid line) and used in the error determination in the numerical model. It can be seen that most assigned errors will be between 0 and 1.5 My.
82
Age (My)
0 5 10 15 20 25
s-52 smoothed, n=15
s-53 smoothed, n=22
s-52 & s-53 smoothed
prob
abili
ty
0 5 10 15 20 25
s-8 smoothed, n=35
s-9 smoothed, n=10
s-8 & s-9 smoothed
prob
abili
ty
a)
b)
Figure 8. Results of repeat sampling to test: a) the spatial variability of the detrital cooling age signal, and; b) the temporal variation of the signal. For each plot, the shaded PDF is the combined data used in the construction of figure 6, while the PDFs represented by black lines are the contributing data. All curves are smoothed with a 2-My scrolling window.
83
Erosion rate (mm/yr)
Not included in model
N
0.94
1.12
0.94
1.3
1.71.9 2.3
2.1
1.97
2.1
Khansar
Nar
Dudh
Dona
Nyadi
Darondi
ChepeKhudi
MiyardiDordi
MarsyandiRiver
2.0
1.5
1.0
0.0
0.5
84
Figure 9. Spatial variation in erosion rates at the drainage-basin scale. Erosion rates are taken from the results of modeling the detrital cooling age PDFs for individual tributaries. The stippled areas indicate zones not included in the calculations and the dashed gray line indicates the approximate path of the trunk stream. Highest erosion rates occur in the middle areas of the Marsyandi Basin, where rivers drain the steep front of the High Himalayas. Slowest erosion rates occur to the north of the topographic axis, in the rain shadow.
AB
AB
AB
AB
ABCC
mixing ratio = 1A:2B
mixing ratio = 1AB:1.8C
a=100
a=110
a=140
PROCEDURE:
i) Assumption: basin A is eroding at 1 unit, per unit area, per unit t ime.
ii) In unit t ime, basin A erodes the area multipl ied by the erosion rate, equall ing 100 unit volumes.
i i i ) Given the mixing rat io 1A:2B, basin B must produce 200 uni t volumes in unit t ime.
iv) With an area of 110 units, B must be eroding at 200/110 = 1.8 units, per unit area, per unit t ime.
v) As a result, the total amount of sediment generated by basins A and B combined (at site AB) wil l be 300 unit volumes in unit t ime.
vi) Therefore, given the mixing ratio 1AB:1.8C, basin C must produce 540 unit volumes in unit t ime, and hence is eroding at 540/140 = 3.8 units, per unit area, per unit t ime.
Figure 10. The procedure used to convert point-counting results into relative erosion rates. Point counting sediment samples from the mouth of drainage A and the mouth of drainage B, in conjunction with a downstream sample AB, can be used to calculate a mixing ratio for the two basins. When combined with basin area, extracted from a DEM, this ratio is used to calculate a relative erosion rate.
85
2.0
1.5
1.0
0.0
Erosion rate (mm/yr)
Not included in model
N
0.04
0.2
0.3
0.82.5
2.1
0.7
1.1
Khansar
Nar
Dudh
Dona
Nyadi
Darondi
ChepeKhudi
MiyardiDordi
MarsyandiRiver
0.5
Figure 11. Spatial variation in erosion rates at the drainage-basin scale. Erosion rates are calculated from the point-counting data using the methodology illustrated in figure 9. Relative erosion rates are normalized by the Dordi Khola to allow direct comparison with figure 8. The stippled areas indicate zones not included in the calculations and the dashed gray line indicates the approximate path of the trunk stream. Note that the overall pattern of erosion is similar to figure 8, with high erosion rates in the middle areas of the Marsyandi Basin, and slowest erosion rates to the north of the topographic axis.
86
87
Table 1. Point-counting data from the Marsyandi Valley. Abbreviations are as follows: n = number
of grains, qtz = quartz, Pl = plagioclase, Kfs = potassium feldspar, ms = muscovite, Bt = biotite,
frag = rock fragments, opq = opaques, other = any other minerals. All errors are 2-σ and are
calculated with the statistical analysis of Van der Plas and Tobi [1965].
88
Sample n qtz Pl Kfs ms Bt frag Opq other
S-1 893 43.3 ±3.3 15.4 ±2.4 3.6 ±1.2 5.3 ±1.5 3.7 ±1.3 17.9 ±2.6 0.3 ±0.4 10.4 ±2.0
S-1.2 798 45.6 ±3.5 14.7 ±2.5 4.6 ±1.5 6.5 ±1.7 4.0 ±1.4 18.5 ±2.8 0.1 ±0.2 5.9 ±1.7
S-2 Khudi 790 37.7 ±3.4 16.2 ±2.6 2.3 ±1.1 10.1 ±2.1 9.6 ±2.1 18.5 ±2.8 0.0 ±0.0 5.6 ±1.6
S-2.2 765 42.7 ±3.6 19.6 ±2.9 2.1 ±1.0 11.9 ±2.3 11.2 ±2.3 7.4 ±1.9 0.2 ±0.3 4.3 ±1.5
S-3 802 26.4 ±3.1 19.6 ±2.8 8.4 ±2.0 2.0 ±1.0 1.6 ±0.9 33.9 ±3.3 0.0 ±0.0 7.9 ±1.9
S-3.2 800 30.3 ±3.2 15.8 ±2.6 10.0 ±2.1 2.6 ±1.1 2.4 ±1.1 35.3 ±3.4 0.1 ±0.2 3.4 ±1.3
S-4 691 29.1 ±3.5 13.7 ±2.6 8.7 ±2.1 1.9 ±1.0 3.2 ±1.3 36.2 ±3.7 0.4 ±0.5 6.8 ±1.9
S-5 Nyadi 745 41.2 ±3.6 20.4 ±3.0 8.6 ±2.1 6.3 ±1.8 4.6 ±1.5 12.6 ±2.4 0.3 ±0.4 5.8 ±1.7
S-6 779 27.3 ±3.2 17.1 ±2.7 9.6 ±2.1 3.5 ±1.3 2.6 ±1.1 35.6 ±3.4 0.8 ±0.6 3.6 ±1.3
S-8 747 28.1 ±3.3 21.8 ±3.0 15.4 ±2.6 1.9 ±1.0 0.7 ±0.6 30.7 ±3.4 0.4 ±0.5 1.1 ±0.8
S-10 Dudh 804 40.2 ±3.5 29.9 ±3.2 16.0 ±2.6 1.7 ±0.9 0.0 ±0.0 9.3 ±2.1 0.1 ±0.2 2.7 ±1.1
S-16 Khansar 786 5.6 ±1.6 1.8 ±0.9 1.4 ±0.8 0.1 ±0.2 0.8 ±0.6 79.1 ±2.9 0.9 ±0.7 10.2 ±2.2
S-17 Nar 769 11.8 ±2.3 2.3 ±1.1 1.4 ±0.9 0.5 ±0.5 0.4 ±0.4 79.2 ±2.9 0.7 ±0.6 3.6 ±1.4
S-19 784 15.9 ±2.6 14.0 ±2.5 7.5 ±1.9 1.8 ±0.9 2.0 ±1.0 53.6 ±3.6 0.6 ±0.6 4.5 ±1.5
S-20 808 27.2 ±3.1 21.9 ±2.9 10.3 ±2.1 1.1 ±0.7 1.5 ±0.8 34.9 ±3.4 0.2 ±0.3 2.8 ±1.2
S-21 Dona 777 29.6 ±3.3 21.6 ±3.0 17.4 ±2.7 0.5 ±0.5 2.8 ±1.2 11.1 ±2.3 0.5 ±0.5 16.3 ±2.7
S-24 768 49.1 ±3.6 9.1 ±2.1 3.1 ±1.3 6.8 ±1.8 3.9 ±1.4 23.4 ±3.1 0.5 ±0.5 3.9 ±1.4
S-36 842 43.7 ±3.4 13.2 ±2.3 4.5 ±1.4 5.1 ±1.5 3.7 ±1.3 25.5 ±3.0 0.6 ±0.5 3.7 ±1.3
S-37 Darondi 869 62.7 ±3.3 13.1 ±2.3 1.2 ±0.7 4.6 ±1.4 2.9 ±1.1 12.5 ±2.2 1.0 ±0.7 1.8 ±0.9
S-38 524 44.1 ±4.3 1.1 ±0.9 0.6 ±0.7 0.0 ±0.0 5.2 ±1.9 47.5 ±4.4 0.8 ±0.8 0.8 ±0.8
S-40 624 55.8 ±4.0 13.3 ±2.7 0.6 ±0.6 7.2 ±2.1 3.8 ±1.5 13.8 ±2.8 0.5 ±0.6 4.5 ±1.7
S-41 633 28.6 ±3.6 8.7 ±2.2 0.8 ±0.7 29.7 ±3.6 23.5 ±3.4 2.2 ±1.2 0.2 ±0.3 6.3 ±1.9
S-43a 821 35.7 ±3.3 16.8 ±2.6 10.0 ±2.1 7.9 ±1.9 8.3 ±1.9 16.7 ±2.6 0.6 ±0.5 3.8 ±1.3
S-44 Dordi 777 43.8 ±3.6 14.3 ±2.5 2.7 ±1.2 9.7 ±2.1 9.1 ±2.1 12.6 ±2.4 1.4 ±0.8 6.4 ±1.8
S-51 614 43.3 ±4.0 7.3 ±2.1 4.9 ±1.7 3.1 ±1.4 2.3 ±1.2 34.5 ±3.8 0.2 ±0.3 4.4 ±1.7
S-52 858 31.6 ±3.2 13.6 ±2.3 5.5 ±1.6 10.6 ±2.1 11.0 ±2.1 22.5 ±2.9 0.5 ±0.5 4.8 ±1.5
S-53 897 29.5 ±3.0 10.9 ±2.1 3.7 ±1.3 10.7 ±2.1 16.1 ±2.5 24.2 ±2.9 0.8 ±0.6 4.0 ±1.3
S-54 Chepe 884 40.4 ±3.3 9.3 ±2.0 2.1 ±1.0 23.2 ±2.8 11.9 ±2.2 7.3 ±1.8 0.3 ±0.4 5.4 ±1.5
S-56 598 52.0 ±4.1 9.2 ±2.4 6.9 ±2.1 2.2 ±1.2 3.8 ±1.6 23.2 ±3.5 1.0 ±0.8 1.7 ±1.0
89
Basin Area (km2) Elevation (m) Lithology
Mean Min Max Relief ~%TSS ~%GH ~%LH
Marsyandi 4760 3332 244 8152 7908
Khansar 713 4794 2634 7824 5190 80 20 -
Nar 884 5209 2634 7097 4463 80 20 -
Dudh 392 4694 1958 7669 5711 10 90 -
Dona 129 4851 1895 8152 6257 100 -
Miyardi 60 4050 1496 5842 4346 - 100 -
Nyadi 215 3440 926 7495 6569 - 80 20
Khudi 136 2565 796 4914 4118 - 90 10
Dordi 351 2885 553 7756 7203 - 70 30
Chepe 309 1808 440 4872 4432 - 50 50
Darondi 609 1470 277 5787 5510 - 40 60
Table 2. Topographic characteristics of the Marsyandi Valley and its associated tributaries. The
approximate litho-tectonic division of the basins are given in percentage area containing: Tethyan
Sedimentary Series (TSS) structurally above the Machhapuchhare detachment fault; Greater
Himalayan sequence (GH) complex, leucogranites, and Annapurna Yellow Formation; Lesser
Himalayan sequence (LH).
Chapter 3
The application of thermal-and-kinematic modeling to constraining rock-particle trajectories, cooling ages of detrital minerals, and the tectonics of the Central Himalaya.
I.D. Brewer and D.W. Burbank
Pennsylvania State University, Department of Geosciences, University Park, Pennsylvania
Abstract
We introduce a new method to use detrital mineral cooling ages in conjunction with a digital
elevation model (DEM) to test numerical models of collisional orogens. We apply this methodology
to the Marsyandi valley, in the central Nepalese Himalaya, where we use a 2-D kinematic-and-
thermal model to predict variations in bedrock cooling ages along an averaged transect within the
Himalaya. The model is based upon a simple ramp-and-flat style decollement, representing the
Main Himalayan Thrust (MHT), and is constrained by the INDEPTH transect, surface geology,
seismicity, and geomorphology. The 2-D kinematic-and-thermal model is extrapolated laterally to
calculate the 3-D distribution of cooling ages predicted for actual Himalayan topography. The
detrital cooling-age signal results from convolving the distribution of cooling ages within a basin,
with the rate at which individual points are eroding, and the distribution of the mineral used as the
thermochronometer. The predicted distributions of cooling ages are compared with detrital 40Ar/39Ar muscovite data to assess varying tectonic scenarios. Model results, assuming that the
Main Boundary Thrust represents the surface expression of the MHT, illustrate that the distribution
of detrital cooling ages is sensitive to how plate convergence is partitioned, with the best-fit model
assigning 5 mm/yr to the motion of the Asian plate and 15 mm/yr to the motion of the Indian plate.
There is, however, a trade off between ramp geometry and convergence rate. A model using the
approximate present position of the Main Central Thrust (MCT) to represent the surface expression
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of the MHT provides a better fit to the observed data and supports evidence for recent activity on
the MCT.
1.0 Introduction
The complexities of the growth and subsequent erosion of orogenic belts have been a focus of
much research in the last decade. The Himalaya, the icon of continental collision, illustrates the
importance of such investigations because the temporal evolution of the orogen has been proposed
as the prominent Cenozoic driving mechanism for strontium and carbon geochemical cycles [Derry
and France-Lanord, 1996; Raymo et al., 1988] and climate change [Kutzbach et al., 1993;
Ruddiman and Kutzbach, 1989]. The development of numerical modeling in geosciences has
greatly increased our insight into how orogenic systems operate [e.g. Beaumont et al., 1992; Koons,
1989; Koons, 1995; Willet, 1999], and while algebraic and numerical descriptions of complex
physical processes are commonly gross simplifications, the results can provide new ideas and
hypotheses to be evaluated with field data.
Such data frequently include bedrock-cooling ages, which are used as a proxy for the erosion rate
in order to measure the strain field. Assumptions are commonly made, however, that limit the
amount of information we can extract from such analyses. Assumptions usually include: 1) vertical
erosion; 2) horizontal isotherms; and 3) an estimated, linear, geothermal gradient. Given the
intricacies of orogenic belts, these assumptions are frequently invalid. Transportation along thrust
faults generally controls deformation, rather than vertical erosion. This lateral rock movement, in
combination with the effects of topography, will deflect isotherms and produce local, non-linear,
geothermal gradients. Thus to extract the maximum amount of geological information from detrital
cooling ages, the complexities of regional tectonics need to be incorporated into numerical
simulations to understand how variations in deformation pathways, convergence rates, topography,
heat production, and lithology influence the spatial distribution of bedrock cooling ages.
Increasingly complex numerical models, however, need to be tested against more comprehensive
sets of field data for corroboration. Thus, in this paper, we focus on the applicability of the modern
detrital cooling-age signal to constraining models of mountain belts. A detrital sample may be more
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advantageous than traditional bedrock thermochronology because it is easily collected, separated,
and analyzed, and potentially provides an integration of cooling ages from an entire drainage basin
(which may include a significant portion of a study area when using samples from large transverse
rivers). Opposingly, bedrock cooling ages are restricted to single locations, typically valley floors,
and usually represent a restricted number of samples which are difficult and expensive to collect.
Investigations of individual basins [Brewer et al., Chapter 1; Stock and Montgomery, 1996] and
drainage networks [Brewer et al., Chapter 2] provide evidence that, given some simple
assumptions, the detrital cooling-age signal can be systematically predicted, and detrital ages from
the foreland can yield information about the tectonics of the hinterland. Yet none of these models
account for the increasingly recognized affect of lateral advection of rock mass through the orogen.
Geodynamic models [e.g. Beaumont et al., 1992; Koons, 1989; Koons, 1995; Willet, 1999] have
addressed lateral advection, but do not investigate the detailed distribution of bedrock cooling ages.
Thermal and metamorphic investigations have included lateral advection, but either do not address
the application to cooling ages [Henry et al., 1997], or do not solve for any altitudinal distribution
of ages [Harrison et al., 1998; Jamieson et al., 1998].
In this paper, we have developed a methodology that allows us to combine more complex
geodynamic models with digital elevation models (DEM). We have developed a new methodology
that builds on previous investigations because predicting the spatial distribution of cooling ages
within a landscape, and the resulting detrital signal derived from eroding that bedrock, requires a
more integrated approach. While our thermal model does not have the sophistication of ramp
timing, metamorphism, or melt generation that have been incorporated into previous models
[Harrison et al., 1998; Henry et al., 1997] we have added additional elements in order to predict the
detrital cooling-age signal.
A basic 2-D kinematic-and-thermal geodynamic model, intended to be a simplification of the
Central Nepal Himalaya, predicts the position of the closure isotherm, the distance a rock has to
travel along a path to the surface, and the rate of movement along that path. In conjunction with
digital topography, this 2-D transect is extrapolated into a 3-D model of bedrock cooling ages. The
resulting map of bedrock cooling ages can be manipulated with GIS software to predict the detrital
cooling-age signal from a basin, once corrected for variations in erosion rate and lithology.
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Comparison with the modern detrital cooling-age results allows us to constrain the 2-D kinematic-
and-thermal model, thereby providing insights into Himalayan deformation.
Although our area of investigation is the Marsyandi valley in Nepal, the technique of predicting
detrital cooling-age signals from geodynamic models may be applied to other collisional orogens.
Thus using our methodology, it is possible to evaluate tectonic and erosion models using detrital
cooling-age signals derived from orogen-scale drainage basins, which may represent an integration
of perhaps tens to thousands of square kilometers. In addition, when such detrital cooling-age
signals are preserved in the stratigraphic record, they provide quantitative constraints for the
extrapolation of numerical models into the geological record, providing the possibility to investigate
the temporal evolution of mountain belts.
2.0 Geological background
The Himalaya mark the southern boundary of a widespread expression of continental collision
throughout Central Asia. Since collision of India with Asia at 55 ± 5 Ma [Searle, 1996], it has been
postulated that some ~2500 km of subsequent continental convergence has been accommodated by
distributed shortening that is manifested by uplift of the Tibetan plateau [e.g Dewey et al., 1988;
England and McKenzie, 1982], underthrusting of India [e.g Powell and Conaghan, 1973], intra-
continental orogeny [e.g Molnar and Tapponier, 1975], and strike-slip tectonics [e.g. Tapponier et
al., 1986; Tapponier et al., 1982]. Global plate motions calculated from NUVEL-1 [DeMets et al.,
1990] predict a total convergence rate of 58 ± 4 mm/yr between India and Asia, and GPS data
[Bilham et al., 1997] indicate that approximately one third of the total convergence currently occurs
across the main Himalayan chain. This is consistent with spirit-leveling investigations [Jackson and
Bilham, 1994] which predicts that convergence results in vertical-uplift rates of up to 7 ± 3 mm/yr
over the topographic divide of the High Himalaya.
Our study area is located in central Nepal, where the Marsyandi River drains the southern edge of
the Tibetan Plateau before flowing south through the main Himalayan chain (Fig. 1). The Tibetan
zone is characterized by a sequence of lower Paleozoic to lower Tertiary marine sediments [Le Fort,
1975]. These are bound in the south by the South Tibetan Detachment System (STDS), which is a
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down-to-the-north normal fault. In the Marsyandi valley, the STDS comprises two detachments that
juxtapose the unmetamorphosed Tethyan carbonates and mudstones of South Tibet against the
Greater Himlaya sequence, with an intervening greenschist-grade marble, the Annapurna Yellow
Formation [Coleman, 1996].
The Greater Himalaya sequence commonly forms the topographic divide and comprises kyanite-
to-sillimanite grade metasedimentary and metaigneous rocks of Neo-Proterozoic [Parrish and
Hodges, 1996] to Cambrian-Ordovician age [Ferra et al., 1983]. Anatectic melting within the
Greater Himalaya, commonly of the lower kyanite-grade schists of Formation I [Barbey et al.,
1996; Harris and Massey, 1994], produces leucogranites that intrude the top of the sequence. In the
study area, the crystallization of the Manaslu leucogranite has been dated at 22.4 ± 0.5 Ma using 232Th/208Pb in monazite [Harrison et al., 1995], and contains an older inherited-Pb monazite
population of ~600 Ma [Copeland et al., 1988]. The Manaslu granite typically yields 40Ar/39Ar
muscovite plateau dates of ~17 to 18 Ma [Coleman and Hodges, 1995; Copeland et al., 1990].
The south-vergent Main Central Thrust zone (MCT) forms the base of the Greater Himalaya
sequence and overthrusts the Lesser Himalayan sequence. The MCT has experienced a poly-phase
history. Earliest motions were synchronous with the regional metamorphism of the Greater
Himalaya sequence, 20 to 23 Ma [Hodges et al., 1996]. Detrital muscovite cooling ages from
tributaries within the Marsyandi valley are typically dominated by populations of 4 to 10 Ma grains
[Brewer et al., Chapter 2] and muscovites collected from the Main Central thrust zone yield dates
of 6.2 ± 0.2 Ma and 2.6 ± 0.1 Ma [Edwards, 1995]. Such cooling ages have been used to argue late-
stage deformation of the MCT [MacFarlane et al., 1992], which this is supported by Th-Pb
microprobe analyses on syn-kinematic monazites [Harrison et al., 1997], although hydrothermal
alteration of the thrust zone has also been proposed [Copeland et al., 1991].
The Lesser Himalayan sequence is predominantly greenschist-grade metasediments [Colchen et
al., 1986] that are Mesoproterozoic to Early Cambrian in age [see Hodges, 2000 for review]. The
southern limit is bound by the south-vergent Main Boundary Thrust (MBT). Movement on the MBT
may have initiated between 9 and 11 Ma [Meigs et al., 1995]. The most recent movement is difficult
to constrain, but must be younger than early Pliocene [DeCelles et al., 1998]. The Main Frontal
Thrust (MFT) represents the distal limit of Himalayan deformation in the foreland, and has an
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estimated shortening rate of 21 ± 1.5 mm/yr over the Holocene, indicating that it is currently the
major active fault [Lave and Avouac, 2000].
3.0 Thermal and Kinematic modeling
As opposed to simple vertical motion of rocks, lateral advection during continental collision often
represents the dominant component of the deformation field. Yet within the geochronological
community, cooling ages have typically been interpreted in one dimension, with erosion rates
calculated assuming that the rock column is moving vertically towards the surface. In a recent
study, Harrison et al. [1998] use 2-D kinematic-and-thermal modeling to investigate anatexis and
metamorphism in the Central Himalaya. Thermochronology data can be compared against their
model because bedrock ages are predicted by tracing particle trajectories through the orogen.
In this paper we adopt a similar basic approach, and present a 2-D kinematic-and-thermal model to
determine the depth of the closure temperature and calculate the path of rock particles through an
orogenic transect. To do this we must first define the decollement geometry within the Himalaya
(section 3.1) and secondly specify the thermal characteristics of the orogen (section 3.2). With an
appropriate kinematic-and-thermal model, we can extrapolate the 2-D solution along strike to
predict the 3-D spatial distribution of bedrock cooling ages over the entire landscape (Fig. 2).
