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Intro to Quantitative Geology www.helsinki.fi/yliopisto

Introduction to Quantitative Geology Lesson 13.1

Basic concepts of thermochronology

Lecturer: David [email protected]

4.12.17

3

mailto:[email protected]

www.helsinki.fi/yliopistoIntro to Quantitative Geology

Goals of this lecture

• Introduce the basic concepts of thermochronology

• Discuss the closure temperature concept and how closure temperatures are estimated

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Why thermochronology?

• Popular dating technique for studying long-term tectonic and erosional processes (i.e., stuff we’ve been learning)

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Spanish Pyrenees



• Inherently linked to crustal heat transfer processes (advection, diffusion, production, etc.)

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�2 =X (Oi � Ei)2

�2i


• Incorporates many equations we’ve seen and many other concepts presented earlier in the course (hillslope processes, river erosion, heat conduction/advection, basic geostatistics)

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Age

Measured age

Predicted ages


Geochronology versus thermochronology

• Geochronology is the science of dating geological materials, and in many ways most radioisotopic chronometers are also thermochronometers

• An important distinction lies in what the ages mean and their interpretation

• Geochronological ages are generally interpreted as ages of the materials (crystallization ages)

• Thermochronological ages are often interpreted as the time since the material cooled below a given temperature (cooling ages)

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General thermochronology terms

• Thermochronometer A radioisotopic system consisting of:

• a radioactive parent

• a radiogenic daughter isotope or crystallographic feature

• the mineral in which they are found

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Chapter 1: Introduction - Figure 1

T0

Tectonics + Surface Processes = Exhumation = Cooling

Spontaneous Nuclear Reaction

Solid-State Diffusion

Time

Tem

per

atu

reTemperature History

Quantitative Thermochronology – p. 3/103

Fig 1.1, Braun et al., 2006

www.helsinki.fi/yliopisto December 4, 2017Low-temperature thermochronology

Geochronology versus thermochronology

• Geochronology is the science of dating geological materials, and in many ways most radioisotopic chronometers are also thermochronometers

• An important distinction lies in what the ages mean and their interpretation

• Geochronological ages are generally interpreted as ages of the materials (crystallization ages)

• Thermochronological ages are often interpreted as the time since the material cooled below a given temperature (cooling ages)

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• Thermochronometry The analysis, practice, or application of a thermochronometer to understand thermal histories of rocks or minerals

• Thermochronology The thermal history of a rock, mineral, or geologic terrane.

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T0




Time

Tem

per

atu






• Thermochronometry The analysis, practice, or application of a thermochronometer to understand thermal histories of rocks or minerals

• Thermochronology The thermal history of a rock, mineral, or geologic terrane.

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T0




Time

Tem

per

atu





The aim of thermochronology

• In most modern applications of thermochronology, the goal is to use the recorded thermal history to provide insight into past tectonic or erosional (surface) processes

• To do this, it is essential to link the temperature to which a thermochronometer is sensitive to a depth in the Earth

• This is not easy, and the field of quantitative thermochronology is growing rapidly as a result

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T0




Time

Tem

per

atu





The essence of thermochronology

• Daughter products are continually produced within a mineral as a result of radioactive decay

• Daughter products may be lost due to thermally activated diffusion

• The temperature below which the daughter product is retained depends on the daughter product and host mineral

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Parent

Daughter

decay

Open SystemClosed System



The essence of thermochronology

• Daughter products are continually produced within a mineral as a result of radioactive decay

• Daughter products may be lost due to thermally activated diffusion

• The temperature below which the daughter product is retained depends on the daughter product and host mineral

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Parent

Daughter

decay



Low T High T Fig 1.3, Braun et al., 2006


The concept of a closure temperature

• The transition from an open to a closed system does not occur instantaneously at a given temperature, but rather over a temperature range known as thepartial retention (or partial annealing) zone