Correcting for the volumetric contributions of thermochronometer (section 3.3), GIS software
allows us to use the resulting “age maps” to extract the modern detrital cooling-age signal. We can
compare the predicted cooling-age signal from a number of different scenarios to the observed
detrital cooling ages of Brewer et al. [Chapter 2] to assess which parameters are consistent with the
data and to test the sensitivity of the model to variations in these parameters.
3.1. Constraints on thrust geometry
In an active orogen, a bedrock cooling age represents the time elapsed since a rock particle passed
through the closure temperature and subsequently reached the surface. The distance traveled in this
time, divided by the cooling age, is a proxy for the time-averaged erosion rate. Therefore, in order
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to predict a bedrock cooling age we need to know: (1) the position of the closure isotherm; (2) the
particle trajectory, and; (3) the rate of particle transport along this trajectory. Due to the strong
dependence of the thermal structure on the rate of rock advection [Brewer et al., Chapter 1;
Mancktelow and Grasemann, 1997; Stüwe et al., 1994], the kinematic structure of the mountain belt
becomes the primary parameter to constrain. By combining heat production with the velocity (speed
and direction) of particles through the orogen, we can model thermal conditions, and more
specifically, the position of the closure isotherm.
For the purposes of modeling, we use a number of simplifications and assumptions to determine
the kinematic structure. First, we use a 2-D model. As a consequence of a scarcity of accurate
subsurface structural data, we assume that it is possible to extrapolate geometrical constraints along
strike. Given the remarkable lateral continuity in the overall structure of the Himalayan orogen (the
major thrust faults can be traced laterally within Nepal and over much of the 2000-km-long range
front), a 2-D approximation is reasonable for the along-strike scale of 100 to 200 km in our model.
Second, although we recognize that the Himalaya has a complex structural architecture, we use
one major decollement to represent the kinematics of the collisional belt. It has been proposed that a
major plate-scale decollement, the Main Himalayan Thrust (MHT), underlies the structure of the
Himalaya [Seeber et al., 1981]. Surface faults are interpreted to sole out into this decollement, with
individual thrusts representing progressively less net displacement from north to south as structures
become progressively younger. Because our intent is to show the major kinematic characteristics of
the orogen, rather than duplicating local complexities, we adopt this orogenic-scale decollement
model. A similar approach was taken by Henry et al. [1997], who modeled the 2-D thermal
structure of the Himalaya using a single crustal-scale decollement dipping at 10° northwards from
the surface outcrop of the MBT. As outlined below, we use a more complex decollement that has 3
dip domains (Figs. 2 & 3), with kink-band folding in the overlying thrust sheet, to mimic the
assumed large-scale structure of the orogen.
With our simplified structure, the MBT represents the surface expression of the MHT (Fig. 3, a).
The average position of the MBT in the study area is constrained by the geomorphic expression of
the southern edge of the Lesser Himalaya, taken from the 90-m DEM. This appears in a distinctly
different location, on the DEM, from Siwalik deformation to the south associated with the MFT. In
our model the MHT dips shallowly 5° - 6° beneath the Lesser Himalaya (Fig. 3, c). This is
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consistent with geological sections [Schelling, 1992], borehole data [Mathur and Kohli, 1964], and
leveling data [Jackson et al., 1992].
From the shallow Lesser Himalayan decollement, we use a 15 to 20° mid-crustal ramp that dips
beneath the High Himalaya (Fig. 3) because a number of sources of evidence suggest that the MHT
steepens beneath the topographic front. Foliation planes in the northern Lesser Himalaya steepen
northwards [Schelling and Arita, 1991] and are interpreted to represent a transition from a flat to
ramp geometry under the topographic front. A cluster of seismicity between 5 and 20 km depth,
centered approximately 80 km north of the MFT (Fig. 3, e) [e.g. Ni and Barazangi, 1984], has
interpreted to represent the stress release on this steeper section of fault [Pandey et al., 1995]. Spirit
leveling indicates short-term rock uplift rates of 4 to 6 mm/yr occur over 40-km wavelengths in the
Higher Himalaya, where 2-D dislocation modeling indicates that this can result from strain
accumulation above a steeper section on a deep decollement [Jackson et al., 1992; Jackson and
Bilham, 1994]. In addition, gravity investigations indicate that the Moho dips at 15-20° under the
topographic front of the Himalayas, suggesting a sharp bend in the Indian Plate [Lyon-Caen and
Molnar, 1983].
The position of the MHT to the north of the mid-crustal ramp is constrained by the INDEPTH
seismic profile. INDEPTH imaged a major reflector dipping northward under southern Tibet that
was interpreted to be the MHT, separating Indian plate from the overthrusting Eurasian plate
[Brown et al., 1996; Nelson et al., 1996]. The ramp is at a depth of 9 seconds (TWT) or
approximately 30-km depth beneath the STDS (figure 3, g). The ramp continues for 65 km to the
north where the reflector disappears, at a depth of approximately 35 km below the surface, under
the southern edge of the Kangmar Dome and ultimately the Yamdrok-Damxung reflector (YDR).
The YDR is thought to represent a partial-melt zone beneath southern Tibet formed by crustal
thickening with resulting anatexis, and the Kangmar Dome has been interpreted as a basement-
cored uplift structure [Nelson et al., 1996].
Because most of the constraints on the deep structure of the Himalaya have to be projected along
strike to the Marsyandi valley area, we use the geomorphology of the Marsyandi valley area to aid
the specific location of ramp-angle domains. Whereas the assumption of a landscape in steady state
is necessary for the thermal model, it is not a prerequisite for this analysis. We simply assume that
the topography reflects a balance between the rock-uplift rate (with respect to the geoid) and the
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erosion rate. For illustration, steep slopes and high relief provide maximum potential energy for
erosion processes, but to maintain such a landscape undergoing rapid erosion, the rock influx must
also be rapid.
We use a swath ~130 km long by 0.6 km wide, orientated with the long axis parallel to the strike of
the orogen (Fig. 1), to extract averaged topographic characteristics of the study area from a
smoothed 90-m DEM, and from a slope map with values calculated using a 180 m by 180 m area.
Topographic envelopes in figure 3 illustrate the minimum elevation and maximum elevation within
the swath, and hence represent the along-strike relief within the study area. The minimum elevation
essentially represents the river profiles, and we interpret the relief to be a proxy for erosion rates
[e.g. Pinet and Souriau, 1988]. The mean elevation is the statistical average of all the cell values
contained within the swath at each location along the transect.
We have divided the study area into four regions based on the slope (Fig. 3, top panel) and elevation
characteristics (Fig. 3, bottom panel). In the north, where the rock flux originates, we observe low
hillslope angles (Fig. 3, iv) and low relief (Fig. 3, i) on the edge of the Tibetan Plateau. Despite the
high elevations of the Tibetan Plateau, this region is indicative of low erosion rates. In our model,
material is advected laterally and we use a hypothetical flat decollement (Fig. 3, j) to represent this
section where the MHT disappears under the partial melt zone of South Tibet. To the south we
observe a zone of increasing relief (Fig. 3, f) and increasing slopes (Fig. 3, iii) that form the
headwaters of Himalayan transverse rivers. This is a zone of higher erosion that we represent by a
shallow ~4° ramp section.
As material moves still further south, the effects of the steep MHT section, underlying the High
Himalaya, are observed. As the material is transported over the ramp inflexion point (Fig. 3, g), the
relief increases markedly (Fig. 3, d) and the slopes are uniformly high (Fig. 3, ii). Tethyan
sedimentary rocks become progressively incised as material moves at 4-5° up the MHT before
becoming rapidly stripped off to the south of the inflection point, as the steep ramp section is
encountered. We interpret the high relief (up to 6 km) and high slopes to the north to indicate
hillslopes at the threshold angle for landslide failure [Burbank et al., 1996], representing high
erosion rates due to the increase in the vertical advection component above the steep ramp. The
tectonic forcing is rapid enough above the steep ramp to maintain the hillslopes at the limit of rock
strength, and the landscape erodes rapidly. The minimum elevations show a rapid increase
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northwards, above the MHT ramp (figure 3, d), suggesting that the rivers increase grade in response
to an increased rock uplift rate [Lave and Avouac, in review; Seeber and Gornitz, 1983; Whipple
and Tucker, 1999].
Once material passes over the steep section on the MHT, and onto the ~5° flat beneath the Lesser
Himalaya (Fig. 3, c), the landscape has lower relief (Fig. 3, b) and lower hillslopes (Fig. 3, i). We
interpret this change to represent a new balance between erosion processes and rock uplift; due to
the decrease in vertical rock-uplift rates, as lateral advection becomes more dominant, less potential
energy per unit time is added to the landscape by rock uplift. In addition to lower erosion rates, the
average slopes in this zone also decrease southwards due to sediment ponding against uplifting
structures in the south, superficially covering valley floors.
3.2. Thermal model
The geometric structure provides a kinematic framework for the model when coupled with a
convergence rate, but the thermal parameters have to be specified before we can predict the depth of
the closure isotherm. Our thermal model has three main components: (1) the thermal properties
assigned to each thermo-lithological package (radioactive heat production, conductivity, and
diffusivity) and the geometry of that package; (2) the kinematics, controlled by the decollement
geometry; (3) a shear-heating term that represents frictional heating on the main decollement.
Because the results of the model are compared against the 40Ar/39Ar analysis on muscovite from
Brewer et al. [Chapter 2], the closure temperature of interest is considered to be the 350°C isotherm
in this model.
The parameterization of our thermal model (Fig. 3) closely resembles that of Henry et al. [1997],
with a thermally inhomogeneous crust underlain by mantle characterized by negligible heat
production and a conductivity of 3.0 Wm-1K-1 [Schatz and Simmons, 1972]. The Indian crust is
bilayered with a 15-km-thick upper crust with heat production of 2.5 µWm-3, and a 25-km-thick
lower crust with heat production of 0.4 µWm-3 [Pinet, 1992]. With our kinematic model, the Lesser
Himalaya and the Greater Himalaya sequence function as a single tectonic unit, and are assigned a
heat production of 2.5 µWm-3 because of high concentrations of radioactive elements [England et
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al., 1992]. The thickness of the Greater Himalaya sequence varies laterally within the Marsyandi
study area, perhaps due to STDS normal faulting at the top of the slab, which is not included in this
model. Therefore we have decided to use a thickness of 22 km for the Greater Himalaya sequence
that is consistent with the INDEPTH geological section, measured from the MHT to the STDS
[Nelson et al., 1996]. In our model, the upper boundary of the Greater Himalaya sequence results in
Tethyan rocks cropping out on the highest peaks, which matches the geology of the range [Colchen
et al., 1986]. Due to the normal faulting and lateral thickness variations, however, the thickness of
22 km is simply considered a thermal parameter for the model, rather than an accurate predictor of
the surface outcrop of Tethyan sediments in the Marsyandi valley. The Tethyan sediments are
assigned heat production of 0.4 µWm-3, because it seems reasonable that they contain a lower
abundance of radioactive isotopes than the Greater Himalaya sequence. Crustal conductivity is set
uniformly to 2.5 Wm-1K-1, and the thermal diffusivity to 0.8 µm2s-1 throughout.
The surface boundary condition is set to 0°C, with the morphology of the interface determined by
the mean elevation calculated by averaging a smoothed 90-m DEM over the previously described
swath (Fig. 1). Due to our 2-D approach, we are ignoring the cooling effects of the relief along the
strike of the orogen. In addition, when extrapolating the thermal model laterally, we are assuming
that there will be no significant deflection of the isotherm by local topography. The basal boundary
is set to a constant mantle heat flow of 15 mWm-2 that is consistent with heat flow values from
Precambrian cratons [Gupta, 1993]. Lateral boundary conditions are set to a constant geothermal
gradient on boundaries with influx of rock mass into model space, whereas they are no heat flow
boundaries if there is a net loss of mass from the system.
A shear-heating term, described by Henry et al. [1997], is used to account for frictional heating
along the basal decollement fault. Two terms are needed to describe the shear heating in both the
brittle and the ductile regime. Heat production is a function of the shear stress and strain rate. Shear
stress is calculated as the minimum of a brittle lithostatic pressure-dependant law (1/10th the
lithostatic pressure) or a ductile temperature-dependant power law. Parameters for the ductile power
law are taken from the moderate friction flow law of Hansen and Carter [1982]. In the ductile
regime the fault zone is 1000-m wide and undergoes uniform strain and heating. This model
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predicts that the brittle-to-ductile transition occurs at ~420°C in the undeformed Indian Plate (see
discussion in Henry et al.[1997]).
The initial starting condition is set by calculating a geothermal gradient [Pollack, 1965] for the
thermal structure described above undergoing no advection of heat. The 2-D finite difference
algorithm of Fletcher [1991] is used to calculate the thermal structure after ~20 My of advection of
rock mass through the orogen. This should approximate the steady-state solution, within the area of
interest, given the thermal response times of the 350°C isotherm [Brewer et al., Chapter 1]. They
show that from initial static conditions, 90-95% of the steady-state solution, for a crustal column
undergoing vertical erosion from depths of 35 km, at rates of 0.1 to 3.0 km/My, is obtained in 10
My. The morphology of the surface boundary in our model is not time dependant, and hence there is
an implicit assumption of steady-state conditions, whereby the mean elevation of the study area is
invariant over timescales of 10 to 20 My and across spatial scales of 100-200 km. This implies that,
the rock influx into the orogenic front is necessarily balanced by the denudation rate over these
timescales.
3.3. Particle trajectories and detrital cooling-age signals
Based on the specified geometric architecture, and given a specified convergence rate, we can find a
solution for the steady-state thermal structure of the orogenic belt (Fig. 4a). The thermal steady state
in the overthrusting plate is a balance between three competing processes. The underthrusting plate
comprises relatively cold material and so cools the overthrusting plate from beneath, resulting in a
downwards deflection of the closure isotherm. In contrast, tectonics and erosion advect hot material
into the overthrusting wedge, thus heating the system and moving the closure isotherm towards the
surface. Counteracting this, from the top of the overthrusting plate, conductive heat loss to the
atmosphere cools the orogenic front.
Once the unique steady-state thermal structure has been defined for a particular ramp geometry and
convergence rate, we can use the kinematic framework to predict cooling ages in the overthrusting
plate. From the geometry of the underlying ramp the velocity vector for each point within the
transect can be calculated, and the trajectories of rock particles traced through the orogen. The
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distance traveled by a particle between passing through the argon closure temperature for muscovite
(~350°C) and reaching the surface (Fig. 4b) can be converted into a cooling age by dividing by the
velocity of the particle into the orogenic front, which is considered to be in topographic steady state.
Because the cooling age for each location in the landscape is a function of the distance that the
particle has had to travel since passing though the closure temperature, mountain summits will have
older cooling ages than valley floors (Fig. 4c). To predict the cooling ages as a function of
landscape position, we use the kinematic-and-thermal model in conjunction with digital topography
to integrate modern topographic parameters into our analysis: for a particular location in the
transect, we measure the distance along the trajectory from the modeled closure temperature to the
actual elevation of that point. Furthermore, if we assume that the kinematic geometry remains
invariant across the width of the study area, the two-dimensional thermal structure can be
extrapolated laterally. With GIS software, we crop and rotate the DEM so that the Y direction is
normal to the strike of the orogen (Fig. 1). The column of Y cells at each value of X can be treated
as an individual transect and a predicted cooling age calculated at each point along the section (e.g.
Fig. 4b). The areal combination of individual columns creates a “cooling-age map” that predicts the
cooling age for every point in the modern landscape. Figure 2 illustrates such an age map draped
over the modern topography.
Now that the distribution of cooling ages within the landscape can be calculated, we want to
model how this is manifest in the sediments eroding off the orogen. The detrital cooling-age signal
is not a simple function of the areal distribution of ages, because the relative proportion of grains of
a certain cooling-age fraction depends upon both: a) the fraction of land with that cooling age, and;
b) how fast that fraction is eroding. The former is calculated with the kinematic-and-thermal model,
but the latter still needs to be determined. Thus we need to calculate the erosion rate in order to
determine the relative contribution of ages from different parts of the topography.
One approach to calculating denudation rates is to simply calculate the vertical erosion
component, which is a common practice in conventional thermochronometry (where erosion rates
are calculated using the cooling age in conjunction with an assumed geothermal gradient).
However, with the effects of rapid lateral advection, the erosion rate calculated with the vertical
component of the particle velocity commonly underestimates the total amount of denudation.
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To compute the total volume of material eroded from a mountain front, both the 2-D velocity field
and the aspect of the topography in relation to it have to be considered. For illustration, we can
consider erosion on the edge of a plateau that is in topographic steady state (Fig. 5). Deformation
occurs as material advects laterally towards the plateau margin, along an underlying decollement,
before passing onto a steeper ramp. With this scenario, the highest erosion rates occur where the
aspect of the topography is normal to the particle trajectory (Fig. 5, i), whereas the lowest erosion
rates occur when the topography is closer to parallel with the velocity field (Fig. 5, iii). The contrast
in erosion rate can be explained by the primarily lateral movement, rather than erosion, of material
until the thrust sheet intercepts the kink bend, at which time it experiences rapid uplift over the
thrust ramp, and subsequent denudation at the topographic front. The geometry clearly illustrates
the difference between the underestimated vertical erosion rate (Fig. 5, (ii)) and the rate of erosion
perpendicular to the transport vector (Fig. 5, (i)). This illustration may be analogous to the
topographic axis of the Himalaya at present: as Tethyan sedimentary rocks of the Tibetan Plateau
move through the kink bend, caused by the ramp in the underlying MHT, they become rapidly
uplifted to cap the highest peaks before being eroded.
Given this relationship, we can calculate the volume of rock eroded for a DEM with cell dimensions
X by Y for direct application to the digital topography (Fig. 6). The expression relates the volume of
rock eroded (V) in time (dt) to the topographic slope and particle velocity in the plane of Y:
XdtvYdtV ).sin(...cos
)( βα
=
(1)
The values β and α are dependant upon the relationship between the topographic surface slope (S),
and the underlying ramp angle, which varies between 0° and 90° and determines (a). If S + a < 90
then β = (S + a) and α = s. If S + a > 90 then β = 180 - (S + a) and α = s. If S is larger than 90, then
a volume can only be calculated if a > (180 - S) in which case β = a – (180 – S) and α = 270 – s,
otherwise the calculated volume becomes negative because the particle trajectory is directed into the
slope, as opposed to out of it. Both angles are measured positively as illustrated in figure 6, and the
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equation assumes that the strike of the topography (parallel to the direction of X) is perpendicular to
the particle transport direction.
Using equation 1, the effects of topographic slope and particle trajectory on the volume of material
eroded can be predicted for a grid cell of unit area, undergoing unit erosion for unit time (Fig. 7).
With vertical erosion (particle trajectory angle = 90°), there is unit erosion independent of the
surface slope. Highest erosion rates, per unit horizontal area, for slopes of 30° to 40° (as is typical in
the Himalaya) occur with particle trajectories of 50° to 60°, and the lowest erosion rates occur as
particle trajectories approach 0°.
For our purposes, topographic steady state means that the spatially averaged characteristics of the
landscape (hypsometry, slope distributions, along-strike averaged morphology) do not vary over the
interval of interest, which is several millions of years in this study. For the thermal modeling, we
use the mean elevation as our topographic surface boundary. Thus if the average topography is
invariant, the steady-state thermal structure will be in equilibrium. However, an exact topographic
steady state, whereby the influx of rock into every point in the landscape is exactly balanced by the
erosional flux out of that point, is problematic; it is clearly unrealistic on small-spatial and short-
temporal scale because minor climatic cycles will cause high-frequency variations in the erosion
rate through time, and because erosion processes are intrinsically variable over short distances.
Providing the time-averaged topographic steady state is maintained, small perturbations will not
affect the thermal structure because it has a much slower response time. However, a cell-by-cell
calculation of erosion rates (e.g. equation 1) over wavelengths of 90 m, based on the topography at
the snapshot in time when the DEM image was produced, will be strongly influenced by local
topographic variations.
To minimize the effects of local, short-term deviations from the average topography, we therefore
divide the topography into three zones (Fig. 8) based upon the overall pattern of mean elevation: the
Tibetan Plateau; the Himalayan front, and; the Lesser Himalaya. The aspects of these strike-parallel
zones, with respect to the plate velocity vector, are then used to determine an “erosion-rate map” for
the study area. Each cell within a zone erodes an equal volume of material for the same particle
trajectory angle, which in reality will vary depending upon the predetermined underlying ramp
geometry. The result of this approach is that predicted erosion rates vary as orogen-parallel swaths,
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rather than on the cell-to-cell scale of a DEM, which is more consistent with the idea of steady-state
topography as discussed above.
We now have a predicted cooling age and erosion rate for each point in the landscape. In order to
predict the distribution of detrital ages produced by erosion of that landscape, we simply need to
combine the volumetric contribution of a predicted age from each one of these locations. We
represent this as a probability density function (PDF), which represents the probability of a
particular cooling-age being found in the sediment and is equivalent to the theoretical PDF of
[Brewer et al., Chapter 1]. The theoretical PDF for a DEM matrix containing x by y cells is
constructed using equation 2:
∑ ∑=
=
=
=
=
xX
X
yY
Ya YX
dtdvYXaP
0 0),().,()( τ
[2]
where the value of τ has to be computed for each grid cell location (X,Y), for each value of Pa(a): if
the cooling age of a cell (ac) is equal to a, then τ = 1, else τ = 0. Pa is the probability of dating a
grain of a particular age (a) and dv/dt is the volume of material a grid cell contributes per unit time.
Once the area under the resulting curve is normalized to unity, the theoretical PDF describing the
distribution of cooling ages is constructed. In this paper, we apply a 0.5 My smoothing function to
the PDFs to minimize the effects of small perturbations. This approach assumes a steady-state
topography, no sediment storage within the catchment, and that muscovite undergoes no mechanical
comminution within the fluvial system. Within mountain belts undergoing high erosion rates,
significant sediment storage is typically not observed, and over the hinterland-to-foreland spatial
scale, Brewer et al. [Chapter 2] argued that the latter process was negligible in the Marsyandi given
the uncertainty in the analysis of 40Ar/39Ar ages.
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4.0 Modeling Results
With the kinematic-and-thermal model, we can now predict the distribution of detrital cooling
ages derived from the erosion of the study area. Two groups of models were run to investigate
relationships between the predicted cooling-age signal and geological parameters. For example, we
can ask: “How are variations in the rate of overthrusting of Asia and underthrusting of India
manifest in the detrital cooling-age signal?” The first set of models examines this question, and the
subsequent comparison of predicted cooling-age signals to actual detrital 40Ar/39Ar age data
[Brewer et al., Chapter 2] allow us to place constraints on these parameters. Likewise, we evaluate
how sensitive the detrital cooling-age signal is to different ramp geometries. We have seen that the
position of the closure isotherm in the overthrusting plate is dependant upon the interaction
between: 1) cooling by the underthrusting plate; 2) heating due to erosion and subsequent lateral
advection of hot material into the system, and; 3) conductive heat loss to the atmosphere (Fig. 4a).
Thus, variations in the ramp geometry underlying the Himalaya should result in different positions
of the closure isotherm, and this should be evident in the predicted distribution of bedrock, and
therefore detrital, cooling ages.
For the second set of models, we examine the effects of drainage basin area and lithological
factors. We want to address the questions: “Is a cooling-age signal from a large, transverse river
representative of the orogen, and to what extent does lithology modify the results?” To investigate
this, we model the detrital signal contributed solely from the modern Marsyandi catchment and
compare the results to the observed data [Brewer et al. Chapter 2]. In order to integrate across the
broadest area possible, we use the most downstream sample collected that we consider to be the best
proxy for the distribution of cooling ages deposited in the foreland. The sand sample was collected
from the modern channel of the Marsyandi River, upstream of the confluence with the Trisuli River
(Fig. 1). Muscovites were separated and 55 grains analyzed at the 40Ar/39Ar laser microprobe
facility at the Massachusetts Institute of Technology.
The 40Ar/39Ar data (Fig. 10) are presented as a summed probability density function (SPDF)
comprising the normalized summation of individual grain PDFs, which in turn represent each age
with a Gaussian distributed analytical error [Deino and Potts, 1992]. Note that the absolute value of
probability displayed on the y-axis of our probability plots is dependent upon the age-bin size
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chosen along the x-axis. The age-bin size is constant for all plots and the numbers are retained to
allow the direct comparison of relative probability between plots, and between the data SPDF and
the theoretical PDFs generated from our modeling. The data shows a broad 4 to 8 Ma young age
population that dominates the signal. Secondary 10 to 15 Ma and 15 to 20 Ma populations are also
evident.
4.1 Kinematics
4.1.1 Convergence rates
GPS studies indicate that the convergence rate of India with southern Tibet is 20.5 ± 2 mm/yr
[Bilham et al., 1997]. This is typically considered to be the rate of underthrusting of India beneath
Asia, but is actually a more complex interaction of tectonics and erosion. For this model the
intersection of the MHT decollement plane with surface topography (Decollement/Surface
Singularity (DSS), figure 3) is our reference frame, because this theoretical point is independent of
how total convergence is partitioned between the two plates. To illustrate the effects of partitioning,
we consider three different scenarios: 1) with India fixed, the convergence rate has to be solely
accommodated by overthrusting of Asia at 20 mm/yr with respect to the DSS (Fig. 9a); 2) with Asia
fixed, convergence has to be accommodated by Indian underthrusting (Fig. 9b; and 3) with equal
division of the 20 mm/yr of convergence between the two plates, the Indian Plate moves at 10
mm/yr northwards, and the Eurasian Plate moves at 10 mm/yr southwards towards the DSS (Fig.
9c). In all these cases, the overall slip rate on the MHT remains a constant 20 mm/yr. The
partitioning of convergence will affect the thermal and velocity structure of the system, and so
determine modeled cooling ages. Because other parameters are reasonably well constrained by the
geology, even if they have to be extrapolated along strike, the partitioning of total convergence
between India and southern Tibet becomes a primary unknown variable. Given this, we used the
model constraints illustrated in figure 2 to examine the sensitivity of the detrital signal, to the
relative convergence rates.
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The results from a number of different simulations illustrate that the detrital cooling ages are very
sensitive to the relative partitioning of convergence, especially at geologically reasonable rates (Fig.
10). Convergence rates of greater than 10 km/My of Asia, with respect to the DSS, result in very
young age populations with peak probabilities representing ages of < 3 My. Harrison et al. [1998]
use equal convergence rates in their model that requires 10 km/My of erosion perpendicular to the
particle trajectory (5 km/My of vertical erosion above a 30-degree ramp) to maintain a steady-state
topographic condition.
The detrital cooling-age signal is more sensitive to slow convergence rates of Asia with respect to
the DSS (Fig. 10). With 4 km/My of convergence, the peak probability occurs between 5 and 10
My, whereas if the convergence rate decreases to 2 km/My, the peak probability shifts markedly to
20 to 25 My. The general trend also indicates that slowing the convergence rate tends to broaden the
range of ages predicted, both for the peak probability and the overall age signal; the older age ‘tails’
lengthen significantly with slower rates (Fig. 10).
In order to assess the appropriate partitioning, we compare the predicted age distribution for
different convergence rates with the observed age distribution for the Marsyandi River. An
important result from this study is that the most likely range of Asia-to-DSS convergence rates is
between 4 and 6 km/My, because the predicted detrital ages fall within the approximate range of
peak probability in the data (indicated by the shaded band of ages on Fig. 10). This is better
illustrated with a direct comparison to the real data for scenarios with Asia-to-DSS convergence
rates of 4, 5, and 6 km/My (Fig. 11, a). The best fit of model to data is generated using 5 km/My of
Asia-to-DSS convergence. Faster convergence produces a younger peak probability (~3 My) that
matches the youngest observed ages well, but the older tail stops at ~17 My, whereas the actual data
contains a peak at 17 to 22 Ma. Slower Asia-to-DSS convergence rates match the older population
in the peak probability of the data, but under predict the young ages. In addition, the older-age tail
stretches out to 30 My, whereas no grains of this age are observed in the data. The best-fit predicted
PDF, using a 5-km/My Asia-to-DSS convergence rate, matches the average population of the peak
probability observed in the data, and fits the older tail well. However, the width of the observed
peak probability, as well as observed ages < 4 Ma and between 7 and 9 Ma, are underrepresented by
the model.
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A general explanation for variations of the detrital cooling ages, caused by different partitioning of
the convergence rate, can be understood within the context of the kinematic-and-thermal system.
Increasing the rate of convergence of Asia (Fig. 12) with respect to the DSS produces younger age
populations by: a) increasing the rate at which rock moves between the blocking temperature and
the surface, and; b) deflecting the closure isotherm towards the surface by advection of hot rock
mass (Fig. 12a). In contrast, increasing the rate of India-to-DSS convergence cools the system by
faster subduction of relatively cold continental plate (Fig. 12b), subduing the effects of warming
due to a thick crust and rapid lateral advection in the overthrusting plate.
4.1.2 Angle of Main Himalayan Thrust ramp
Whereas the kinematic model is a simplification of the complex geology of the Himalaya, it is
useful to examine the sensitivity of the model to other potentially important parameters, such as
possible variations in ramp geometry. The position of the MBT is constrained by surface geology,
and the depth seismicity at the top of the MHT ramp is relatively well known. Therefore, the main
geometric variable is the steepness of the MHT ramp underlying the main topographic front.
Until now, we have used a ramp angle of 18° that represents a reasonable approximation of the
main decollement beneath the Himalaya. However, because of the fact that constraints are
extrapolated along strike, and due to the nature of the data, there is some uncertainty in the exact
structure. Therefore, to investigate whether insight into ramp geometry may be gleaned from detrital
cooling-age data, two additional end-member models were run with ramp angles of 13 degrees (Fig.
13b, i) and 23 degrees (Fig. 13b, ii). The lateral position of the ramp inflection point, on the
northern end, was fixed because we have assumed a link between the TSS outcrop, surface
topography, and the kink bend in the underlying decollement. As a consequence, the depth of the
main decollement under the STDS becomes ~25 km and ~35 km, respectively, as opposed to the
original ~30 km constrained by INDEPTH [Nelson et al., 1996].
The two end-member scenarios were modeled while maintaining the best-fit partitioning of the
convergence rate (5 mm/yr to Asia and 15 mm/yr to India). The steeper ramp angle (Fig. 13a, PDF
i) produces a match to the younger ages, but does a very poor job of representing the 5-10 Ma age
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population observed in the data. The shallower ramp angle (Fig. 13a, PDF v) produces a 8 to 10 My
peak, as seen in the data, but contains no population of ages < 6 My, despite their dominance of the
observed ages. Therefore, these results indicate that initial model produces a better overall fit to the
data for a convergence rate partitioned with 5 mm/yr of motion to Asia and 15 mm/yr to India and a
ramp angle of ~18°.
Because the effect of decreasing the ramp angle increases the peak probability age, it seems
reasonable that an improved fit might be obtained by both decreasing the ramp angle and increasing
the convergence rate of Asia with respect to the DSS. In contrast, the opposite scenario is also
reasonable: increasing the ramp angle while slowing the convergence rate of Asia with respect to
the DSS. To test this, two further models were run. Partitioning the total convergence rate into 4
mm/yr Asia and 16 mm/yr India, while maintaining the steep-ramp geometry, produces a PDF with
a peak probability at ~5 My (Fig. 13a, PDF ii). This result is very similar to our initial best fit (Fig.
13a, PDF iii), although is less well represented in the 6 to 13 My age range. Partitioning the total
convergence rate, with a shallow ramp geometry, into 6 mm/yr Asia and 14 mm/yr India produces a
peak probability at ~6 My (Fig. 13a, PDF iv). Again, the younger, < 5 Ma, age population observed
in the data is absent from the resulting PDF.
From this sensitivity analysis, it is clear that predictions of the detrital cooling-age signal from the
orogenic front are dependant upon the relationship between the angle of the thrust ramp underlying
the topographic front of the Himalaya, and the relative partitioning of convergence. The initial
model containing an 18° ramp and a convergence rate of 5 mm/yr Asia and 15 mm/yr India,
produced a reasonable overall fit to the data. However, with the uncertainty in ramp angles,
geometry of the decollement, and the random process of selecting grains for analysis, which
produces a certain amount of uncertainty in the data SPDF [Brewer et al., Chapter 1], it would seem
the convergence rates resulting from our investigation could vary by approximately ± 1 mm/yr,
assuming other parameters are reasonable. Given that our end member ramp angles were ± 5
degrees, more accurate constraints on the ramp geometry would significantly improve the
confidence of the results.
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4.2 The modeled Marsyandi valley detrital cooling age signal
Until now, we have been considering the detrital age distribution from a rectangular swath across
the orogen (Fig. 1). A sand sample collected from a riverbed, however, is actually an integration of
the specific points contained within the upstream catchment area. Hence, detrital cooling-age
signals need to be analyzed within the framework of the drainage network: the distribution of
probability within a basin PDF will be modified by the morphology of the basin in relation to the
distribution of bedrock cooling ages. With GIS software, the spatial extent of the area draining any
point in the river network can be calculated from a DEM, and then used as a template to extract the
distribution of cooling ages in the catchment. After correcting for spatial variations in erosion rate
via equation 1, the integrated cooling-age signal can be determined for the specific drainage basin.
Using this methodology, we can reexamine our previous results within the specific area of the
Marsyandi valley (Fig. 11, b). The results show that in comparison to the rectangular swath (Fig. 11,
a) the populations of peak probabilities are enhanced when correcting for the drainage area of the
Marsyandi, while the older age populations become less important. This is because the Marsyandi
contains more areas with younger ages than old, in comparison to the general swath represented by
the model. The effects of changes in catchment morphology need to be considered within the
context of volumetric contributions: a small increase of area within a rapidly eroding zone will have
a much larger effect than the equivalent increase of area within a zone that is producing less
sediment. If we compare the distribution of cooling ages generated using a 5 km/My convergence
rate (of southern Tibet with respect to the DSS) to the observed data, we can see that the relative
importance of the older tail is a better match with the observed data when the basin morphology is
considered, but the 6 to 8 My peak is again underrepresented by the model and the likelihood of
dating the most common age are too high.
The dashed line in figure 12b is a synthetic PDF from Brewer et al. [Chapter 2] that is generated by
a model based upon 40Ar/39Ar data from a further 11 sample sites within the Marsyandi basin.
Individual tributary PDFs are modeled assuming vertical erosion and mixed together, as a function
of basin area and contribution of thermochronometer, to produce a resulting trunk-stream signal (a
theoretical NIB-S24 PDF) [Brewer et al., Chapter 1; Brewer et al., Chapter 2]. While the synthetic
PDF generated by the study underrepresents the 8 to 13 Ma age population found in many
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tributaries within the Marsyandi valley and suffers from the limitations of model assumptions, it
provides the only integration of all the data within the basin and is thus shown for comparison. The
theoretical PDF in our model, generated using a 5 km/My convergence rate of southern Tibet with
respect to the DSS, also produces the best fit to this theoretical PDF.
4.4 The effects of lithology
All the results thus far have an implicit assumption of uniform distribution of thermochronometer
across the catchment area. Clearly this is not true in the Himalaya, which contains a wide range of
lithologies ranging from carbonate mudstones to granites. The contribution of thermochronometer
to the fluvial system is dependant upon the percentage of thermochronometer (of the correct size
fraction) per unit volume of material eroded. In this instance, the specification of a correct size
fraction is an analytical constraint: Brewer et al., [Chapter 1; Chapter 2] use a grain fraction of 500
to 2000 µm to ensure that individual muscovite grains contain enough radiogenic 40Ar to detect.
Thus, with some knowledge of the geology within the catchment area, a lithology correction factor
can be applied to produce a refined predicted cooling-age signal at the basin mouth.
Without a detailed investigation of bedrock geology, the distribution of thermochronometer within
the catchment is difficult to constrain. However, in order to examine how lithological contrasts
affect the signal, we use point-counting data [Brewer et al., Chapter 2] to constrain the contribution
of muscovite from individual tributaries within the overall Marsyandi valley. For those tributaries or
areas of the trunk stream that were not sampled and counted, we assign reasonable values based on
averages from the surrounding basins. Individual tributary basins are assigned a lithological
correction factor in ARCINFO, and then combined with the erosion-rate map and cooling-age map
to predict a synthetic cooling-age signal for the basin mouth.
The results (Fig. 14) illustrate that in this case, the lithological correction that we used produced a
worse fit to the observed data than the PDF predicted with uniform distribution of
thermochronometer. The PDF generated with a lithological correction factor tends to concentrate
the probability within younger ages, whereas the older 6 Ma age population observed in the data
becomes even more underrepresented. This might be due to the resolution of our point-counting
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data: our approach assumes a uniform distribution of thermochronometer within each tributary
catchment and the strong heterogeneity that probably exists from lithology to lithology, especially
in contrasting litho-tectonic zones, is unconstrained. For example, tributaries were sampled just
upstream of their junction with the Marsyandi River, and those to the south of the Main Central
Thrust typically span both Greater Himalayan and Lesser Himalayan sequences. Point counting
commonly predicted at least 2-fold differences between these two zones. In addition, the effect of
the low contribution by areas in the Tethyan sedimentary series has already been partially accounted
for in each of the models. Due to the ramp geometry, large areas of land to the north of the
topographic divide (in the sedimentary rocks of southern Tibet) have ages that are not reset – they
are advected into the orogen above the closure temperature (Fig. 2). These are not considered when
predicting the age distribution at the basin mouth and therefore a major lithological correction has
been made by default in all of the model runs. However, the general lithological correction
technique we presented above, would almost certainly produce improved results in areas with better
lithological constraints, or areas with dramatic contrasts in the fraction of thermochronometer (that
are not accounted for by un-reset cooling ages).
5.0 Discussion
5.1 Modeling
We have presented a modeling technique for predicting the distribution of cooling ages in sediment
samples from orogenic rivers. The use of a kinematic-and-thermal framework, in conjunction with
the topography, drainage-basin morphology, and lithological characteristics of the bedrock
represents a new approach that can help calibrate and test concepts of orogenic evolution and
thermochronological interpretation. Combining the 90-m DEM with the thermal-and-kinematic
model helps overcome three major problems of geochronological models: 1) the assumption of flat
isotherms; 2) the variation of bedrock cooling ages with elevation, and; 3) the effect of non-vertical
advection. These are solved simultaneously, as an integral part of the model. The assumption of flat
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isotherms is replaced by a thermal model that accounts for perturbations caused by 1) the long-
wavelength, strike-normal, topography, and 2) the advection of rock through the system. The
variation of bedrock cooling ages with elevation can be predicted because we know the relationship
between the topography and thermal structure: assumptions of linear and vertical age gradients are
no longer required. The effects of lateral velocity fields are already incorporated into the thermal
model, and the variation of bedrock cooling ages with position in the landscape is a function of the
trajectory of individual rock particles through the orogen.
In this paper, we have illustrated this new approach using a simplified model of Himalayan
tectonics to predict the distribution of detrital-muscovite cooling ages observed at the mouth of the
Marsyandi drainage basin. Despite many uncertainties in the kinematic-and-thermal parameters, and
the simplicity of the single-decollement model, the results mimic the major attributes of the
observed data. Various scenarios allow us to examine the effects of 1) changing the ramp geometry
of the major decollement, and 2) varying the partitioning of Indo-Asian convergence with respect to
the DSS. We take the Decollement/Surface Singularity (DSS) as our reference point because it is
independent of the rate of underthrusting or overthrusting (Fig. 3). The best result was found to be
~5 km/My assigned to Asia-to-DSS convergence, and 15 km/My to India-to-DSS convergence.
However, lessening the ramp angle in conjunction with an increase in the rate of overthrusting, or
increasing the ramp angle and decreasing the rate of overthrusting, also produced reasonable results.
Thus within the likely range of ramp geometry and convergence partitioning, 5 ± 1 mm/yr is the
predicted value for the sustained late Cenozoic overthrusting by Asia. This is in contrast to the 10
mm/yr used in the by Harrison et al. [1998] and so has implications for models of Himalayan
anatexis and metamorphism.
To examine some of the differences between our approach and traditional thermochronology, we
can examine the predictions of our optimal model along a strike-normal transect (Fig. 15). The
predicted bedrock ages (Fig. 15b) increase northwards over the topographic front and southwards
over the lower Himalaya as a function of particle trajectory, depicted in figure 2. We can compare
the distribution of ages to the erosion rate predicted from a) our model of erosion rate (equation 1),
and b) that predicted from the vertical component of the overthrusting vector (Fig. 15c). The former
predicts much higher volumes of sediment eroded from the topographic front region, whereas the
latter predicts uniform volumes of sediment eroded from the width of the orogen. Both, however,
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illustrate significant variations in bedrock cooling age across zones of equal erosion. If we consider
the zone of equal erosion shaded in figure 15, we can see that the predicted maximum ages vary
from ~10 to 28 My across the region. This has important implications because traditional
thermochronological approaches, assuming vertical erosion, would yield spurious estimates of the
relative denudation rates. Thus we can see that the affects of lateral advection are very important,
and certainly need to be considered when using cooling rates as a proxy for erosion in active
orogenic belts.
The importance of some of the simplifications incorporated into the kinematic-and-thermal model
need be considered. In the thermal model, the assumption of a 0°C topographic-surface boundary
temperature will produce errors as there is a change in temperature with elevation in the
atmosphere. To investigate this, we ran a model using a 20°C topographic-surface boundary
temperature. This resulting PDF displayed a shift of < 0.5 My for the youngest ages, and had
negligible effect on the older ages. This indicates that for our purposes, this simplification was
reasonable and did not affect our conclusions. However, for more detailed modeling, a lapse-rate
function should be included to account for the changes in temperature with altitude.
The thermal characteristics of the rocks of the Himalayan orogen, and additional thermal processes,
are also simplistically represented by the model. The distribution of radioactive heat-producing
elements within the orogen, the applicability of the shear-heating model, the effects of anatexis, and
the effects of fluids are all largely unknown. In this paper, we have taken the most applicable
estimates for the thermal parameters and have not conducted a full sensitivity analysis of these.
Henry et al. [1997] conducted a more rigorous examination of the effects of various heat production
and heat flow scenarios. Here we are more concerned with introducing the methodology required to
predict the distribution of bedrock cooling ages and the resulting detrital age signal, rather than
producing the best thermal model for the Himalaya.
To extrapolate our 2-D model into 3D, we have to assume that whereas the average strike-normal
topography is accounted for in the model, the strike-parallel topography causes no isotherm
deflection. Brewer et al. [Chapter 1] illustrated that for vertical erosion rates of 3 mm/yr and 6 km
of topographic relief, the isotherm deflection was negligible with respect to the analytical
uncertainty associated with 40Ar/39Ar dating using detrital muscovite. Unfortunately, the
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applicability of this result to this investigation is difficult to ascertain. In our thermal model, the
crustal column is not eroding vertically, but erodes normal to the transport direction. Therefore, the
“apparent” relief, that might be applicable, is not measured normal to the geoid, but is measured
parallel to the particle transport direction.
To illustrate this effect in the Himalaya, we can look at the apparent relief for various particle
trajectories (Fig. 16). The bottom panel illustrates that the average relief over the Himalayan
topographic axis is about 8 km for a particle trajectory of 20°. This result, however, taken within the
framework of vertical erosion [Brewer et al., Chapter 1] is not strictly applicable to the situation:
cooling occurs through the top of the thrust sheet, and not just the eroding front edge. As a result,
the whole system will be cooled more, with the closure isotherm deeper and hence less deflected by
topography, than predicted from vertical erosion alone. Thus, although our 2-D extrapolation and
assumption of no topographic-induced deflection of the 350°C isotherm is probably reasonable, a
combined topographic and 3-D, kinematic-and thermal model is necessary to rigorously examine
the thermal interactions between particle trajectory and landscape morphology. This will be
especially important when considering the effects of topography upon lower-temperature isotherms,
such as might be predicted for fission-track or (U-Th)/He investigations.
5.2 The single-decollement model
The evolution of the Himalaya, over the time frame of the thermochronometer, is probably the most
difficult variable to constrain and has large effects on the thermal structure and the trajectory of
particles through the orogen. In this paper we have assumed that deformation field in the Himalaya
can be adequately represented by a single decollement. However, the effects of MCT movement on
the bedrock cooling ages [e.g. Harrison et al., 1998] and the process of tectonic unroofing by the
STDS are difficult to model because the timing, displacement, and duration of faulting is largely
unconstrained except in some rare circumstances [e.g. Hodges et al., 1998; Hodges et al., 1992].
Consequently, we ignore the normal faulting of the STDS, and assume that the Lesser Himalaya and
Greater Himalaya tectono-stratigraphic units are kinematically linked.
117
The effects of transitory thermal fields on the distribution of bedrock cooling ages have not been
investigated, but we can test the effects of having solely the MCT active and at thermal steady state.
To do this, we take the approximate outcrop of the MCT and extend the ramp north at ~18° from
this (Fig. 13b, (iii)), to create a “paleo-MCT” parallel to our modern decollement. We consider the
cooling-age PDF from the whole range front, because the drainage-basin shape would likely be
different if solely the MCT were active. The resulting theoretical PDF (Fig. 17) is less spiky that
previous predicted PDFs and contains a dominant population from 5 to 10 My, and an older 15 to
20 My population. This result actually fits the broad young population in the data better than
scenarios assuming that the MHT can be approximated by the position of the MBT. To see whether
the predicted cooling-age signal was simply a function of the contributing area, we conducted one
further test. We used the distribution of bedrock cooling ages predicted from the model assuming
that the MBT provides a good approximation for the MHT, and just considered contributions from
the area above the approximate present location of the MCT. This had the effect of reducing the
peak probability of the young age population, but did not resemble the width of the 5 to 10 My peak
seen using the paleo-MCT model.