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Parent

Daughter

decay




Fig 1.6a, Braun et al., 2006


Dep

th /

Tem

per

atu

re

partialretention

zone

Exhumed PRZ

Present-dayPRZ

Apparent age Apparent age

Elev

atio

n

Present-dayMean surface

elevation

Ro

ck u

plif

t

Den

ud

atio

nSu

rfac

eu

plif

t

Paleo-surfaceelevation

Iso

stat

icre

bo

un

dTe

cto

nic

up

lift

a

b

t1

t

t1+ t

Den

ud

atio

n

Modified from Fitzgerald et al. (1995) - Reproduced with permission from the American Geophysical Union


Daughter concentration /Apparent age

Partial retention/annealing zone


The concept of a closure temperature

• The transition from an open to a closed system does not occur instantaneously at a given temperature, but rather over a temperature range known as thepartial retention (or partial annealing) zone

• The partial retention zone temperature range spans from the point at which nearly all produced daughter products are lost to diffusion to where they are nearly all retained

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Parent

Daughter

decay






Dep

th /

Tem

per

atu

re

partialretention

zone

Exhumed PRZ

Present-dayPRZ


Elev

atio

n


elevation

Ro

ck u

plif

t

Den

ud

atio

nSu

rfac

eu

plif

t


Iso

stat

icre

bo

un

dTe

cto

nic

up

lift

a

b

t1

t

t1+ t

Den

ud

atio

n






Effective closure temperature, defined

• Defined by Dodson (1973), the closure temperature is the ‘temperature of a thermochronological system at the time corresponding to its apparent age’

• This concept is quite useful, as we can thus relate a measured age to a temperature in the Earth

• Unfortunately, closure temperatures vary as a function of the thermochronological system, mineral size, chemical composition and cooling rate

• This definition also only works when cooling is monotonic (no reheating)

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Dep

th /

Tem

per

atu

re

partialretention

zone

Exhumed PRZ

Present-dayPRZ


Elev

atio

n


elevation

Ro

ck u

plif

t

Den

ud

atio

nSu

rfac

eu

plif

t


Iso

stat

icre

bo

un

dTe

cto

nic

up

lift

a

b

t1

t

t1+ t

Den

ud

atio

n





Effective closuretemperature

Tc


Influence of cooling rate on effective Tc

• In general, the effective closure temperature for a given thermochronometer system will increase with increasing cooling rate

• For the retention of 4He in apatite, the effective closure temperature is ~40°C at a cooling rate of 0.1 °C/Ma and ~80°C at a rate of 100°C/Ma

• The absolute difference in effective closure temperature is also larger for higher temperature thermochronometers

• ~40°C for 4He in apatite

• ~130°C for 40Ar in hornblende

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ANRV273-EA34-14 ARI 17 April 2006 23:42

KsArZHe

AFT

THe

AHe

ZFT

radiation-damaged

zirconBiAr

zero-damagezircon

Tagami et al.

HbAr

Apatite FT

Zircon FT

0.1 1 10 1000

50

100

150

200

250

300

350

400

0.1 1 10 1000

100

200

300

400

500

600

Eff

ectiv

e cl

osur

e te

mpe

ratu

re (°

C)

Eff

ectiv

e cl

osur

e te

mpe

ratu

re (°

C)

Cooling rate (°C Myr-1) Cooling rate (°C Myr-1)

Renfrew

averagecompostion

Tioga

MuAr

Figure 2Effective closure temperature (Tc) as a function of cooling rate for common He, FT, and Arthermochronometers. Estimates shown here are based on Equation 7 and parameters inTables 1–2. Results were calculated using the CLOSURE program.

such cases, the closure temperature concept does not strictly apply, and this couldpotentially confound attempts to relate thermal and exhumational histories. This un-derscores the need to consider the conditions of a mineral’s formation, as well as itscooling path, in interpreting thermochronologic histories.