The predicted age distribution from the model with the paleo-MCT is subject to certain caveats,
however. Firstly, we have to maintain the modern topography in the model, even though if solely
the MCT were active, the Lesser Himalayan landscape would not be so developed. Secondly, the
ramp geometry of the paleo-MCT is poorly constrained. The position of the MCT today may not be
a good proxy for the location of the paleo-MCT. Subsequent movement along the MHT could
translate the paleo-MCT, possibly rotating it as it passes through kink bends caused by the modern
steep ramp underlying the topographic front. Therefore, without isolating the detrital signal from the
Lesser Himalaya, and without a more thorough definition of the true age distribution through dating
more grains, it is difficult to distinguish conclusively between a long-lived, active MCT controlling
erosion and our initial MHT model.
The predicted PDF for the paleo-MCT suggests that our simplification of the MHT may not be the
best solution, and that perhaps both the MCT and MBT are active. Evidence of Late Miocene to
Pliocene metamorphism of the Main Central Thrust zone and its footwall [Copeland et al., 1991;
Harrison et al., 1997; MacFarlane et al., 1992; Macfarlane, 1993] supports theories of recent
activity. Even if the MCT is not actually currently active, we may still be seeing the cooling-age
118
response to that system, despite the deformation stepping foreland-wards. Certainly, a more
complex kinematic and thermal history, containing multiple fault activity is likely. However, further
geological constraints are needed on the temporal activity of faulting within the study area before
more complex modeling becomes justified.
5.3 The stratigraphic record
One major motivation for trying to understand the generation of cooling-age signals is that in
addition to the possibilities of testing numerical models for modern situations, dating detrital
minerals from the stratigraphic record provide a means to constrain orogenic evolution through
time. Although bedrock geochronological data may be collected to calibrate models of modern
orogenic deformation, constraints through geological time are sparse because bedrock
thermochronology is limited to the rocks exposed at the surface today. Therefore, by dating
minerals from the geological record, we can combine the precise controls of thermochronology with
the record of sedimentation preserved in the foreland basin, thus providing a quantitative temporal
record of orogenic exhumation.
Insights from this investigation indicate that the foreland signal should be representative of the
orogenic signal providing that a major transverse river is sampled. For example, when comparing
the entire swath (Fig. 11a) and the Marsyandi valley (Fig. 11b) it is encouraging to note that
whereas drainage-basin shape does modify the cooling-age signal, the overall pattern remains
consistent. Thus, although one can imagine scenarios in which this will not be true, an average
transverse river should be broadly representative of the overall cooling-age signal derived from a
hinterland that does not vary widely along strike, such as the Himalayan orogen. Additionally, if
one could isolate and examine the stratigraphic record of sediments eroded from the Marsyandi,
small changes in the areal extent of the drainage system through time would result in insignificant
changes to the SPDF when compared to the analytical uncertainty of dating. Whether minor
temporal changes in topographic characteristics, drainage-basin shape, and lithological contribution
could be extracted from the geological record would depend upon the sensitivity of the
thermochronometer and the number of grains dated from the detrital sample [Brewer et al., Chapter
119
1]. It seems that whereas minor changes in these parameters would not affect the overall distribution
of ages in the sediment, major changes in partitioning the convergence rate (Fig. 10) and ramp
geometry (Fig. 13) should be detectable. To extract maximum information, however, calibrating the
modern detrital cooling-age signal with the modern geodynamics is of prime importance.
6.0 Tectonic implications for the Himalaya
While the main thrust of this paper is developing the methodology of modeling detrital cooling-age
distributions, we discuss the implications of our results in the context of Himalayan tectonics. With
recognition of the importance of the relative partitioning of the total convergence rate, we can
divide models for the kinematics of the Himalaya into three end-member types, categorized on the
relative motion of the DSS towards a marker in South Tibet (i.e. the Indus Suture Zone (ISZ)).
From an initial starting condition (Fig. 18a) the evolution of different models can be examined in
the context of the detrital cooling ages of Brewer et al. [Chapter 2], the kinematic-and-thermal
modeling in this paper, and observable geology.
The first end-member model, and perhaps the most intuitive, is the growth of the mountain belt
through time by thrust-and-fold belt style imbrication of material scraped off the down-going plate
(Fig. 18b). The convergence rate (V) is accommodated by the underthrusting of India beneath Asia.
If the topography is already at threshold conditions, then the DSS will have to move away from the
ISZ at a rate proportional to the material added to the system (Vadd) either by: a) increasing the
width of the orogenic belt with a critical-wedge-type model, or perhaps; b) building elevation to the
limit of rock strength and propagating a self-similar profile as the Tibetan Plateau widens.
The second end-member model requires a steady-state condition, with mass added to the system by
tectonics being removed by erosion (Fig. 18c), while the DSS remains fixed with respect to the ISZ
through time. Finite-element models of orogens predict that deformation can be localized by erosion
[Beaumont et al., 1992; Willet, 1999]. In which case, high erosion rates on the southern front of the
Himalaya might be “sucking” out the metamorphic core of the Himalaya, the Greater Himalayan
Sequence, from beneath (a molten) southern Tibet, with the mountain front maintaining its position
120
with respect to southern Tibet. This is one proposed explanation of the STDS, the MCT, and the
inverted metamorphic sequence found in the Greater Himalaya.
The third model involves the progressive erosion of southern Tibet, and is the simplified thermal-
and-kinematic model we present in this paper (Fig. 18d). With a fixed India-to-Asia convergence
rate, the relative partitioning of velocity controls the rate of erosion in the Himalaya. With no
normal shear on the STDS, and no internal deformation, the DSS will move towards the ISZ,
resulting in the relative retreat of the southern margin of the Tibetan Plateau.
These three models illustrate end-member scenarios for how the southern margin of the Tibetan
Plateau evolves through time, and although we do not believe that any of them is strictly correct, it
is illuminating to examine the geology within this framework. We can argue that, whereas it is clear
from Himalayan faults and exhumation patterns that periodic mass addition must be occurring (Fig.
18b), this is not the dominant process operating today. At some time in the evolution of the
Himalaya, significant mass-addition is necessary to achieve significant topography by the early
Miocene [France-Lanord et al., 1993; Najman et al., 1997] and Eohimalayan metamorphism [see
Hodges, 2000 for review]. At present, however, the Himalaya are narrow (the distance from the
topographic divide to the deformation front is only ~100 km), with a poorly developed foreland
fold-and-thrust belt considering that collision has been occurring since ~55 Ma. This style of narrow
deformation, deeply-exhumed crust, and an overfilled foreland basin may be typical of windward
orogenic fronts [Hoffman and Grotzinger, 1993], and perhaps indicates that exhumation is localized
to the very edge of the Tibetan Plateau. In addition, if the plateau is widening significantly, the
presence of the TSS capping the high peaks is also problematic; it is difficult to widen the plateau
while maintaining a sedimentary cover across south Tibet and onto the topographic axis.
The presence of the STDS indicates that normal shear had an active role in the evolution of the
Himalaya (Fig. 18c), with evidence that the MCT and STDS moved simultaneously during the
Miocene [Hodges et al., 1992], but there is currently little evidence of significant modern activity
on the STDS. Because normal faulting is a necessary prerequisite of a mass-balance type model,
either it seems unlikely that this mechanism occurs today, or the present role of the STDS has been
significantly underestimated.
If the STDS is inactive, and there is no internal deformation, then mass must be removed from the
edge of southern Tibet (Fig. 18d), resembling the model developed to predict the distribution of
121
cooling ages. The range front is eroded plateau-wards, with the Greater Himalayan sequence and
Tibetan sediments uplifting passively as the effects of the underlying and northwards-moving MHT
ramp are felt. This model supports the idea that retreat of the Tibetan Plateau has resulted in the
Kathmandu Syncline klippe [Masek et al., 1994] and explains the current association of Tibetan
sedimentary rocks and Greater Himalaya sequence, although it cannot explain the original
juxtaposition of rocks with such contrasting metamorphic grades.
Our model suggests that, in order to match the cooling-age data, ~25% of the current total
convergence across the DSS has to be partitioned into the overthrusting slab since closure (at least 5
to 7 My for the younger ages). This seems to negate a large-scale net mass addition to the system
with deformation moving progressively towards the foreland, as would occur with a traditional fold-
and-thrust belt model. Our model supports evidence for recent movement on the MCT [Harrison et
al., 1997; MacFarlane et al., 1992], rather than Holocene movement on the MFT [Lave and
Avouac, 2000] as being representative of the geodynamics from 0 to 5 Ma. Neither the paleo-MCT
model nor the MHT model required significant normal shear to explain the range in ages observed
in the data. However, if extrusion of the high-grade metamorphic core was occurring due to normal
shear located strictly between the Greater Himalayan sequence and the TSS, this would not be
distinguishable in our model.
Given the complex geological history, the record of detrital cooling ages from the foreland basin
could provide insight into how the Himalayan evolves. If a model of quasi-mass balance were
correct (Fig. 18c), then the detrital cooling age record in the foreland might be expected to show age
populations representing high erosion rates through time. Fluctuations in the older-age populations
might be expected if normal faulting cut through the Greater Himalayan sequence. With a model for
the erosional rollback of the plateau margin, we would predict a fairly uniform signal though time
with relatively constant older age populations controlled simply by the geometry of the detachment.
If an accretion model were representative (Fig. 18b), the age signal would vary with each thrust
sheet added; distinct populations of ages might be expected, perhaps with un-reset ages more
dominant (reflecting the original age of the rock rather than a cooling age). Thus, if we can explain
the modern detrital cooling signal with a specific deformation geometry, the record of ages in the
foreland could provide valuable insights into the growth of the Himalaya.
122
If the single decollement model is representative of the current kinematics, then Himalayan
topography is a consequence of interaction with the underlying Indian Plate. Thus the rate of
erosion on the topographic front might control the rollback of the Indian Plate inflexion point
towards southern Tibet, and potentially the rate of Indian underthrusting with respect to the DSS. As
a consequence, the erosion rate becomes a key parameter in constraining the kinematics of the
Himalaya. Moreover, changes in kinematics on the southern boundary of the collision zone could
affect the far-field deformation within Central Asia [e.g. England and Houseman, 1988]. As local
bedrock incision rates up to 10 mm/yr have been documented along the Indus River [Burbank et al.,
1996], erosion could potentially accommodate up to one half of the convergence between India and
South Tibet. Our model indicates that one-quarter of the convergence can currently be attributed to
erosion of material off the orogenic front. Therefore it seems likely that changes in the time-
averaged erosion rate, perhaps due to long-term climate change or the initiation of the Indian
Monsoon, could significantly affect the evolution of the Himalaya and consequently the
development of the Tibetan Plateau and far-field deformation.
7.0 Conclusions
Previous kinematics-and-thermal geochronological models [e.g. Harrison et al., 1998] have not
considered either the effects of actual topography upon the distribution of cooling ages, or the
resulting detrital cooling-age signal. In this paper we have introduced a new method of combining
digital elevation models with numerical kinematic-and-thermal modeling to predict cooling-age
distributions. For a given kinematic-and-thermal structure, the spatial variation of bedrock cooling
ages can be predicted. Once corrected for the relative erosion rate, which may be modeled as a
function of the underlying ramp angle in steady-state landscapes, the cooling-age signal can be
determined for any catchment area. Because detrital mineral samples are easily collected, rapidly
dated, and represent an integration of information from a large spatial area, this provides a good
method of testing increasingly complex numerical simulations.
We have applied this new methodology to modeling the detrital cooling-age signal of the Marsyandi
valley in Central Nepal. The results illustrate that the distribution of bedrock cooling ages is
123
sensitive to the relative partitioning of the total convergence rate between southern Tibet and India.
With a single decollement and the surface outcrop of the MBT representing the modern MHT, the
detrital cooling age data of [Brewer et al., Chapter 2] are most closely matched using a convergence
rate of India 15 km/My, and Asia 5 km/My, with respect to the DSS. There is a trade-off between
ramp angle and convergence rate, but within reasonable geometrical limits, and assuming the
thermal structure is appropriate, the convergence rate can be constrained to ± 1 mm/yr.
Modification of the detrital cooling-age signal by drainage-basin shape and distribution of
thermochronometer is a secondary effect within the Marsyandi drainage basin.
In an attempt to evaluate the relative importance of the Main Central Thrust, two models were
developed: in one, the fundamental Main Himalayan Thrust transfers all motion to the Main
Boundary Thrust; in the second, the motion is transferred to the MCT. Whereas both models fit the
data adequately, given the uncertainties in the observed data SPDF, the active MCT models
produced a better fit. The predicted PDF displays a broader distribution of younger ages that are
more representative of the observed data. Hence our model supports theories suggesting that the
MCT has active recently [Harrison et al., 1997; MacFarlane et al., 1992].
If the simplified two-plate, single-decollement model is considered to be a reasonably good
approximation of Himalayan kinematics, then it has important implications for the development of
the Himalayan orogen. If the STDS is inactive, then erosion rates are controlling the relative
migration of the Himalayan topographic front with respect to southern Tibet. Therefore, the
Himalayan erosion rate is controlling the southern boundary condition of the Tibetan Plateau, and
changes in that boundary condition could affect the deformation field of Central Asia. A change in
climate that resulted in more efficient erosion on the southern boundary would imply that a larger
fraction of the total convergence could be accommodated, thus potentially affecting intra-
continental orogensis many thousands of kilometers away.
This study provides insights into how the detrital cooling-age signal reflects the deformation pattern
within a collisional orogen. Detrital-mineral thermochronology can provide an efficient way to test
ideas of orogenic development, and the methodology introduced in this paper can be combined with
many other numerical models to predict the distribution of detrital cooling-ages. With better
temporal controls on the timing and activity of faults, future kinematic-and-thermal models would
be greatly improved. The effects of topographic deflection of the closure isotherm, particularly
124
important for lower temperature thermochronometers such as apatite fission-track and (U-Th)/He,
could be investigated with fully 3-D thermal models. In addition, if used in combination with
landscape evolution models, the assumption of topography in steady state could be addressed. The
greatest advantage to detrital, as opposed to bedrock, thermochronology is that the stratigraphic
record provides a window into the past. Therefore, models of orogenic evolution, calibrated by the
modern detrital cooling-age signal, can now be assessed against detailed, quantitative field data
from the foreland.
N
Marsyandi drainagebasin
South Tibet
Gangetic foredeep
Himalayas
Tibetan plateau
India
45 mm/yr
Topographic axis
65 km
Stu
dy a
rea
TOPOGRPAHIC SWATH
X
Y
Figure 1. Location of the Marsyandi drainage basin and the study area, aligned with the strike of the orogen. The white dot indicates the location of the geochronological sample at the mouth of the Marsyandi catchment (S-24: [Brewer et al., Chapter 2]). The topographic image is derived from a 90-m DEM, and the approximate location of the topographic axis is shown for reference. The hatched area shows a representation of the swath used for the topographic analysis (discussed in text). This swath is scrolled normal to the strike (in the direction illustrated by the arrows) and topographic characteristics calculated over the strike-parallel window.
125
350oC
0
2
4
6
8
N
S
ab
d
DSS
Ages not reset
MHTage
p
Age (My)
Indian Plate
closure
isotherm
~40 km
Eurasian
Plate
c
Figure 2. Conceptual basis for the combined thermal, kinematic, and detrital model. With a simplified ramp-flat geometry and known convergence rate, the velocity (speed and trajectory angle) of particles through the orogen can be calculated. Within the predetermined kinematic framework, the thermal structure after 20 My is calculated, and the depth of the closure temperature for muscovite (350oC) extracted. Extrapolating the 2D thermal structure into 3D, we use a 90-m DEM to calculate how long it takes each point in the landscape to pass through the closure temperature and reach the surface along the specified particle path (distance of the black arrows divided by the convergence rate of the southern Tibet with respect to the DSS). The youngest ages are created by trajectory (b) because the 350oC isotherm is closest to the surface along this trajectory. Trajectory (a) produces the oldest cooling-ages because it travels along a flat (under the Lesser Himalaya) before reaching the surface. Particles moving along (c), travel the further than (b), and give intermediate ages, whereas trajectory (d) advects rock into the orogen above the closure temperature, and so can be assigned an original-rock age. The insert depicts a hypothetical distribution of detrital ages from the outlined catchment.
126
10
20
30
0
2
4
6
8
400 12080 160 200 240
40
50-40
distance from MBT (km)
elev
atio
n a.
s.l.
(km
)
MBT
mean topography(min and max envelope)
NS
(a) (b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)
Indian UC
Indian LC
TS
GH
DSS
(iii)(iv)
10
20
30
mea
n sl
ope
(o)
(i)
(ii)
dept
h b.
s.l.
(km
)
MFT
A = 2.5 m Wm-3
A = 0.4 m Wm-3
A = 2.5 mWm-3
A = 0.4 mWm-3
K = 2.5 Wm-1K-1
K = 2.5 Wm-1K-1
Foreland Lesser Himalayas Higher Himalayas Tibetan Plateau
MantleA = 0 Wm-3 K = 3.0 Wm-1K-1
K = 2.5 Wm-1K-1
Figure 3. Constraints used for the kinematic-and-thermal model. The top panel illustrates the mean slope calculated over a scrolling swath oriented normal to the transect and is divided into four domains. The lower panel shows the thermal conductivity (K) and radioactive heat production (A) assigned to the Tibetan zone sediments (TSS), Greater Himalayan sequence (GH), and the Indian upper crust (UC) and lower crust (LC). The Main Himalayan Thrust (MHT) ramp geometry that we initially use is illustrated, outcropping at the location of the Main Boundary Thrust (MBT). The approximate location of the Main Frontal Thrust (MFT) is indicated. Note the change in scale above sea level to illustrate the minimum, maximum and average elevations. Ramp constraints (section 3.1) and the decollement/surface singularity (DSS) - which is used as a reference marker - are discussed in the text.
127
Seismicity
MHT
2000
4000
6000
8000
0100 140
elev
atio
n (m
) max.
mean
min.
topographic envelope
5.6 My
6.2 My
4.9 My
20 12040 60 80 100 180160140 200
0
10
20
30
40
dept
h (k
m) 50oC 150oC
250oC
350oC
450oC
Asia
India
a) Thermal model
b) Particle trajectories and cooling ages
c) Topographic influence
(b)
0
10
20
12060 80 100 140
dept
h (k
m)
350oCIndia
Asia
(c)
24 km28 km59 km
Age calculation:(i) 59 km = 11.8 My 5 km/My(ii) 28 km = 5.6 My 5 km/My(iii) 24 km = 4.8 My 5 km/My
(i) (ii) (iii)
5 km/My
15 km/My
120distance (km)
TRAJECTORY
(ii)(iii)
Figure 4. The three components needed to construct cooling ages for the landscape. (a) The depth of the 350oC isotherm is modeled for the specified convergence rate and ramp geometry. In this case the total convergence rate was partitioned into 15 mm/yr of Indian underthrusting and 5 mm/yr of Asian erosion. (b) An enlarged portion of the top panel illustrating how the cooling ages are calculated. The distance a particle travels between passing through the closure temperature and reaching the surface (indicated by the black arrows), is divided by the convergence rate partitioned to southern Tibet with respect to the DSS. (c) Particles following the same flow line in 2D travel different distances along strike, because a 3-D landscape has a range of topography. Hence, when the real topography is used, each incremental change in the transect location along strike will result in a different pattern of predicted bedrock cooling ages. The ages of maximum, minimum, and mean topography are shown for illustration.
128
Thrust sheet
(iii) Advection of topography // to particle direction, hence
minimum erosion.
(i) Advection of topography I to particle direction, hence
maximum erosion.
(iii)
(i)
displacement in time (dt).Volume erodedin dt.
=
=
Kin
k ba
nd
present topography
Particle trajectory
V
V
Vz
(ii)
(ii) Vertical component of erosion
Figure 5. Volume of material eroded in a time increment (dt) depends upon the aspect of the topography in relation to the particle velocity (V). The black topography is the present topographic profile. The gray line mirroring the present topography illustrates the volume of rock eroded in dt with an assumption of complete steady-state conditions. When the particle velocity is normal to the topography, maximum volumes of material are eroded (i). When the particle velocity is parallel to the topography, the topography becomes advected laterally and little erosion occurs (iii). Note that the volume of eroded material is underestimated if solely the vertical component (Vz) of the particle velocity is used in the calculation (ii).
129
X
Y+a
+S
v.dt
Particle velocity
Average slope Volume of rock
eroded in dt
DEM
v
Figure 6. Calculation of volume of rock eroded in time increment (dt) for one digital-elevation model (DEM) grid cell, assuming a steady-state landscape. The volume of rock eroded for a given particle speed (v) and time (dt) is dependent upon the topographic slope (S) and particle direction, which is controlled by the angle of the underlying thrust ramp (a). The values beta and alpha are dependent upon the relationship between the topographic surface slope, as described in the text. Both angles are measured positively as illustrated above, and the average topographic slope is assumed to be parallel to the Y direction.
130
10 20 30 40 50 60 70 80 90Particle trajectory angle (ofrom horizontal )
0.2
0.4 0.60.6
0.8
0.8
0.8
1
1
1
1
11
11
1.2
1.21.2
1.21.41.4
1.4
1.6
1.6
1.61.8 1.8
5
10
15
20
25
30
35
40
45
50
55
60
topo
grap
hic
slop
e (o
)
00
Figure 7. Relationship between the topographic slope and particle trajectory angle in determining the volume of material eroded from a DEM cell. The X and Y cell dimensions, dt, and particle speed are set to unity. A key to interpreting this figure is to recall that the surface area of the landscape represented by the 1x1 DEM cell varies as a function of slope. Note that when the particle trajectory is vertical, one unit volume is eroded from the landscape, independently of the topography. As the topographic slope approaches the plane of the particle trajectory, the volume of material eroded approaches zero because material is advected parallel to the slope.
131
Mea
n el
evat
ion
(m)
distance (km)
-1000
0
1000
2000
3000
4000
5000
6000
0 40 80 120 160 200 240 280
= mean elevation
= best fit line segment
Lesser Himalayas
Tibetan Plateau
Topographic front
Indi
an P
late
Figure 8. The three linear segments (black dashed lines) used as a proxy for the regional slope, taken from a transect normal to the strike of the orogen. The mean elevation, averaged over the ~120 km by 0.6 km swath, is shown by the thick gray line.
132
AsiaIndia
AsiaIndia
AsiaIndia
a) India fixed
b) Asia fixed
c) Equal partitioning
20 mm/yr
20 mm/yr
10 mm/yr
10 mm/yr
DSS
Figure 9. Three scenarios for partitioning convergence rate between India and south Tibet. (a) India fixed, movement of Asia at 20 mm/yr with respect to the DSS. (b) Asia fixed, convergence accommodated by Indian under thrusting. (c) Equal division between the two plates: the Indian plate moves at 10 mm/yr northwards, and the Eurasian plate moves at 10 mm/yr southwards with respect to the decollement/surface singularity (DSS).
133
0 5 15 20 25 301024
68
10
12
140
0.01
0.02
0.03
0.04
0.05
age (My)
prob
abili
ty
Asia convergence rate
(km/My)
shear=36 vertical
modeled PDF
data
22 My
8 My
2 My
1 My
4 My
1.5 My
0 5 10 15 20 25 30age (My)
prob
abili
ty
Observed data
n=55
Figure 10. Effects of partitioning the relative convergence rate between India and Asia, can be observed in the modeled detrital cooling-age signals. The age signals are represented by probability density functions (PDF) and represent the reset-age signal from the width of the study area (Fig. 1). The convergence rate varies between 2 and 14 km/My for Asia, keeping the total convergence rate (20 mm/yr) and all else constant. The gray band (labeled 'data') represents an approximate range of ages for the highest concentration of probability for the observed data PDF (shown in inset: sample S-24 in the analyses of Brewer [in review-b]). The data is a sample collected from 200-m upstream of the confluence of the Marsyandi and Trisuli rivers (Fig. 1).
134
5 10 15 20 25
Pro
ba
bil
ity
0
0.01
0.02
i) Asia 6, India 14 km/Myii) Asia 5, India 15 km/Myiii) Asia 4, India 16 km/My
i) i i ) i i i )
data
0 5 10 15 20 25 30age (My)
Pro
ba
bil
ity
0
0.01
0.02
0.03
i)
i i )i i i ) data
synthet ic PDF (Brewer et a l , [ in review])
a)
b)
entire swath
Marsyandi basin
3 My
5 My
8 My
3 My
5 My
8 My
Figure 11. (a) The modeled cooling age signal from the entire mountain front compared against the data from the mouth of the Marsyandi (solid black line). Asian overthrusting rate of 4 to 6 km/yr mimic the general pattern of observed detrital data. The PDF generated with Asia = 5 km/My, India = 15 km/My (ii) displays the best fit to the 20 Ma age population observed in the data PDF. (b) The same model scenarios, but corrected for the age-signal generated specifically from the Marsyandi basin. Note that the peak probabilities are enhanced, while the older 'tails' have diminished importance. The dashed line is the predicted PDF at the mouth of the Marsyandi based upon an integration of individual tributary models and assuming vertical erosion [Brewer et al., Chapter 2 ].
135
20 12040 60 80 100 180160140 200
0
10
20
30
40
dept
h (k
m) 50oC
150oC
250oC
350oC
450oC
Asia
India
20 12040 60 80 100 180160140 200
0
10
20
30
40
dept
h (k
m) 50oC
150oC
250oC
350oC
450oC
Asia
India
distance (km)
4 mm/yr
16 mm/yr
8 mm/yr
12 mm/yr
a)
b)
Figure 12. The steady-state thermal structure with 20 mm/yr of total convergence with (a) 4 mm/yr of total convergence partitioned into Asia, and (b) 8 mm/yr of convergence partitioned into Asia. Note the relative response of the 350oC isotherm.
136
age (My)
prob
abili
ty
12060 80 100 180160140 200
0
10
20
30
40
dept
h (k
m) Asia
India +/- 5 km depth
MCTLesser Himalaya
distance (km)
15 mm/yr
5 mm/yr
(i)
(ii)
(iii)
a)
b)
data
0 5 10 15 20 25 300
0.005
0.01
0.015
0.02
0.025
Asia India Decollementdepth
(i)(ii)(iii)(iv)(v)
5 mm/yr
5 mm/yr
4 mm/yr
6 mm/yr5 mm/yr
15 mm/yr
15 mm/yr
15 mm/yr
16 mm/yr
14 mm/yr
35km35km
25km25km
30km
(ii) 5 My
(iv) 6 My
(i) 3 My
(iii) 5 My
(v) 8 My
STDS
Figure 13. (a) The distribution of cooling ages derived from different ramp geometries. PDFs (i) and (ii) were run using a steeper 23o ramp (illustrated by panel b, ramp geometry (ii)) with 5 mm/yr and 4 mm/yr assigned to convergence of southern Tibet with respect to the DSS, respectively. PDF (iii), outlined by the dashed line, indicates the original ramp geometry for comparison. PDFs (iv) and (v) use a shallower geometry (illustrated by panel b, ramp geometry (i)) with 6 mm/yr and 5 mm/yr assigned to convergence of southern Tibet with respect to the DSS, respectively. The data curve in panel a is from Brewer et al., Chapter 2 ]. Ramp geometry (iii) illustrated in panel b is used for generating the PDF shown in figure 16.
137
0 5 10 15 20 25 300
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
age (My)
prob
abili
ty
(ii) no lithological correction
(i) PDF withlithological correction HIGH
LOW
Lithological contribution
India 5 mm/yr, Asia, 15 mm/yr
Figure 14. A comparison of the distribution of detrital cooling ages using (i) a lithological correction and (ii) no lithological-correction factor. The insert illustrates the spatial variation in the lithological correction factor over the Marsyandi basin, taken from the point-counting results of Brewer et al. [Chapter 2 ].
138
0
10
20
30
0 50 100 150 200 250 3000
5000
10000
MCT
a) topography
b) ages
c) relative erosion rate
max
minmean
max
min
mean
UNRESET
vertical componentof plate velocitymodeled erosion
rate
Figure 15. Transects illustrating (a) the topography, (b) predicted cooling ages from our model, and (c) a comparison between vertical erosion rates predicted from ramp geometry and our modeled rates (which are a function of the trajectory of rock particles in relation to the averaged topography). The convergence was partitioned into 5 mm/yr of Asianoverthrusting and 10 mm/yr of Indian underthrusting with respect to the DSS. The approximate modern location of the modern MCT is shown in the top panel. The vertical gray bar is a zone of predicted equal erosion (c).
139
distance (km)
elev
atio
n (m
)ag
e (M
y)re
lativ
e ra
te
S N
0 40 80 120 160 200 240 2800
5000
10000
15000
distance (km)
appa
rent
rel
ief (
m)
20o40o90o01000200030004000500060007000
elev
atio
n (2
-sig
ma)
(m
)
20
40
90
angle of particle trajectory
apparent relief
10 20 30 40 50 60 70 80 9002468
101214
mea
n re
lief (
m)
particle trajectory (o)
HHWTLH
Figure 16. Variation of "apparent" relief as a function of particle trajectory. Apparent relief (ii) was taken from the 2-s envelope of elevation (i). The actual relief (shown by the shaded gray curve is generated using a particle trajectory angle of 90 degrees. The thin black lines illustrate the apparent relief for the particle trajectories indicated by the arrows. (iii) The average apparent relief as a function of ramp angle for the whole transect (WT), the Lesser Himalaya (LH), and Higher Himalaya (HH).
140
0 5 10 15 20 25 300
0.005
0.015
0.02
age (my)
prob
abili
ty
(ii) MCT ACTIVE
(i) MBT ACTIVE
0.01
DATA
Figure 17. A comparison of the distribution of detrital ages from an orogenic swath in the study area with: (i) the MHT represented by the MBT being the active fault, and; (ii) the MHT represented by activity on solely the MCT (with geometry illustrated in Fig. 13b, (iii)). The data from Brewer et al. [Chapter 2 ] is shown for comparison by the black line. Note that with the MCT active, there is a more dominant 6 t 10 My signal.
141
NSHimalayas
Tibetan Plateau
TS
GHIndian Plate
ISZ
PMZ
a) T0 - Initial condition
b) T1 - Mass addition to the system
c) T1 - Mass balance
d) T1 - Mass removal from the system
MFT
STDS
MHT
V/2
V/2V/2
V/2
V
Vadd
DS
SD
SS
142
Figure 18. A cartoon showing three end-member models for Himalayan evolution. From a starting condition (a) the displacement markers (indicated by black dots) indicate the displacement at T1 after displacement at V mm/yr with models for: (b) mass addition to the system; (c) mass balance; (d) mass removal from the system. The reference point is considered to be the decollement/surface singularity (DSS), which is the intersection between the Main Himalayan Thrust (MHT) and the surface. The Main Frontal Thrust (MFT) is currently the most active fault to the south. The South Tibetan Detachment System (STDS) is found to the north of the topographic axis and separates the Greater Himalayan sequence (GH) from the Tibetan zone sediments (TS) and a partial melt zone (PMZ) has been imaged by INDEPTH. The initial position of the Indus Suture Zone (ISZ) is indicated, with vertical arrows in the north illustrating the position of the ISZ at T1.
143
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154
Appendix 1
1.0 Thermochronology
The following is intended as a brief overview of thermochronology for readers not familiar with the
basic techniques of 40Ar/39Ar dating. For further explanation, detailed experimental procedures may
be found in McDougall and Harrison [1988]. Renne [2000] provides a useful review, with emphasis
on Quaternary applications.
1.1 The decay equation
Isotopes of some elements are unstable such that they spontaneously disintegrate, undergoing
radioactive decay to form new elements. The statistically averaged rate of disintegration is constant
for a particular isotope, and will not vary with temperature or pressure. If the rate of disintegration
is known, one can use the ratio between the number of parent atoms (the original element present)
and the number of daughter atoms (produced by the decay of the parent atoms) to calculate the time
elapsed since decay initiated, and there were no daughter atoms present.
155
The rate of decay of parent atoms into daughter atoms (dN/dt) is dependent upon the number of
radioactive atoms present (N) and the decay constant (λ), or half-life, which represents the rate of
disintegration.
λNdtdN
−=
(1)
This can be rearranged to give:
∫∫ =− dtN
dN λ
(2)
Once integrated:
CtN +−=− .ln λ
(3)
The constant of integration (C) can be evaluated from the condition that N = N0, when
t = 0:
0ln NC −=
(4)
Substituting equation 4 in equation 3, we obtain:
0ln.ln NtN −=− λ
(5)
156
N is the number of parent atoms that remain at time (t) after the disintegration of the original
number of parent atoms (N0) began. N0 is typically calculated by measuring N and the number of
daughter (ND) atoms present.
DNNN +=0
(6)
Thus we can combine equation 5 and 6 and solve for t:
λ−+−
=)ln(ln DNNNt
(7)
1.2 The potassium/argon decay scheme
K4019 decays into both Ca40
20 by β- decay and into 40Ar by electron capture (with release of a neutrino
and γ radiation). The latter scheme represents only 11.16% of the K4019 decay, but is of most interest
to thermochronologists:
γν ++→+ − AreK 4018
4019
(8)
With 40K/40Ar dating, the parent isotope (potassium) and daughter isotope (argon) have to be
determined independently. Potassium may be measured using wet chemistry procedures (amongst
other techniques), whereas 40Ar is measured on a mass spectrometer.
157
1.3 The 40Ar/39Ar analytical method
The 40Ar/39Ar technique was formalized by Merrihue and Turner, (1966). It is based on the same 40K/40Ar decay scheme, but follows different analytical procedure. The 40Ar/39Ar dating method is
more accurate than conventional 40K/40Ar dating because both isotopes can be measured at once,
and only the ratios rather than the exact amounts of isotopes are measured [see Faure, 1986]. It is
based upon the fact that K can be calculated from the amount of 39Ar produced during neutron
activation induced by irradiation.
1) Samples are irradiated to transform a portion of 39K to 39Ar (denoted as 39ArK):
pArnK k +→+ 3918
3919
(9)
where the amount of 39ArK produced is proportional to the amount of 39K in the sample.
2) As the ratio 39K/40K is known to be constant in nature, the amount of 40K in the sample can be
calculated. Thus, this in theory determines N, and ND (40Ar*; the * indicating a radiogenic source)
can be measured directly on the mass spectrometer. In reality, only the ratio of 40Ar to 39Ar is
needed to calculate the age:
+= 1.*ln.1
39
40
JArArt
kλ
(10)
As the exact amount of 39ArK produced during irradiation depends upon the duration of exposure
and neutron flux, a fluence correction factor (J) is calculated from dating monitors of known age.
These are typically placed at several locations within the irradiation package.
158
1.4 Closure temperatures
Equation 7 is used to calculate a date: the time (t) elapsed since parent isotopes started to decay into
daughter isotopes, since N = N0. At this stage, however, it is useful to consider what our “date”
actually represents. With the 40K/40Ar decay system, our date records the time at which the daughter
isotope (Ar) starts to accumulate within the crystal, and this is a function of temperature. At high
temperatures the argon can escape rapidly out of the crystal by diffusion because of high lattice and
component (Ar) energy. Only when the crystal cools below a certain temperature, the “closure
temperature”, does the argon become trapped and the radioactive “clock” starts to record the
elapsed time. In reality, diffusion processes do not stop (approach zero) abruptly at a specific
temperature, but cease over a range of temperature: the closure zone. The closure temperature
represents the theoretical temperature that yields the same age as if closure occurred at a discrete
temperature [Dodson, 1973]. We take the closure temperature of muscovite to be ~350 ± 25oC, but
this will vary with grain size and the rate of cooling. The “cooling age” is the time elapsed since the
sample cooled through the closure temperature and reach the surface of the Earth.
Thermochrononology is primarily used to measure either the age of formation of a rock (typically
using geochronometers with closure temperatures close to the crystallization temperature of the
rock), or constrain the rate of cooling (typically using geochronometers with lower closure
temperatures to examine the erosion history the sample). To illustrate the effects of closure
temperatures on cooling ages, we can consider the history of a sedimentary rock that undergoes
regional metamorphism in a continent collision zone (Fig. 1). The rock is deposited at the surface of
the earth before being buried as crustal thickening proceeds during the collision (Fig. 1 i). As a
result of crustal thickening, the rock may undergo anatexis at high temperatures (Fig. 1 ii), resulting
in the formation S-type granites such as the High Himalayan leuco-granites observed in the
Himalaya. We can consider two decay schemes in two different minerals: U-Pb in monazite, and
K-Ar in muscovite. The U-Pb system typically has higher closure temperatures because lead is
relatively immobile. Thus the time at which the rock passes through the U-Pb closure isotherm in
monazite (Fig. 1, iii) records the early crystallization phase as the granite begins to cool (providing
it is reset by burial). As the orogen undergoes erosion, rocks approach the surface and experience
progressive cooling. When the rock cools through the K-Ar closure isotherm for muscovite (Fig. 1,
159
iv), the rock has already undergone significant exhumation and is at ~350°C. It continues to cool
and is sampled at the surface today (Fig. 1, v).
As we know the age of a sample (tc-tp) and can calculate the depth of the closure isotherm (zx-zc)
using an assumed geothermal gradient, we can use the cooling age as a proxy for the erosion rate
(dz/dt). From the arrows over the time axis of figure 1, we can see that the cooling age recorded by
U-Pb decay in monazite and K-Ar decay in muscovite integrate the cooling rate over very different
time periods. Thus, for the applications in this paper, trying to constrain the short-to-medium term
erosion history of an orogen, we use the lower-temperature geochronometer: the K-Ar series in
muscovite.
300
400
200
100
0
500
600
700
800
time b.p., t K-Ar msc age
Temperature (oC)
appr
oxim
ate
dept
h, z
(K
m)
10
20
FT apatite
FT zirconK-Ar biotite
K-Ar muscovite
K-Ar hornblende
U-Pb monazite
Helium
Geochronometerr
Bur
ial
Exhum
ation
ZONE OF ANATEXIS
U-Pb mzt age
rock trajectory
(i)
(ii)(iii)
(iv)
(v)
Figure 1. Diagram illustrating the T-t path of a rock particle undergoing burial metamorphism and subsequent exhumation. With a geothermal gradient of 35oC the closure temperature of muscovite (msc), ~350oC, occurs at 10 km (zc). Thus, if we have a cooling age (tc) of 10 Ma, for example, an erosion rate can be calculated: 10 km in 10 My = 1.0 km/My. U-Pb in monazite (mzt) has a higher closure temperature, and therefore records a longer cooling histroy than K-Ar in muscovite. Other geochronomters are shown on the left axis at the approximate temperature corresponding to their closure. Fission-track (FT) geochronometers are illustrated for reference, but are not isotope based.
160
Zx
Zc
tp tc 0
161
Appendix 2
1.0 40Ar/39Ar results and protocols
Muscovite mineral separates were irradiation at the McMaster University research reactor. The
irradiation package included aliquots of the neutron-fluence monitor Fish Canyon sanidine (28.02
Ma, Renne et al. [1998]), as well as a variety of salts that served as monitors for interfering nuclear
reactions. The muscovites and monitors were analyzed at the 40Ar/39Ar laser microprobe facility at
MIT [Hodges and Bowring, 1995]. Gas was extracted from individual mica crystals by fusion in the
defocused beam of an Argon laser. This operated at 18 W for a period of approximately 10 seconds.
The extracted gas was analyzed on an MAP 215-50 mass spectrometer, using a Johnston electron
multiplier, after purification to remove reactive species. At the beginning of each analytical session
and after every tenth analysis of an unknown, the total system blanks were measured. Apparent ages
(dates) calculated for each muscovite are reported in Table 1 with an estimated 2-σ uncertainty
obtained by propagating all analytical uncertainties. In order to illustrate the proportion of this
uncertainty that is attributable to uncertainties in the neutron flux during sample irradiation, age
uncertainties are shown with and without propagated error in the irradiation parameter J (Table 1,
iii). The Number of moles of K-derived 39Ar (39ArK) released during fusion (Table 1, i) and the
percentage of radiogenic 40Ar (40Ar*) in the total 40Ar for each analysis (Table 1, ii) are also
reported.
For all geological analysis, a lower cutoff of 40% 40Ar* was used to eliminate spurious data (Fig.
1). Grains yielding less than 40% 40Ar* have little radiogenic argon, in comparison to 40Ar
contained within the mass spectrometer blank, due to: a) incomplete ablation; b) impure muscovite,
or; c) very young ages. Many of the grains rejected were from the first run of sample S-24 that
162
experienced some analysis problems. The very young ages observed in the sample are not found in
any of the catchment signals and so were deemed geologically unreasonable. The data have a strong
linear dependence of percentage 40Ar with age below the cutoff (Fig. 3), whilst they are more
scattered above the cutoff. The age of different samples should not be directly proportional to the
amount of 40Ar* because grains of the same age will have 40Ar concentrations in proportion to the
amount of 40K that the mineral initially contained. Based on this interpretation, it might be argued
that this cutoff could occur anywhere between 25% and 60% radiogenic 40Ar. We felt that a 40%
cutoff was the best solution as spurious ages were removed while not cutting too many younger
grains from the results.
0 5 10 15 20 25 300
10
20
30
40
50
60
70
80
90
100
Age (Ma)
%40
Ar
(rad
ioge
nic)
40% 40Ar cutoff
range in plausible %40Ar cutoffs
Figure 1. Age versus percentage of radiogenic 40Ar for the geochronological analyses presented in this paper. To eliminate spurious ages, a number of plausible possibilities (within the range of the dashed lines) were investigated to find a lower limit of radiogenic 40Ar. A 40% cutoff was judged the most appropriate, and analyses with less radiogenic 40Ar (within the shaded area) were rejected.
163
164
Sample grain 36Ar/40Ar 39Ar/40Ar 39Ark 40Ar* Age
(x10-4) (x10-1) (x10-14moles)(i) (%)(ii) (Myr)(iii) (with J) (w/o J)
NIB-S2 1 5.64 ± 0.65 6.28 ± 0.32 7.760 83.1 8.64 ± 0.56 0.56
NIB-S2 2 3.07 ± 0.48 5.86 ± 0.44 8.804 90.7 10.09 ± 0.84 0.84
NIB-S2 3 7.13 ± 1.20 7.60 ± 0.45 3.591 78.6 6.77 ± 0.58 0.58
NIB-S2 4 9.00 ± 2.51 8.95 ± 0.17 2.765 73.1 5.34 ± 0.56 0.56
NIB-S2 5 4.21 ± 0.54 6.36 ± 0.36 5.095 87.3 8.96 ± 0.60 0.60
NIB-S2 6 3.57 ± 0.46 5.47 ± 0.33 6.388 89.2 10.64 ± 0.73 0.73
NIB-S2 7 8.47 ± 1.75 6.89 ± 0.12 2.536 74.7 7.08 ± 0.51 0.51
NIB-S2 8 10.04 ± 3.34 6.84 ± 0.32 1.293 70.1 6.70 ± 1.03 1.03
NIB-S2 9 5.58 ± 1.53 6.11 ± 0.21 1.895 83.3 8.89 ± 0.60 0.60
NIB-S2 10 11.57 ± 5.34 10.17 ± 0.76 3.077 65.5 4.22 ± 1.11 1.11
NIB-S2 11 11.74 ± 4.91 6.60 ± 0.41 1.959 65.1 6.44 ± 1.54 1.54
NIB-S2 12 10.12 ± 3.74 7.26 ± 0.25 3.131 69.8 6.29 ± 1.03 1.03
NIB-S2 13 21.04 ± 8.69 9.97 ± 0.66 1.313 37.6 2.47 ± 1.71 1.71
NIB-S2 14 8.00 ± 7.10 6.48 ± 0.13 1.519 76.1 7.66 ± 2.11 2.11
NIB-S2 15 8.36 ± 3.92 7.14 ± 0.16 2.447 75.0 6.87 ± 1.07 1.07
NIB-S2 16 7.03 ± 3.65 5.38 ± 0.13 2.390 79.0 9.58 ± 1.34 1.33
NIB-S2 17 8.87 ± 3.41 7.19 ± 0.23 3.029 73.5 6.68 ± 0.95 0.95
NIB-S2 18 9.09 ± 7.34 7.42 ± 0.22 1.522 72.9 6.42 ± 1.92 1.92
NIB-S2 19 5.82 ± 4.39 6.99 ± 0.18 2.279 82.5 7.71 ± 1.23 1.23
NIB-S2 20 7.14 ± 4.94 7.78 ± 0.22 2.232 78.6 6.60 ± 1.24 1.24
NIB-S2 21 11.49 ± 14.81 6.41 ± 0.20 0.841 65.8 6.71 ± 4.44 4.44
NIB-S2 22 14.94 ± 6.18 8.49 ± 0.27 1.925 55.6 4.29 ± 1.42 1.42
NIB-S2 23 11.83 ± 7.61 7.62 ± 0.17 1.370 64.8 5.56 ± 1.93 1.93
NIB-S2 24 8.10 ± 4.83 11.58 ± 0.08 2.707 75.6 4.28 ± 0.80 0.80
NIB-S3 1 10.82 ± 10.02 8.82 ± 0.36 8.000 67.7 5.02 ± 2.20 2.20
NIB-S3 2 3.60 ± 3.62 3.45 ± 0.07 8.604 89.2 16.81 ± 2.04 2.04
NIB-S3 3 16.94 ± 21.41 7.81 ± 0.53 3.317 49.8 4.17 ± 5.30 5.30
NIB-S3 4 32.45 ± 57.47 8.67 ± 1.47 1.382 4.1 0.31 ± 12.78 12.78
NIB-S3 5 5.43 ± 8.39 4.58 ± 0.18 4.955 83.8 11.91 ± 3.55 3.55
NIB-S3 6 5.29 ± 9.53 4.09 ± 0.18 3.862 84.2 13.40 ± 4.50 4.50
NIB-S3 7 13.71 ± 14.14 7.89 ± 0.46 5.013 59.3 4.91 ± 3.47 3.47
NIB-S3 8 10.60 ± 18.80 4.67 ± 0.32 2.236 68.5 9.57 ± 7.77 7.77
165
NIB-S3 9 18.35 ± 26.63 8.24 ± 0.76 2.786 45.6 3.62 ± 6.25 6.25
NIB-S3 10 5.87 ± 6.54 4.64 ± 0.20 6.384 82.5 11.58 ± 2.77 2.76
NIB-S3 11 11.22 ± 17.54 3.60 ± 0.26 1.862 66.7 12.08 ± 9.41 9.41
NIB-S3 12 19.11 ± 31.17 10.50 ± 1.08 3.021 43.3 2.70 ± 5.74 5.74
NIB-S3 13 4.17 ± 8.21 3.50 ± 0.16 3.822 87.5 16.26 ± 4.56 4.56
NIB-S3 14 6.76 ± 7.31 4.28 ± 0.20 5.301 79.8 12.15 ± 3.34 3.34
NIB-S3 15 4.67 ± 8.23 3.32 ± 0.16 3.637 86.1 16.84 ± 4.82 4.82
NIB-S3 16 20.85 ± 48.49 10.72 ± 1.54 2.000 38.2 2.33 ± 8.73 8.73
NIB-S3 17 5.51 ± 4.52 10.22 ± 0.28 20.366 83.3 5.34 ± 0.87 0.87
NIB-S3 18 9.47 ± 17.26 11.41 ± 0.87 5.956 71.6 4.11 ± 2.94 2.94
NIB-S3 19 16.28 ± 24.93 9.52 ± 0.88 3.468 51.7 3.55 ± 5.07 5.07
NIB-S3 20 7.56 ± 11.69 4.85 ± 0.34 3.729 77.5 10.42 ± 4.71 4.71
NIB-S3 21 4.81 ± 1.95 8.62 ± 0.07 2.404 85.4 6.48 ± 0.44 0.44
NIB-S3 22 3.13 ± 0.22 4.01 ± 0.03 10.537 90.6 14.70 ± 0.18 0.16
NIB-S3 23 2.28 ± 0.29 3.50 ± 0.04 4.678 93.1 17.28 ± 0.29 0.27
NIB-S3 24 0.95 ± 0.15 3.89 ± 0.05 8.745 97.0 16.21 ± 0.26 0.24
NIB-S3 25 2.86 ± 0.09 4.68 ± 0.04 13.589 91.3 12.72 ± 0.13 0.11
NIB-S3 26 4.61 ± 0.48 9.10 ± 0.12 5.029 86.0 6.18 ± 0.14 0.14
NIB-S3 27 1.70 ± 0.23 3.28 ± 0.03 4.390 94.8 18.77 ± 0.25 0.23
NIB-S3 28 11.78 ± 1.15 9.80 ± 0.05 3.541 64.9 4.34 ± 0.23 0.23
NIB-S3 29 1.27 ± 0.19 3.20 ± 0.05 5.506 96.1 19.48 ± 0.33 0.31
NIB-S3 30 0.95 ± 0.14 3.40 ± 0.05 8.499 97.0 18.57 ± 0.29 0.27
NIB-S3 31 4.63 ± 0.64 12.08 ± 0.15 6.143 85.8 4.66 ± 0.12 0.12
NIB-S3 32 0.82 ± 0.19 3.59 ± 0.02 6.124 97.4 17.64 ± 0.19 0.16
NIB-S3 33 1.84 ± 0.11 3.28 ± 0.04 6.743 94.4 18.70 ± 0.27 0.25
NIB-S3 34 3.50 ± 0.77 13.56 ± 0.09 5.000 89.1 4.31 ± 0.12 0.11
NIB-S3 35 5.42 ± 0.44 11.62 ± 0.17 15.101 83.5 4.71 ± 0.11 0.11
NIB-S3 36 1.36 ± 0.17 3.61 ± 0.06 8.951 95.8 17.25 ± 0.31 0.30
NIB-S3 37 1.52 ± 0.32 3.57 ± 0.05 5.560 95.3 17.35 ± 0.32 0.30
NIB-S3 38 1.80 ± 0.19 3.38 ± 0.06 5.269 94.5 18.16 ± 0.36 0.34
NIB-S3 39 2.64 ± 0.53 5.39 ± 0.03 4.636 92.0 11.12 ± 0.21 0.20
NIB-S3 40 0.91 ± 0.25 3.24 ± 0.07 6.554 97.2 19.49 ± 0.48 0.47
NIB-S3 41 3.04 ± 0.20 3.53 ± 0.15 5.865 90.8 16.76 ± 0.78 0.77
NIB-S3 42 10.36 ± 1.47 6.52 ± 0.75 12.855 69.2 6.93 ± 1.18 1.18
NIB-S3 43 3.89 ± 0.69 3.68 ± 0.43 7.647 88.4 15.63 ± 2.08 2.08
166
NIB-S3 44 6.97 ± 1.20 3.32 ± 0.50 4.565 79.3 15.52 ± 2.93 2.93
NIB-S3 45 13.38 ± 3.24 10.49 ± 1.99 10.773 60.2 3.76 ± 1.23 1.23
NIB-S3 46 11.30 ± 2.29 6.91 ± 1.14 5.997 66.4 6.27 ± 1.60 1.60
NIB-S3 47 3.83 ± 0.33 3.15 ± 0.16 7.119 88.6 18.30 ± 1.09 1.08
NIB-S3 48 13.88 ± 2.32 9.18 ± 0.86 4.980 58.7 4.19 ± 0.78 0.78
NIB-S3 49 3.67 ± 0.41 3.39 ± 0.20 5.982 89.0 17.05 ± 1.12 1.11
NIB-S3 50 3.67 ± 0.45 3.58 ± 0.09 5.223 89.0 16.17 ± 0.53 0.53
NIB-S5 1 3.14 ± 0.87 9.81 ± 0.18 11.799 90.3 5.98 ± 0.22 0.21
NIB-S5 2 5.97 ± 2.75 13.13 ± 0.44 8.808 81.8 4.06 ± 0.43 0.43
NIB-S5 3 6.45 ± 2.50 8.52 ± 0.25 5.395 80.6 6.15 ± 0.60 0.60
NIB-S5 4 4.85 ± 1.99 8.40 ± 0.24 7.480 85.3 6.60 ± 0.51 0.50
NIB-S5 5 5.87 ± 1.28 12.46 ± 0.25 11.484 82.1 4.30 ± 0.23 0.22
NIB-S5 6 3.07 ± 2.45 10.26 ± 0.24 8.469 90.5 5.74 ± 0.48 0.48
NIB-S5 7 10.79 ± 1.18 9.25 ± 0.18 18.189 67.8 4.77 ± 0.28 0.27
NIB-S5 8 14.90 ± 1.10 4.99 ± 0.07 13.785 55.8 7.25 ± 0.45 0.45
NIB-S5 9 21.36 ± 7.99 9.06 ± 0.88 1.638 36.7 2.64 ± 1.77 1.77
NIB-S5 10 6.03 ± 1.87 8.91 ± 0.42 4.718 81.8 5.97 ± 0.53 0.52
NIB-S5 11 5.64 ± 2.69 13.27 ± 0.57 5.499 82.8 4.07 ± 0.44 0.44
NIB-S5 12 4.67 ± 2.43 8.48 ± 0.30 6.285 85.8 6.58 ± 0.61 0.61
NIB-S5 13 23.73 ± 5.47 7.63 ± 0.40 1.420 29.8 2.54 ± 1.41 1.41
NIB-S5 14 10.35 ± 7.82 12.11 ± 0.70 1.643 69.0 3.71 ± 1.27 1.27
NIB-S5 15 5.13 ± 2.10 10.61 ± 0.73 5.111 84.4 5.18 ± 0.56 0.56
NIB-S5 16 12.19 ± 9.76 11.44 ± 0.68 1.717 63.6 3.62 ± 1.66 1.66
NIB-S5 17 9.79 ± 5.04 8.41 ± 0.30 1.901 70.8 5.47 ± 1.18 1.18
NIB-S5 18 0.30 ± 13.14 15.60 ± 1.33 1.545 98.4 4.11 ± 1.65 1.65
NIB-S5 19 2.81 ± 0.97 6.89 ± 0.30 7.637 91.4 8.61 ± 0.49 0.48
NIB-S5 20 31.46 ± 7.82 13.02 ± 0.19 2.137 7.0 0.35 ± 1.15 1.15
NIB-S5 1 11.59 ± 11.68 12.66 ± 0.29 5.907 65.3 3.36 ± 1.77 1.77
NIB-S5 2 9.87 ± 7.29 12.94 ± 0.71 9.884 70.4 3.54 ± 1.11 1.11
NIB-S5 3 19.86 ± 17.36 9.63 ± 0.23 3.023 41.1 2.78 ± 3.45 3.45
NIB-S5 4 14.11 ± 12.32 9.90 ± 0.57 4.385 58.0 3.81 ± 2.40 2.40
NIB-S5 5 43.41 ± 43.42 14.05 ± 0.77 1.757 0.0 0.00 ± 5.92 5.92
NIB-S5 6 16.47 ± 12.44 8.60 ± 0.36 3.758 51.1 3.86 ± 2.78 2.78
NIB-S5 7 11.50 ± 5.57 13.55 ± 0.70 13.512 65.6 3.16 ± 0.82 0.82
NIB-S5 8 10.81 ± 4.55 9.48 ± 0.16 12.143 67.7 4.65 ± 0.92 0.92
167
NIB-S5 9 20.34 ± 18.75 10.79 ± 0.64 3.131 39.7 2.40 ± 3.34 3.34
NIB-S5 10 19.77 ± 14.84 9.94 ± 0.64 3.741 41.4 2.71 ± 2.88 2.88
NIB-S5 11 6.10 ± 5.92 8.01 ± 0.12 7.360 81.6 6.62 ± 1.42 1.42
NIB-S5 12 12.22 ± 12.44 14.20 ± 0.45 6.195 63.5 2.92 ± 1.68 1.68
NIB-S5 13 19.28 ± 22.50 8.44 ± 0.28 2.041 42.9 3.30 ± 5.10 5.10
NIB-S5 14 15.56 ± 15.15 7.87 ± 0.18 2.825 53.8 4.44 ± 3.68 3.68
NIB-S5 15 11.95 ± 12.96 10.37 ± 0.23 4.344 64.3 4.04 ± 2.39 2.39
NIB-S5 16 15.71 ± 15.07 10.77 ± 0.26 3.904 53.3 3.22 ± 2.68 2.68
NIB-S5 17 35.61 ± 46.91 11.83 ± 0.70 1.369 0.0 0.00 ± 7.60 7.60
NIB-S5 18 9.92 ± 5.78 7.15 ± 0.22 6.818 70.4 6.40 ± 1.57 1.57
NIB-S5 19 11.99 ± 11.58 8.45 ± 0.27 4.000 64.3 4.95 ± 2.63 2.63
NIB-S5 20 16.52 ± 17.56 9.82 ± 0.27 3.036 50.9 3.38 ± 3.42 3.42
NIB-S6 1 0.42 ± 1.22 3.61 ± 0.17 3.280 98.6 17.66 ± 1.07 1.05
NIB-S6 2 2.47 ± 1.64 6.27 ± 0.50 3.669 92.4 9.56 ± 0.97 0.96
NIB-S6 3 12.32 ± 5.93 5.93 ± 0.19 1.612 63.4 6.94 ± 1.94 1.94
NIB-S6 4 1.10 ± 0.71 3.59 ± 0.19 5.279 96.6 17.37 ± 1.04 1.02
NIB-S6 5 1.91 ± 1.08 3.52 ± 0.17 3.753 94.2 17.30 ± 1.08 1.06
NIB-S6 6 3.74 ± 1.90 3.06 ± 0.15 3.202 88.8 18.72 ± 1.57 1.55
NIB-S6 7 2.01 ± 1.88 3.64 ± 0.17 2.688 93.9 16.68 ± 1.29 1.27
NIB-S6 8 0.85 ± 0.54 3.45 ± 0.17 6.855 97.3 18.21 ± 0.99 0.96
NIB-S6 9 0.47 ± 2.68 3.85 ± 0.16 1.653 98.4 16.52 ± 1.51 1.50
NIB-S6 10 2.18 ± 1.34 3.96 ± 0.21 4.928 93.4 15.26 ± 1.08 1.06
NIB-S6 11 0.37 ± 2.72 4.85 ± 0.18 2.395 98.7 13.18 ± 1.19 1.18
NIB-S6 12 0.14 ± 0.98 3.54 ± 0.18 4.118 99.4 18.13 ± 1.09 1.07
NIB-S6 13 48.18 ± 12.66 13.40 ± 0.66 1.382 0.0 0.00 ± 1.79 1.79
NIB-S6 14 0.11 ± 3.32 3.79 ± 0.17 1.257 99.5 16.96 ± 1.83 1.82
NIB-S6 15 8.29 ± 1.77 3.65 ± 0.08 2.184 75.4 13.37 ± 1.01 1.00
NIB-S6 16 0.43 ± 3.51 4.06 ± 0.10 1.350 98.5 15.71 ± 1.70 1.69
NIB-S6 17 1.96 ± 12.51 4.99 ± 0.16 0.471 94.0 12.19 ± 4.79 4.79
NIB-S6 18 3.59 ± 4.06 10.60 ± 0.70 2.560 88.9 5.46 ± 0.84 0.83
NIB-S6 19 0.27 ± 2.18 3.49 ± 0.09 2.253 99.0 18.36 ± 1.29 1.28
NIB-S6 20 9.95 ± 2.10 3.60 ± 0.09 1.796 70.5 12.68 ± 1.19 1.18
NIB-S6 21 3.71 ± 0.31 3.15 ± 0.03 3.443 88.9 18.24 ± 0.34 0.27
NIB-S6 22 1.78 ± 0.22 3.40 ± 0.08 8.769 94.6 17.96 ± 0.50 0.46
NIB-S6 23 2.07 ± 0.24 3.81 ± 0.02 6.270 93.7 15.91 ± 0.23 0.15
168
NIB-S6 24 3.85 ± 0.90 13.26 ± 0.18 6.579 88.0 4.33 ± 0.15 0.15
NIB-S6 25 7.81 ± 2.89 10.61 ± 0.22 1.477 76.5 4.69 ± 0.54 0.53
NIB-S6 26 5.75 ± 0.43 3.01 ± 0.02 5.762 82.9 17.79 ± 0.36 0.30
NIB-S6 27 2.66 ± 0.47 3.42 ± 0.05 3.279 92.0 17.36 ± 0.41 0.36
NIB-S6 28 1.42 ± 0.18 3.24 ± 0.06 7.298 95.6 19.09 ± 0.45 0.39
NIB-S6 29 0.77 ± 0.11 3.54 ± 0.03 8.725 97.6 17.83 ± 0.27 0.18
NIB-S6 30 1.21 ± 0.58 3.21 ± 0.03 4.320 96.3 19.39 ± 0.46 0.40
NIB-S6 31 4.19 ± 1.39 6.89 ± 0.06 2.342 87.3 8.23 ± 0.40 0.39
NIB-S6 32 2.04 ± 0.55 4.46 ± 0.03 2.951 93.8 13.60 ± 0.30 0.26
NIB-S6 33 0.86 ± 0.24 3.47 ± 0.04 7.301 97.3 18.14 ± 0.31 0.23
NIB-S6 34 3.35 ± 0.25 7.80 ± 0.14 10.005 89.8 7.48 ± 0.18 0.16
NIB-S6 35 1.69 ± 0.26 3.27 ± 0.02 5.578 94.9 18.74 ± 0.29 0.20
NIB-S6 36 1.07 ± 0.29 3.24 ± 0.04 5.326 96.7 19.29 ± 0.35 0.28
NIB-S6 37 1.33 ± 0.38 3.40 ± 0.07 3.568 95.9 18.23 ± 0.47 0.43
NIB-S6 38 2.27 ± 0.34 4.87 ± 0.03 5.639 93.1 12.38 ± 0.21 0.16
NIB-S6 39 0.94 ± 0.31 3.44 ± 0.07 7.076 97.0 18.21 ± 0.47 0.42
NIB-S6 40 5.22 ± 1.44 11.33 ± 0.08 4.799 84.1 4.83 ± 0.25 0.25
NIB-S6 41 4.24 ± 0.62 9.55 ± 0.08 5.042 87.1 5.93 ± 0.15 0.14
NIB-S6 42 4.14 ± 0.24 6.75 ± 0.12 13.783 87.5 8.41 ± 0.20 0.18
NIB-S6 43 2.25 ± 0.27 3.49 ± 0.05 5.085 93.2 17.24 ± 0.36 0.30
NIB-S6 44 1.34 ± 0.33 3.14 ± 0.03 4.578 95.9 19.69 ± 0.37 0.29
NIB-S6 45 2.15 ± 0.32 4.30 ± 0.09 8.379 93.5 14.08 ± 0.37 0.33
NIB-S6 46 1.40 ± 0.49 3.18 ± 0.04 4.364 95.7 19.44 ± 0.46 0.41
NIB-S6 47 3.72 ± 1.08 5.66 ± 0.02 2.836 88.8 10.18 ± 0.39 0.37
NIB-S6 48 2.51 ± 0.53 3.27 ± 0.03 3.246 92.4 18.26 ± 0.42 0.37
NIB-S6 49 2.16 ± 0.40 4.21 ± 0.08 4.746 93.4 14.35 ± 0.37 0.34
NIB-S6 50 2.75 ± 0.54 4.44 ± 0.04 4.945 91.7 13.35 ± 0.31 0.27
NIB-S8 1 1.17 ± 0.18 3.38 ± 0.19 10.033 96.4 18.41 ± 1.09 1.07
NIB-S8 2 2.65 ± 0.34 3.30 ± 0.12 5.779 92.0 18.03 ± 0.77 0.74
NIB-S8 3 3.63 ± 0.86 3.45 ± 0.42 11.365 89.1 16.71 ± 2.31 2.30
NIB-S8 4 1.45 ± 0.17 3.51 ± 0.19 10.690 95.5 17.59 ± 1.02 1.00
NIB-S8 5 1.49 ± 0.21 3.28 ± 0.21 7.991 95.4 18.77 ± 1.27 1.25
NIB-S8 6 4.02 ± 0.35 3.28 ± 0.21 6.238 88.0 17.34 ± 1.25 1.24
NIB-S8 7 0.92 ± 0.23 3.56 ± 0.14 10.337 97.1 17.62 ± 0.73 0.71
NIB-S8 8 1.02 ± 0.20 3.36 ± 0.19 8.765 96.8 18.61 ± 1.10 1.08
169
NIB-S8 9 2.46 ± 0.54 3.45 ± 0.13 3.931 92.6 17.33 ± 0.77 0.74
NIB-S8 10 1.15 ± 0.40 3.65 ± 0.13 6.942 96.4 17.09 ± 0.69 0.66
NIB-S8 11 2.63 ± 0.45 3.71 ± 0.30 11.485 92.1 16.05 ± 1.45 1.43
NIB-S8 12 1.50 ± 0.25 3.48 ± 0.19 9.587 95.4 17.70 ± 1.04 1.02
NIB-S8 13 2.45 ± 0.25 3.60 ± 0.19 6.635 92.6 16.61 ± 0.97 0.95
NIB-S8 14 2.01 ± 0.31 3.47 ± 0.16 9.348 93.9 17.49 ± 0.87 0.85
NIB-S8 15 2.43 ± 0.33 3.62 ± 0.16 8.191 92.7 16.55 ± 0.83 0.81
NIB-S8 16 1.14 ± 0.24 3.44 ± 0.19 6.462 96.5 18.10 ± 1.07 1.05
NIB-S8 17 2.17 ± 0.33 3.80 ± 0.10 7.448 93.4 15.89 ± 0.50 0.47
NIB-S8 18 2.00 ± 0.32 3.66 ± 0.24 8.758 93.9 16.60 ± 1.17 1.16
NIB-S8 19 1.47 ± 0.20 3.54 ± 0.10 8.720 95.5 17.43 ± 0.57 0.53
NIB-S8 20 1.21 ± 0.44 3.69 ± 0.18 4.093 96.2 16.85 ± 0.89 0.86
NIB-S8 21 3.26 ± 5.52 3.70 ± 0.19 4.293 90.2 15.75 ± 2.98 2.97
NIB-S8 22 4.74 ± 3.66 3.30 ± 0.09 5.930 85.9 16.83 ± 2.18 2.17
NIB-S8 23 6.38 ± 2.31 3.04 ± 0.06 8.623 81.0 17.22 ± 1.52 1.50
NIB-S8 24 3.64 ± 2.89 3.49 ± 0.12 7.674 89.1 16.50 ± 1.71 1.70
NIB-S8 25 3.92 ± 5.78 3.56 ± 0.18 3.919 88.3 16.02 ± 3.22 3.22
NIB-S8 26 3.39 ± 3.67 5.21 ± 0.22 9.067 89.7 11.17 ± 1.44 1.44
NIB-S8 27 2.79 ± 4.35 3.45 ± 0.16 5.056 91.6 17.18 ± 2.56 2.55
NIB-S8 28 2.64 ± 3.26 3.87 ± 0.17 7.795 92.0 15.38 ± 1.77 1.76
NIB-S8 29 4.78 ± 6.51 3.54 ± 0.23 3.483 85.7 15.68 ± 3.69 3.69
NIB-S8 30 1.73 ± 2.41 3.39 ± 0.06 8.984 94.7 18.07 ± 1.41 1.40
NIB-S8 31 3.59 ± 3.03 3.26 ± 0.12 6.868 89.2 17.69 ± 1.92 1.91
NIB-S8 32 3.87 ± 4.93 3.40 ± 0.14 4.397 88.4 16.81 ± 2.87 2.86
NIB-S8 33 2.64 ± 4.76 3.26 ± 0.15 4.390 92.1 18.26 ± 2.93 2.93
NIB-S8 34 5.72 ± 7.70 3.22 ± 0.17 2.789 83.0 16.65 ± 4.65 4.65
NIB-S8 35 2.40 ± 4.26 3.60 ± 0.12 5.358 92.8 16.64 ± 2.33 2.32
NIB-S9 1 5.85 ± 0.42 3.02 ± 0.05 6.157 82.6 17.56 ± 0.46 0.42
NIB-S9 2 7.14 ± 2.51 3.98 ± 0.32 3.525 78.7 12.71 ± 1.73 1.73
NIB-S9 3 9.09 ± 0.44 2.56 ± 0.03 5.610 73.0 18.33 ± 0.46 0.41
NIB-S9 4 5.75 ± 0.47 3.25 ± 0.01 6.019 82.9 16.38 ± 0.34 0.28
NIB-S9 5 7.49 ± 0.41 3.41 ± 0.03 4.449 77.7 14.65 ± 0.34 0.29
NIB-S9 6 3.98 ± 0.28 3.06 ± 0.02 6.356 88.1 18.50 ± 0.31 0.22
NIB-S9 7 2.19 ± 0.48 3.42 ± 0.03 6.617 93.4 17.56 ± 0.38 0.32
NIB-S9 8 4.29 ± 0.48 3.21 ± 0.02 2.572 87.2 17.42 ± 0.38 0.32
170
NIB-S9 9 3.53 ± 0.25 3.23 ± 0.05 5.307 89.4 17.77 ± 0.41 0.36
NIB-S9 10 7.64 ± 0.35 2.78 ± 0.04 5.692 77.3 17.83 ± 0.43 0.38
NIB-S12 1 6.92 ± 3.24 3.63 ± 0.08 8.576 79.4 14.06 ± 1.73 1.73
NIB-S12 2 4.71 ± 4.33 3.45 ± 0.05 6.025 85.9 15.99 ± 2.39 2.38
NIB-S12 3 8.74 ± 8.32 4.00 ± 0.12 3.642 74.0 11.90 ± 3.96 3.96
NIB-S12 4 3.83 ± 4.74 4.44 ± 0.14 7.147 88.5 12.83 ± 2.07 2.07
NIB-S12 5 12.08 ± 12.29 3.93 ± 0.24 2.423 64.2 10.50 ± 5.99 5.99
NIB-S12 6 0.51 ± 0.49 4.67 ± 0.18 3.967 98.3 13.53 ± 0.58 0.56
NIB-S12 7 1.66 ± 0.35 4.37 ± 0.18 8.458 94.9 13.97 ± 0.64 0.62
NIB-S12 8 3.82 ± 0.44 3.94 ± 0.10 6.132 88.5 14.44 ± 0.48 0.45
NIB-S12 9 2.12 ± 0.37 4.54 ± 0.09 8.846 93.5 13.26 ± 0.35 0.31
NIB-S12 10 1.82 ± 0.26 3.89 ± 0.08 7.595 94.4 15.61 ± 0.41 0.37
NIB-S12 11 2.66 ± 0.40 4.05 ± 0.07 8.246 92.0 14.58 ± 0.36 0.32
NIB-S12 12 2.22 ± 0.34 3.38 ± 0.10 7.074 93.3 17.70 ± 0.61 0.58
NIB-S12 13 3.62 ± 0.68 4.03 ± 0.11 5.776 89.1 14.23 ± 0.57 0.54
NIB-S12 14 6.04 ± 0.52 3.49 ± 0.03 3.213 82.0 15.10 ± 0.36 0.31
NIB-S12 15 4.60 ± 0.88 3.29 ± 0.03 1.689 86.3 16.84 ± 0.57 0.54
NIB-S12 16 3.44 ± 0.47 4.23 ± 0.08 8.163 89.6 13.64 ± 0.40 0.37
NIB-S12 17 2.73 ± 0.51 4.09 ± 0.03 8.756 91.7 14.41 ± 0.31 0.26
NIB-S12 18 4.93 ± 0.77 4.14 ± 0.11 4.046 85.3 13.25 ± 0.54 0.52
NIB-S12 19 3.01 ± 0.50 3.87 ± 0.03 6.367 90.9 15.09 ± 0.32 0.28
NIB-S12 20 4.70 ± 0.53 3.98 ± 0.13 6.174 85.9 13.90 ± 0.59 0.56
NIB-S12 21 3.51 ± 0.45 3.25 ± 0.03 3.669 89.5 17.70 ± 0.38 0.32
NIB-S12 22 6.97 ± 0.64 3.68 ± 0.02 2.357 79.2 13.86 ± 0.38 0.35
NIB-S12 23 4.00 ± 0.38 3.94 ± 0.01 4.656 88.0 14.35 ± 0.25 0.19
NIB-S12 24 2.26 ± 0.28 4.05 ± 0.11 7.697 93.1 14.78 ± 0.48 0.45
NIB-S12 25 2.58 ± 0.55 3.95 ± 0.07 8.216 92.2 14.99 ± 0.43 0.40
NIB-S24 1 17.56 ± 61.51 8.61 ± 1.60 0.582 47.9 3.57 ± 13.53 13.53
NIB-S24 2 9.94 ± 19.30 10.53 ± 0.74 2.216 70.3 4.29 ± 3.48 3.48
NIB-S24 3 7.60 ± 43.69 10.80 ± 1.49 0.995 77.1 4.59 ± 7.67 7.67
NIB-S24 4 13.61 ± 11.46 6.10 ± 0.28 2.217 59.6 6.26 ± 3.57 3.57
NIB-S24 5 7.66 ± 13.40 7.45 ± 0.40 2.299 77.1 6.63 ± 3.42 3.42
NIB-S24 6 19.83 ± 51.39 8.12 ± 1.32 0.635 41.2 3.26 ± 11.99 11.99
NIB-S24 7 9.25 ± 16.02 8.43 ± 0.61 2.134 72.4 5.51 ± 3.62 3.62
NIB-S24 8 39.45 ± 33.94 6.83 ± 0.86 0.834 0.0 0.00 ± 9.37 9.37
171
NIB-S24 9 15.14 ± 42.92 12.37 ± 1.85 1.170 54.9 2.86 ± 6.59 6.59
NIB-S24 10 10.38 ± 47.47 11.64 ± 1.74 0.992 68.9 3.81 ± 7.73 7.73
NIB-S24 11 14.18 ± 26.68 9.25 ± 0.79 1.410 57.8 4.02 ± 5.47 5.47
NIB-S24 12 9.42 ± 17.06 8.31 ± 0.49 2.028 71.9 5.55 ± 3.90 3.90
NIB-S24 13 17.59 ± 38.69 7.47 ± 0.93 0.779 47.8 4.11 ± 9.81 9.81
NIB-S24 14 3.83 ± 11.16 4.06 ± 0.25 1.450 88.5 13.94 ± 5.26 5.25
NIB-S24 15 5.11 ± 30.70 13.64 ± 1.34 1.822 84.3 3.98 ± 4.27 4.27
NIB-S24 16 7.67 ± 2.18 6.37 ± 0.31 5.835 77.1 7.76 ± 0.81 0.80
NIB-S24 17 14.03 ± 4.52 10.21 ± 1.14 4.092 58.2 3.67 ± 1.05 1.05
NIB-S24 18 3.40 ± 3.91 6.28 ± 0.27 1.476 89.7 9.14 ± 1.26 1.25
NIB-S24 19 6.71 ± 6.40 12.88 ± 1.19 1.695 79.6 3.98 ± 1.04 1.04
NIB-S24 20 1.93 ± 2.78 4.50 ± 0.29 1.616 94.1 13.37 ± 1.49 1.48
NIB-S24 21 64.48 ± 9.31 16.87 ± 1.85 2.418 0.0 0.00 ± 0.80 0.80
NIB-S24 22 49.89 ± 5.20 8.96 ± 0.52 1.659 0.0 0.00 ± 1.00 1.00
NIB-S24 23 38.25 ± 3.87 9.34 ± 0.60 2.255 0.0 0.00 ± 0.75 0.75
NIB-S24 24 17.49 ± 2.23 9.85 ± 0.86 5.203 48.1 3.14 ± 0.65 0.65
NIB-S24 25 3.61 ± 2.64 7.65 ± 0.62 2.665 89.0 7.46 ± 0.94 0.93
NIB-S24 26 25.33 ± 2.40 7.71 ± 0.62 2.595 25.0 2.09 ± 0.74 0.74
NIB-S24 27 4.78 ± 1.43 8.32 ± 0.63 4.781 85.5 6.59 ± 0.67 0.66
NIB-S24 28 80.25 ± 10.44 10.35 ± 1.27 1.101 0.0 0.00 ± 0.99 0.99
NIB-S24 29 66.94 ± 7.68 3.93 ± 0.39 0.501 0.0 0.00 ± 2.50 2.50
NIB-S24 30 40.10 ± 3.17 12.29 ± 0.61 2.614 0.0 0.00 ± 0.46 0.46
NIB-S24 31 32.50 ± 2.44 6.69 ± 0.42 1.756 4.0 0.38 ± 0.71 0.71
NIB-S24 32 9.07 ± 0.97 6.15 ± 0.40 5.777 73.0 7.61 ± 0.72 0.71
NIB-S24 33 11.35 ± 2.23 3.67 ± 0.25 4.466 66.3 11.57 ± 1.60 1.59
NIB-S24 34 38.16 ± 3.50 8.01 ± 0.44 1.790 0.0 0.00 ± 0.79 0.79
NIB-S24 35 92.19 ± 11.74 14.79 ± 1.75 1.368 0.0 0.00 ± 0.76 0.76
NIB-S24 36 29.76 ± 4.13 11.10 ± 0.59 2.870 12.0 0.70 ± 0.72 0.72
NIB-S24 37 1.29 ± 4.15 12.05 ± 0.75 3.171 95.6 5.10 ± 0.73 0.73
NIB-S24 38 5.28 ± 1.44 2.84 ± 0.20 4.504 84.3 18.90 ± 1.81 1.79
NIB-S24 39 26.52 ± 3.75 9.10 ± 0.83 2.640 21.5 1.52 ± 0.88 0.88
NIB-S24 40 10.12 ± 2.64 6.61 ± 0.46 4.601 69.9 6.78 ± 1.00 0.99
NIB-S24 41 29.54 ± 3.59 10.87 ± 0.89 2.830 12.6 0.75 ± 0.67 0.67
NIB-S24 42 32.68 ± 4.47 9.54 ± 0.66 2.245 3.4 0.23 ± 0.89 0.89
NIB-S24 43 17.99 ± 2.15 6.23 ± 0.40 2.662 46.7 4.81 ± 0.86 0.86
172
NIB-S24 44 63.33 ± 7.14 8.75 ± 0.73 1.063 0.0 0.00 ± 1.21 1.21
NIB-S24 45 50.75 ± 5.59 8.91 ± 0.60 1.350 0.0 0.00 ± 1.06 1.06
NIB-S24 46 16.57 ± 1.27 5.37 ± 0.31 2.701 50.9 6.07 ± 0.74 0.74
NIB-S24 47 5.99 ± 1.77 5.77 ± 0.42 5.589 82.1 9.11 ± 0.99 0.98
NIB-S24 48 26.25 ± 1.93 10.19 ± 0.39 2.641 22.3 1.41 ± 0.39 0.39
NIB-S24 49 0.81 ± 2.76 10.18 ± 0.50 2.920 97.1 6.13 ± 0.60 0.60
NIB-S24 50 348.34 ± 162.79 0.02 ± 0.01 0.000 0.0 0.07 ± 2689 2689
NIB-S24 51 61.18 ± 5.95 11.85 ± 0.95 1.316 0.0 0.00 ± 0.69 0.69
NIB-S24 52 27.27 ± 3.38 6.06 ± 0.20 1.511 19.4 2.05 ± 1.07 1.07
NIB-S24 53 37.90 ± 3.92 9.76 ± 0.66 1.750 0.0 0.00 ± 0.73 0.73
NIB-S24 54 28.80 ± 2.41 7.93 ± 0.48 1.873 14.8 1.20 ± 0.63 0.63
NIB-S24 55 8.42 ± 0.80 4.85 ± 0.32 3.915 74.9 9.88 ± 0.90 0.89
NIB-S24 56 25.60 ± 1.51 9.54 ± 0.30 2.531 24.2 1.63 ± 0.33 0.33
NIB-S24 57 18.67 ± 3.32 3.25 ± 0.10 2.008 44.7 8.81 ± 1.99 1.99
NIB-S24 58 15.65 ± 1.40 9.11 ± 0.37 3.954 53.5 3.77 ± 0.39 0.38
NIB-S24 59 68.80 ± 8.72 9.61 ± 0.82 0.949 0.0 0.00 ± 1.39 1.39
NIB-S24 60 65.10 ± 7.68 11.22 ± 0.87 1.172 0.0 0.00 ± 1.07 1.07
NIB-S24 61 25.50 ± 2.02 10.23 ± 0.37 2.726 24.5 1.54 ± 0.40 0.40
NIB-S24 62 49.77 ± 5.50 12.26 ± 0.73 1.675 0.0 0.00 ± 0.78 0.78
NIB-S24 63 31.40 ± 3.10 10.09 ± 0.71 2.184 7.2 0.46 ± 0.60 0.60
NIB-S24 64 29.34 ± 2.28 11.33 ± 0.49 2.624 13.2 0.75 ± 0.40 0.40
NIB-S24 65 50.03 ± 6.75 12.40 ± 1.42 1.684 0.0 0.00 ± 0.80 0.80
NIB-S24 66 0.28 ± 0.67 8.91 ± 0.48 7.766 98.7 7.11 ± 0.43 0.41
NIB-S24 67 39.43 ± 5.00 8.36 ± 0.77 1.441 0.0 0.00 ± 1.05 1.05
NIB-S24 68 5.13 ± 1.46 4.56 ± 0.13 3.749 84.6 11.86 ± 0.74 0.72
NIB-S24 69 1.10 ± 3.29 11.29 ± 0.42 3.366 96.2 5.48 ± 0.59 0.59
NIB-S24 70 16.73 ± 2.93 4.07 ± 0.21 1.207 50.5 7.93 ± 1.52 1.52
NIB-S24 71 1.92 ± 2.11 6.87 ± 0.67 1.029 94.0 8.77 ± 1.08 1.07
NIB-S24 72 19.03 ± 1.47 6.10 ± 0.15 2.178 43.6 4.59 ± 0.51 0.51
NIB-S24 73 72.55 ± 7.32 9.80 ± 0.86 0.918 0.0 0.00 ± 0.90 0.90
NIB-S24 74 1.96 ± 0.66 8.24 ± 0.31 5.080 93.8 7.31 ± 0.34 0.32
NIB-S24 75 53.24 ± 7.48 8.97 ± 0.90 1.144 0.0 0.00 ± 1.31 1.31
NIB-S24 76 34.39 ± 3.86 10.26 ± 0.69 2.027 0.0 0.00 ± 0.71 0.71
NIB-S24 77 10.59 ± 1.25 6.66 ± 0.40 4.276 68.5 6.59 ± 0.66 0.65
NIB-S24 78 37.56 ± 3.96 8.51 ± 0.69 1.539 0.0 0.00 ± 0.83 0.83
173
NIB-S24 79 21.48 ± 1.87 8.86 ± 0.34 2.804 36.4 2.64 ± 0.45 0.45
NIB-S24 80 56.01 ± 8.60 9.76 ± 1.02 1.184 0.0 0.00 ± 1.40 1.40
NIB-S24 81 51.95 ± 5.85 9.87 ± 0.64 1.122 0.0 0.00 ± 1.01 1.01
NIB-S24 82 54.25 ± 5.40 11.12 ± 0.75 1.210 0.0 0.00 ± 0.78 0.78
NIB-S24 83 28.08 ± 2.93 8.53 ± 0.32 1.794 16.9 1.28 ± 0.67 0.67
NIB-S24 84 1.64 ± 0.16 0.25 ± 0.02 0.900 95.2 229.15 ± 17.51 17.26
NIB-S24 85 50.32 ± 5.71 10.53 ± 0.72 1.237 0.0 0.00 ± 0.92 0.92
NIB-S24 86 38.09 ± 3.71 8.80 ± 0.54 1.364 0.0 0.00 ± 0.76 0.76
NIB-S24 87 19.17 ± 1.64 8.71 ± 0.30 2.682 43.2 3.18 ± 0.41 0.41
NIB-S24 88 26.20 ± 2.56 5.04 ± 0.19 1.136 22.5 2.87 ± 1.00 1.00
NIB-S24 89 30.71 ± 2.64 7.54 ± 0.23 1.451 9.2 0.79 ± 0.67 0.67
NIB-S24 90 8.74 ± 1.26 6.38 ± 0.53 4.314 73.9 7.43 ± 0.90 0.89
NIB-S24 91 25.55 ± 2.04 6.33 ± 0.25 1.463 24.4 2.48 ± 0.66 0.66
NIB-S24 92 11.15 ± 3.23 3.44 ± 0.30 3.892 66.9 12.43 ± 2.35 2.34
NIB-S24 93 6.70 ± 1.50 4.46 ± 0.41 6.279 80.0 11.46 ± 1.45 1.44
NIB-S24 94 37.05 ± 3.88 9.96 ± 0.53 1.589 0.0 0.00 ± 0.72 0.72
NIB-S24 95 38.53 ± 3.58 8.56 ± 0.40 1.313 0.0 0.00 ± 0.77 0.77
NIB-S24 96 0.63 ± 0.81 3.00 ± 0.21 3.473 98.0 20.82 ± 1.58 1.55
NIB-S24 97 21.98 ± 1.99 9.02 ± 0.28 2.425 34.9 2.49 ± 0.45 0.45
NIB-S24 98 44.34 ± 4.50 9.51 ± 0.60 1.267 0.0 0.00 ± 0.82 0.82
NIB-S24 99 8.31 ± 3.01 6.14 ± 0.43 3.184 75.2 7.85 ± 1.17 1.17
NIB-S24 100 37.00 ± 4.18 10.17 ± 0.51 1.624 0.0 0.00 ± 0.76 0.76
NIB-S24 101 12.14 ± 2.10 5.18 ± 0.16 3.481 63.9 7.90 ± 0.85 0.84
NIB-S24 102 37.72 ± 4.22 8.74 ± 0.46 1.370 0.0 0.00 ± 0.89 0.89
NIB-S24 103 16.38 ± 1.32 6.30 ± 0.25 2.274 51.4 5.23 ± 0.53 0.53
NIB-S24 104 39.69 ± 4.96 9.35 ± 0.51 1.391 0.0 0.00 ± 0.98 0.98
NIB-S24 105 37.21 ± 3.66 8.37 ± 0.38 1.328 0.0 0.00 ± 0.81 0.81
NIB-S24 106 31.58 ± 2.69 6.76 ± 0.33 1.265 6.7 0.63 ± 0.77 0.77
NIB-S24 107 20.58 ± 1.94 10.02 ± 0.38 2.875 39.0 2.50 ± 0.41 0.41
NIB-S24 108 17.13 ± 1.54 9.97 ± 0.52 3.438 49.1 3.17 ± 0.41 0.41
NIB-S24 109 4.56 ± 1.13 7.33 ± 0.37 3.632 86.2 7.54 ± 0.53 0.52
NIB-S24 110 11.72 ± 1.22 3.33 ± 0.18 1.679 65.3 12.51 ± 1.18 1.17
NIB-S24 111 22.99 ± 2.78 8.90 ± 0.26 2.286 31.9 2.30 ± 0.61 0.61
NIB-S24 112 22.13 ± 2.20 9.52 ± 0.29 2.542 34.4 2.32 ± 0.46 0.46
NIB-S24 113 1.30 ± 2.66 10.77 ± 0.42 2.944 95.6 5.71 ± 0.53 0.52
174
NIB-S37 1 11.72 ± 8.65 7.25 ± 0.18 7.821 65.1 5.57 ± 2.18 2.18
NIB-S37 2 25.20 ± 39.33 8.90 ± 0.55 2.116 25.4 1.77 ± 8.08 8.08
NIB-S37 3 65.34 ± 124.12 12.16 ± 2.22 0.915 0.0 0.00 ± 18.60 18.60
NIB-S37 4 26.74 ± 25.92 6.26 ± 0.38 2.245 20.9 2.07 ± 7.57 7.57
NIB-S37 5 43.61 ± 82.42 7.24 ± 0.90 0.816 0.0 0.00 ± 20.81 20.81
NIB-S37 6 14.83 ± 31.28 6.33 ± 0.34 1.878 56.0 5.48 ± 9.02 9.02
NIB-S37 7 32.32 ± 82.90 8.22 ± 1.00 0.920 4.5 0.34 ± 18.45 18.45
NIB-S37 8 15.62 ± 30.44 10.53 ± 0.85 3.208 53.5 3.16 ± 5.30 5.30
NIB-S37 9 9.00 ± 13.22 5.83 ± 0.37 4.123 73.2 7.78 ± 4.18 4.18
NIB-S37 10 60.11 ± 135.09 7.70 ± 1.53 0.535 0.0 0.00 ± 32.01 32.01
NIB-S37 11 15.48 ± 29.53 9.43 ± 0.67 2.968 54.0 3.56 ± 5.73 5.73
NIB-S37 12 26.52 ± 57.53 7.59 ± 0.70 1.224 21.5 1.76 ± 13.85 13.85
NIB-S37 13 11.16 ± 19.71 6.73 ± 0.44 3.173 66.8 6.15 ± 5.36 5.36
NIB-S37 14 14.50 ± 14.80 5.03 ± 0.33 3.185 57.0 7.01 ± 5.41 5.41
NIB-S37 15 32.07 ± 58.07 11.96 ± 1.05 1.921 5.2 0.27 ± 8.88 8.88
NIB-S37 16 3.90 ± 0.47 2.33 ± 0.09 5.137 88.4 23.36 ± 1.12 1.09
NIB-S37 17 5.12 ± 0.94 8.51 ± 0.41 5.894 84.5 6.16 ± 0.41 0.40
NIB-S37 18 6.85 ± 0.73 4.29 ± 0.08 3.885 79.6 11.46 ± 0.43 0.41
NIB-S37 19 9.72 ± 5.10 7.63 ± 0.41 1.258 71.0 5.77 ± 1.29 1.29
NIB-S37 20 6.99 ± 2.07 8.67 ± 0.14 2.794 79.0 5.65 ± 0.45 0.45
NIB-S37 21 13.66 ± 1.16 5.23 ± 0.10 3.095 59.5 7.05 ± 0.46 0.45
NIB-S37 22 10.95 ± 6.39 8.16 ± 0.75 0.879 67.4 5.12 ± 1.58 1.57
NIB-S37 23 6.74 ± 2.96 9.54 ± 0.28 1.660 79.7 5.19 ± 0.60 0.60
NIB-S37 24 8.43 ± 1.81 5.83 ± 0.09 2.201 74.9 7.95 ± 0.59 0.59
NIB-S37 25 7.58 ± 2.03 9.01 ± 0.44 10.050 77.2 5.32 ± 0.53 0.53
NIB-S37 26 2433.01 ± 18561.7 205.66 ± 1562.98 1.621 0.0 0.00 ± 14.66 14.66
NIB-S37 27 49.54 ± 6.15 0.16 ± 0.01 0.041 0.0 0.00 ± 65.89 65.89
NIB-S37 28 10.65 ± 3.15 7.81 ± 0.53 2.287 68.3 5.42 ± 0.90 0.89
NIB-S37 29 16.51 ± 7.36 11.66 ± 0.24 1.266 50.9 2.72 ± 1.16 1.16
NIB-S37 30 16.74 ± 4.49 7.90 ± 0.15 1.520 50.3 3.95 ± 1.05 1.05
NIB-S37 31 12.32 ± 4.78 7.58 ± 0.33 1.306 63.4 5.18 ± 1.20 1.20
NIB-S37 32 15.88 ± 1.82 7.26 ± 0.28 3.493 52.9 4.52 ± 0.54 0.54
NIB-S37 33 4.18 ± 8.74 9.10 ± 0.44 0.609 87.2 5.95 ± 1.78 1.78
NIB-S37 34 1.73 ± 0.95 7.02 ± 0.07 4.971 94.6 8.35 ± 0.28 0.26
NIB-S37 35 5.78 ± 2.51 5.15 ± 0.27 1.123 82.7 9.93 ± 1.08 1.08
175
NIB-S40 1 6.76 ± 13.78 8.90 ± 0.48 4.258 79.7 5.46 ± 2.80 2.80
NIB-S40 2 10.47 ± 22.71 8.93 ± 0.70 2.556 68.8 4.70 ± 4.59 4.59
NIB-S40 3 7.34 ± 3.55 6.16 ± 0.24 11.554 78.1 7.71 ± 1.12 1.10
NIB-S40 4 8.75 ± 12.11 6.51 ± 0.40 3.533 73.9 6.92 ± 3.38 3.38
NIB-S40 5 31.89 ± 57.31 12.89 ± 1.33 1.486 5.7 0.27 ± 7.99 7.99
NIB-S40 6 17.03 ± 30.60 6.82 ± 0.42 1.451 49.5 4.43 ± 8.06 8.06
NIB-S40 7 11.88 ± 20.84 11.70 ± 0.90 3.637 64.5 3.37 ± 3.22 3.22
NIB-S40 8 11.62 ± 25.72 7.79 ± 0.68 1.992 65.4 5.12 ± 5.95 5.95
NIB-S40 9 405.89 ± 1313.25 2.68 ± 4.94 0.016 0.0 0.00 ± 724.56 724
NIB-S40 10 14.95 ± 16.72 7.50 ± 0.55 2.918 55.6 4.52 ± 4.03 4.03
NIB-S40 11 9.27 ± 18.31 8.16 ± 0.45 2.944 72.3 5.40 ± 4.04 4.04
NIB-S40 12 10.04 ± 10.84 9.79 ± 0.77 5.947 70.0 4.36 ± 2.04 2.04
NIB-S40 13 8.04 ± 19.08 6.93 ± 0.59 2.400 76.0 6.68 ± 4.98 4.98
NIB-S40 14 9.22 ± 14.08 8.55 ± 0.62 3.975 72.4 5.17 ± 3.00 2.99
NIB-S40 15 9.25 ± 26.65 9.61 ± 0.78 2.378 72.3 4.59 ± 4.99 4.99
NIB-S40 16 11.09 ± 7.58 6.63 ± 0.18 1.626 67.0 6.15 ± 2.07 2.06
NIB-S40 17 5.56 ± 3.59 6.02 ± 0.06 3.133 83.3 8.42 ± 1.09 1.07
NIB-S40 18 5.10 ± 1.17 6.76 ± 0.10 12.052 84.7 7.62 ± 0.39 0.34
NIB-S40 19 9.32 ± 3.75 7.49 ± 0.13 3.809 72.2 5.87 ± 0.92 0.91
NIB-S40 20 7.32 ± 5.32 6.56 ± 0.11 2.329 78.1 7.25 ± 1.47 1.46
NIB-S40 21 7.48 ± 3.42 8.73 ± 0.09 4.843 77.6 5.42 ± 0.72 0.71
NIB-S40 22 6.67 ± 6.62 8.12 ± 0.19 2.277 80.0 6.00 ± 1.48 1.47
NIB-S40 23 7.49 ± 1.12 5.03 ± 0.10 8.893 77.7 9.38 ± 0.52 0.46
NIB-S40 24 4.23 ± 4.39 5.27 ± 0.06 2.291 87.3 10.06 ± 1.52 1.49
NIB-S40 25 6.62 ± 5.16 7.68 ± 0.08 2.806 80.1 6.36 ± 1.22 1.21
NIB-S44 1 1.74 ± 14.36 8.16 ± 0.74 0.552 94.5 7.05 ± 3.23 3.22
NIB-S44 2 9.02 ± 6.28 8.44 ± 0.17 1.182 73.0 5.27 ± 1.35 1.34
NIB-S44 3 5.70 ± 2.77 8.94 ± 0.20 2.596 82.8 5.65 ± 0.59 0.57
NIB-S44 4 6.35 ± 10.74 12.13 ± 1.03 0.983 80.7 4.07 ± 1.65 1.64
NIB-S44 5 4.55 ± 8.99 7.63 ± 0.09 1.511 86.2 6.88 ± 2.12 2.11
NIB-S44 6 44.65 ± 13.95 9.61 ± 0.75 1.025 0.0 0.00 ± 2.57 2.57
NIB-S44 7 3.08 ± 2.17 7.96 ± 0.66 5.565 90.5 6.93 ± 0.82 0.80
NIB-S44 8 1.43 ± 4.54 8.07 ± 0.22 1.949 95.4 7.20 ± 1.04 1.03
NIB-S44 9 6.32 ± 8.48 9.30 ± 0.16 1.411 81.0 5.31 ± 1.64 1.64
NIB-S44 10 4.18 ± 3.86 7.26 ± 0.55 3.541 87.3 7.32 ± 1.15 1.14
176
NIB-S44 11 4.76 ± 3.33 8.03 ± 0.67 3.733 85.6 6.49 ± 0.99 0.97
NIB-S44 12 2.46 ± 4.30 10.88 ± 0.88 3.519 92.2 5.17 ± 0.85 0.84
NIB-S44 13 7.77 ± 4.77 8.36 ± 0.40 2.022 76.7 5.59 ± 1.08 1.07
NIB-S44 14 4.06 ± 4.67 8.27 ± 0.19 1.558 87.6 6.46 ± 1.04 1.03
NIB-S44 15 5.56 ± 6.26 5.63 ± 0.16 1.124 83.3 9.00 ± 2.02 2.01
NIB-S44 16 2.01 ± 4.11 9.45 ± 0.74 2.723 93.6 6.04 ± 0.94 0.93
NIB-S44 17 8.21 ± 2.53 10.94 ± 0.43 7.538 75.3 4.21 ± 0.48 0.47
NIB-S44 18 11.48 ± 3.59 9.16 ± 0.75 3.287 65.8 4.38 ± 0.87 0.87
NIB-S44 19 5.73 ± 7.72 7.42 ± 0.41 1.154 82.7 6.79 ± 1.92 1.91
NIB-S44 20 20.07 ± 22.18 8.97 ± 0.71 0.472 40.5 2.76 ± 4.46 4.46
NIB-S44 21 1.83 ± 4.60 11.09 ± 0.31 1.321 94.1 5.18 ± 0.77 0.76
NIB-S44 22 4.86 ± 2.46 10.44 ± 0.14 2.003 85.2 4.98 ± 0.45 0.43
NIB-S44 23 6.61 ± 0.75 8.25 ± 0.23 6.180 80.1 5.92 ± 0.30 0.26
NIB-S44 24 6.87 ± 0.71 7.43 ± 0.07 6.169 79.4 6.51 ± 0.25 0.19
NIB-S44 25 7.21 ± 0.63 8.66 ± 0.13 9.533 78.4 5.52 ± 0.22 0.17
NIB-S44 26 3.59 ± 0.64 4.25 ± 0.07 2.929 89.2 12.75 ± 0.48 0.36
NIB-S44 27 13.28 ± 2.94 9.05 ± 0.33 2.153 60.5 4.08 ± 0.63 0.62
NIB-S44 28 11.42 ± 2.98 12.85 ± 0.64 2.068 65.8 3.13 ± 0.48 0.47
NIB-S44 29 7.19 ± 1.02 8.24 ± 0.12 3.437 78.4 5.80 ± 0.29 0.25
NIB-S44 30 16.81 ± 1.03 7.14 ± 0.08 3.750 50.1 4.28 ± 0.29 0.27
NIB-S44 31 9.55 ± 0.76 7.93 ± 0.10 5.262 71.5 5.50 ± 0.24 0.19
NIB-S44 32 10.26 ± 2.84 10.67 ± 0.55 2.772 69.3 3.97 ± 0.56 0.55
NIB-S44 33 6.75 ± 1.52 8.33 ± 0.15 3.728 79.7 5.83 ± 0.38 0.35
NIB-S44 34 14.96 ± 3.07 8.28 ± 0.16 1.350 55.6 4.09 ± 0.69 0.68
NIB-S44 35 13.45 ± 1.19 6.32 ± 0.09 3.469 60.1 5.79 ± 0.39 0.36
NIB-S44 36 6.40 ± 0.94 6.98 ± 0.02 5.453 80.8 7.05 ± 0.30 0.24
NIB-S44 37 12.78 ± 2.62 8.38 ± 0.21 1.638 62.0 4.51 ± 0.60 0.59
NIB-S44 38 23.05 ± 4.96 7.59 ± 0.29 0.988 31.8 2.55 ± 1.19 1.19
NIB-S44 39 11.74 ± 0.70 6.92 ± 0.03 4.474 65.1 5.73 ± 0.23 0.18
NIB-S44 40 22.83 ± 2.17 4.60 ± 0.18 1.217 32.5 4.29 ± 0.93 0.93
NIB-S52 1 6.62 ± 13.71 3.25 ± 0.15 2.056 80.3 14.84 ± 7.49 7.49
NIB-S52 2 43.06 ± 37.57 8.81 ± 4.66 2.611 0.0 0.00 ± 7.04 7.04
NIB-S52 3 194.53 ± 425.04 0.03 ± 0.02 0.001 0.0 0.04 ± 26808 26808
NIB-S52 4 29.64 ± 63.17 7.15 ± 0.92 0.980 12.4 1.05 ± 15.74 15.74
NIB-S52 5 22.75 ± 57.58 8.37 ± 0.96 1.262 32.6 2.36 ± 12.25 12.25
177
NIB-S52 6 5.17 ± 1.06 8.17 ± 0.07 3.640 84.4 6.24 ± 0.25 0.24
NIB-S52 7 6.04 ± 2.15 7.18 ± 0.12 1.346 81.9 6.89 ± 0.55 0.55
NIB-S52 8 1.01 ± 0.73 3.14 ± 0.10 2.030 96.9 18.53 ± 0.74 0.71
NIB-S52 9 0.07 ± 1.33 8.19 ± 0.07 2.505 99.4 7.33 ± 0.31 0.29
NIB-S52 10 2.72 ± 0.73 6.24 ± 0.10 3.488 91.7 8.86 ± 0.28 0.26
NIB-S52 11 2.75 ± 0.28 6.86 ± 0.11 11.024 91.5 8.06 ± 0.18 0.16
NIB-S52 12 2.22 ± 0.29 3.29 ± 0.09 6.611 93.3 17.03 ± 0.58 0.54
NIB-S52 13 3.24 ± 0.53 5.20 ± 0.14 6.528 90.2 10.45 ± 0.38 0.36
NIB-S52 14 8.85 ± 1.06 7.74 ± 0.09 3.247 73.6 5.74 ± 0.27 0.26
NIB-S52 15 3.06 ± 0.49 6.71 ± 0.11 6.582 90.7 8.15 ± 0.22 0.19
NIB-S52 16 5.14 ± 1.23 10.79 ± 0.06 3.876 84.4 4.73 ± 0.21 0.21
NIB-S52 17 4.73 ± 1.21 5.30 ± 0.10 2.299 85.8 9.76 ± 0.47 0.45
NIB-S52 18 4.73 ± 0.77 10.15 ± 0.16 6.427 85.6 5.10 ± 0.18 0.16
NIB-S52 19 114.57 ± 13.61 0.29 ± 0.01 0.011 0.0 0.00 ± 81.67 81.67
NIB-S52 20 2.89 ± 0.64 6.67 ± 0.09 5.836 91.2 8.24 ± 0.23 0.21
NIB-S53 1 16.48 ± 41.07 9.43 ± 0.84 2.417 51.1 3.28 ± 7.76 7.76
NIB-S53 2 36.26 ± 89.63 11.93 ± 1.84 1.403 0.0 0.00 ± 13.37 13.37
NIB-S53 3 18.23 ± 34.90 8.16 ± 0.73 2.459 46.0 3.41 ± 7.62 7.62
NIB-S53 4 6.69 ± 9.58 5.50 ± 0.38 6.062 80.0 8.77 ± 3.17 3.17
NIB-S53 5 31.74 ± 56.76 6.91 ± 0.63 1.283 6.2 0.54 ± 14.64 14.64
NIB-S53 6 11.86 ± 30.51 3.03 ± 0.24 1.049 64.8 12.88 ± 17.88 17.87
NIB-S53 7 21.42 ± 35.48 9.86 ± 0.98 2.924 36.5 2.24 ± 6.42 6.42
NIB-S53 8 14.24 ± 39.82 6.71 ± 0.72 1.773 57.7 5.20 ± 10.58 10.58
NIB-S53 9 22.06 ± 22.13 6.17 ± 0.51 2.986 34.7 3.40 ± 6.40 6.40
NIB-S53 10 10.16 ± 26.88 4.39 ± 0.33 1.724 69.8 9.58 ± 10.89 10.89
NIB-S53 11 128.58 ± 307.72 0.30 ± 0.14 0.010 0.0 0.00 ± 1799 1799
NIB-S53 12 40.95 ± 90.38 7.82 ± 1.13 0.913 0.0 0.00 ± 20.57 20.57
NIB-S53 13 13.03 ± 29.41 7.30 ± 0.42 2.615 61.3 5.07 ± 7.17 7.17
NIB-S53 14 273.34 ± 738.60 0.44 ± 0.48 0.007 0.0 0.00 ± 2744 2744
NIB-S53 15 12.65 ± 27.63 9.07 ± 0.49 3.476 62.3 4.16 ± 5.42 5.42
NIB-S53 16 3.05 ± 0.72 8.17 ± 0.07 7.683 90.6 6.70 ± 0.19 0.17
NIB-S53 17 1.56 ± 0.16 3.45 ± 0.03 8.090 95.2 16.57 ± 0.27 0.18
NIB-S53 18 5.21 ± 2.08 7.61 ± 0.09 1.479 84.3 6.69 ± 0.50 0.49
NIB-S53 19 3.89 ± 0.29 7.71 ± 0.18 9.797 88.2 6.90 ± 0.21 0.19
NIB-S53 20 4.21 ± 1.13 3.66 ± 0.02 1.612 87.4 14.37 ± 0.58 0.55
178
NIB-S53 21 3.41 ± 0.64 3.15 ± 0.02 2.373 89.8 17.10 ± 0.44 0.39
NIB-S53 22 3.56 ± 0.89 6.80 ± 0.05 4.072 89.2 7.92 ± 0.26 0.24
NIB-S53 23 8.61 ± 1.64 3.46 ± 0.03 0.765 74.4 12.92 ± 0.86 0.84
NIB-S53 24 5.67 ± 5.59 7.38 ± 0.08 0.601 83.0 6.79 ± 1.35 1.35
NIB-S53 25 3.49 ± 1.19 2.90 ± 0.05 1.369 89.5 18.51 ± 0.82 0.79
NIB-S53 26 0.08 ± 0.53 3.53 ± 0.06 2.348 99.6 16.97 ± 0.44 0.39
NIB-S53 27 1.57 ± 0.48 7.46 ± 0.07 4.970 95.0 7.69 ± 0.16 0.13
NIB-S53 28 6.75 ± 0.87 7.09 ± 0.04 4.650 79.8 6.79 ± 0.24 0.22
NIB-S53 29 1.42 ± 1.84 7.62 ± 0.07 2.335 95.4 7.56 ± 0.44 0.43
NIB-S53 30 27.81 ± 2.37 10.54 ± 0.11 1.858 17.7 1.02 ± 0.40 0.40
NIB-S54 1 30.02 ± 3.24 0.01 ± 0.00 0.008 11.3 623.84 ± 448.15 448.10
NIB-S54 2 4.78 ± 5.43 7.77 ± 0.08 1.399 85.5 6.58 ± 1.23 1.23
NIB-S54 3 13.58 ± 1.79 5.06 ± 0.34 5.537 59.7 7.05 ± 0.96 0.95
NIB-S54 4 9.78 ± 5.67 8.44 ± 0.09 1.477 70.8 5.02 ± 1.19 1.18
NIB-S54 5 9.98 ± 1.79 5.29 ± 0.31 4.846 70.3 7.94 ± 0.87 0.86
NIB-S54 6 10.17 ± 2.36 3.92 ± 0.26 3.136 69.8 10.63 ± 1.43 1.42
NIB-S54 7 2.43 ± 1.63 5.07 ± 0.40 3.340 92.6 10.90 ± 1.09 1.08
NIB-S54 8 4.15 ± 2.04 10.92 ± 1.10 5.408 87.3 4.79 ± 0.64 0.64
NIB-S54 9 3.30 ± 2.90 5.08 ± 0.05 1.185 90.0 10.58 ± 1.02 1.01
NIB-S54 10 21.98 ± 4.21 7.32 ± 0.16 1.787 34.9 2.85 ± 1.02 1.02
NIB-S54 11 19.36 ± 3.63 3.72 ± 0.18 1.783 42.7 6.85 ± 1.83 1.83
NIB-S54 12 1.26 ± 2.42 6.27 ± 0.49 3.149 96.0 9.15 ± 1.01 1.00
NIB-S54 13 26.06 ± 6.02 6.84 ± 0.06 1.408 22.9 2.01 ± 1.55 1.55
NIB-S54 14 59.39 ± 17.50 11.53 ± 1.22 1.042 0.0 0.00 ± 2.56 2.56
NIB-S54 15 0.22 ± 5.74 5.80 ± 0.21 0.919 99.1 10.20 ± 1.78 1.78
NIB-S54 16 1.65 ± 6.54 6.44 ± 0.07 1.227 94.8 8.79 ± 1.79 1.79
NIB-S54 17 5.60 ± 2.37 5.81 ± 0.36 2.201 83.2 8.55 ± 0.95 0.94
NIB-S54 18 3.29 ± 12.51 6.41 ± 0.60 0.511 90.0 8.39 ± 3.54 3.54
NIB-S54 19 13.87 ± 8.33 6.39 ± 0.06 1.236 58.8 5.50 ± 2.29 2.29
NIB-S54 20 7.00 ± 1.98 7.47 ± 0.73 4.055 79.0 6.33 ± 0.89 0.89
NIB-S54 21 33.83 ± 46.87 0.38 ± 0.07 0.004 -0.3 0.07 ± 217.03 217.03
NIB-S54 22 29.52 ± 24.86 5.42 ± 0.58 0.164 12.7 1.41 ± 8.11 8.11
NIB-S54 23 6.03 ± 2.54 7.54 ± 0.21 2.234 81.9 6.50 ± 0.64 0.63
NIB-S54 24 13.28 ± 2.07 6.47 ± 0.21 1.480 60.6 5.60 ± 0.63 0.63
NIB-S54 25 5.86 ± 0.69 8.18 ± 0.07 10.543 82.3 6.03 ± 0.18 0.16
179
NIB-S54 26 11.01 ± 1.66 7.47 ± 0.07 3.284 67.2 5.38 ± 0.40 0.40
NIB-S54 27 11.00 ± 2.82 7.03 ± 0.19 2.297 67.3 5.72 ± 0.74 0.74
NIB-S54 28 22.34 ± 1.73 3.90 ± 0.02 2.277 33.9 5.20 ± 0.78 0.78
NIB-S54 29 5.49 ± 1.15 8.01 ± 0.06 6.887 83.4 6.23 ± 0.27 0.26
NIB-S54 30 8.09 ± 2.19 9.55 ± 0.52 2.700 75.7 4.75 ± 0.52 0.52
NIB-S54 31 1.98 ± 1.18 4.45 ± 0.23 1.835 93.9 12.58 ± 0.84 0.83
NIB-S54 32 0.81 ± 0.66 6.92 ± 0.09 5.025 97.3 8.40 ± 0.22 0.20
NIB-S54 33 15.98 ± 3.07 7.04 ± 0.25 1.098 52.6 4.47 ± 0.81 0.81
NIB-S54 34 18.57 ± 3.11 4.85 ± 0.24 0.828 45.0 5.55 ± 1.24 1.23
NIB-S54 35 6.05 ± 1.77 6.47 ± 0.05 1.654 81.9 7.56 ± 0.50 0.49
NIB-S54 36 6.90 ± 1.47 6.31 ± 0.15 3.807 79.4 7.52 ± 0.47 0.47
NIB-S54 37 1.40 ± 0.31 2.08 ± 0.06 3.658 95.8 27.34 ± 0.94 0.88
NIB-S54 38 10.29 ± 4.12 6.97 ± 0.25 1.358 69.4 5.95 ± 1.08 1.08
NIB-S54 39 6.77 ± 1.32 7.79 ± 0.06 3.570 79.7 6.12 ± 0.31 0.30
NIB-S54 40 10.01 ± 2.39 8.85 ± 0.27 1.738 70.1 4.75 ± 0.52 0.51
Table 1. Assigned uncertainty corresponds to 2-σ error. (i) Number of moles of K-derived 39Ar
(39ArK) released during fusion. (ii) Percentage of radiogenic 40Ar (40Ar*) in the total 40Ar for each
analysis. (iii) Age uncertainties are shown with and without propagated error in the irradiation
parameter J. Grains with shaded values are those cut from the analysis because they contained less
than 40% 40Ar*.
180
Appendix 3
1.0 Comparing PDF curves
To quantify the match (or mismatch) between two PDF curves, we calculated the sum of the
difference in the distribution of probability (Pdiff) between the theoretical probability (Ptheoretical) and
grab-sample probability (Pgrab). This was computed over each age increment (t), and expressed in
terms of a percentage of total probability:
100*2
)()(0
tPtPP
grabltheoretica
t
tdiff
−=
∑∞=
=
(1)
This provides the percentage mismatch of the entire probability signal in the units of percentage
probability. Any two PDF curves may be analyzed this way, although the exact value of mismatch
will be affected by the age increment (t).
Several other statistical comparison techniques were considered for comparing PDFs, but
rejected:
1) Correlation coefficient between idealized PDF and grab sample PDF.
The value of a correlation coefficient is dependant upon the number of discrete points, and so is
very dependant upon the age increment (t). In addition, a simple regression line, in combination
with an r-square test, measures the fit of the two curves to the regression line. We know, however,
181
that in our analysis the theoretical PDF is “correct” and so only need a measure of how well the
synthetic grab-sample fits this.
2) Forced correlation coefficient.
A correlation coefficient based on the deviation of the grab-sample points from a regression line
forced to intercept at (0,0) and with slope of one (an ideal fit of grab-sample to theoretical PDF
curve would lie exactly on this line). This is a good measure of the deviation from the exact match,
but is hard to interpret directly in terms of probability.
3) Percentage residuals.
Expressing the absolute residuals as a percentage of the real probability at that age :
100.)(
)()()(
−=
tP
tPtPtP
ltheoretica
grabltheoretica
(2)
This is easily understood on the PDF plot, but weights the differences in small probabilities
(primarily on the “tails” of the Gaussian curves) too much.
4) The Bootstrap and Jackknife.
Bootstrapping and Jackknifing are non-parametric tests of a population. When used on a “grab-
sample” population they provide a good test of the stability of the population, but do not measure
how well the grab sample matches the theoretical population.
Therefore, we feel that our comparison of the area under two PDF curves is a reasonable
solution. It is easily visualized on the PDF plot, simply understood in terms of probability, and
weights each age increment equally.
VITA. IAN D. BREWER
Date Organization Description
1987-1993 Poole Grammar School,
England
GCSEs, A-Levels
1993-1996 Oxford University, England Bachelors Degree in Earth Sciences
1996-1997 University of Southern
California, Los Angeles,
USA
Teaching and Research Assistant.
Started PhD Program (supervisor; Dr
D.W.Burbank)
1997-2001 The Pennsylvania State
University, USA
Teaching and Research Assistant.
PhD Program (supervisor; Dr
D.W.Burbank)
2001-2005 Shell International
Exploration and Production,
The Netherlands and New
Zealand.
Exploration Geoscientist