Figure 2b provides a comparison of the various Tc estimates for apatite and zirconFT dating. Tc for the average apatite is only ∼10◦C higher than that for an end-member fluorapatite, as represented by the Renfrew apatite. In contrast, the Tc forthe Tioga apatite is ∼60◦C above that for the average apatite. This range in Tc

would give a 7 Myr spread of FT ages for a typical orogenic cooling rate of ∼10◦CMyr−1. FT dating of detrital apatites in thermally reset sandstones commonly yieldsover-dispersed grain ages, which means that the range of grain ages is much greaterthan expected owing to analytical errors alone. This result is probably a consequenceof a mix of apatite compositions, which gives a mix of retention behaviors. The Tc

estimates shown here indicate that the youngest grains in a grain age distributionshould be dominated by low-retentivity apatites. Peak-fitting methods can be usedto isolate the minimum age, which is the age of the youngest fraction of grain ages(Galbraith & Green 1990; Galbraith & Laslett 1993; Brandon 2005, as summarized

www.annualreviews.org • Thermochronology of Orogenic Erosion 433

Ann

u. R

ev. E

arth

Pla

net.

Sci.

2006

.34:

419-

466.

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Reiners and Brandon, 2006


What causes cooling?

• With the idea of an effective closure temperature, we now have the main concept of thermochronology - a date will ideally reflect the time since the rock sample was at Tc

• But, what causes cooling?

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Erosional exhumation

• Occurs as a result of erosion and removal of overlying rock bringing relatively warm rock to the surface

• Can take place in convergent, extensional, strike-slip or inactive tectonic settings

• Most common “cooling type” for thermochronology

2121

Erosion at surface

Rivers/glaciersLandslides, hillslope

diffusion, etc.

Mountains

Crustal block






2222

Rock uplift

Erosion at surface


diffusion, etc.

Mountains

Crustal block






2323

Rock uplift

Erosion at surface


diffusion, etc.

Rock exhumation path

Mountains

Crustal block


Tectonic exhumation

• Generally occurs in extensional settings

• Uplifted footwall will also experience some erosional exhumation in most cases

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Exhumed rocks

Crustal block

Rock uplift


Other cases of rock cooling

• Rock cooling can also occur

• Following emplacement of an igneous body or volcanic deposit

• Typically, thermochronology is not useful in these cases as the cooling is rapid and geochronological and thermochronological ages will be similar

• Following reheating by

• Burial in a sedimentary basin and subsequent exhumation

• Emplacement of proximal igneous intrusions or volcanics

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t =1

�ln

✓1 +

Nd

Np

◆

Radioisotopic chronometer ages

• The general equation for an isotopic age iswhere ! is the isotopic age, " is the radioactive decay constant,

#d is the concentration of the daughter product and #p is the concentration of the parent isotope

• For thermochronometers, we know that the concentration of the daughter product will vary not only as a result of radioactive decay, but also due loss via solid-state diffusion

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@Nd

@t

= D(T )@

2Nd

@x

2+ P

Solid-state diffusion

• Thermochronometer daughter products are not suitable to be incorporated in the host mineral’s crystal lattice

• As ‘foreign’ isotopes, they are thus mobile and will diffuse within the crystal

• Their diffusion can be modelled using the standard diffusion equation where $(%) is the temperature dependent diffusivity (see next

slide), ∂2#d/∂&2 is the second derivative of the daughter

product concentration and ' is the daughter production rate

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1-D

Parent and daughterisotopes in a crystal

Alpha decay

Parent isotope

“Normal” atomDaughter isotope


D(T )

a2=

D0

a2e�Ea/(RTK)

Temperature-dependent diffusion

• Temperature dependence for diffusion is typically modelled aswhere $0 is the diffusivity at infinite temperature (diffusion

constant), ( is the diffusion domain, )a is the activation energy,

* is the gas constant and %K is temperature in Kelvins

• For simple systems, the diffusion domain ( is typically the size of the mineral itself

• The activation energy )a is the minimum energy that must be put into the system in order for diffusion to occur

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Temperature-dependent diffusion

• With the temperature-dependent diffusion concept in mind, there are essentially 3 different temperatures we might consider

• The ‘open system’ temperature %o The time/temperature that corresponds to the lower limit to the fully open system

• The closure temperature %cThe temperature of the system at the time corresponding to its age (Dodson)

• The blocking temperature %bThe upper temperature limit of fully closed system behavior

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Chapter 2: Basics of Thermochronology - Figure 1

Tem

pe

ratu

re

tc

Tc

tb

Tb

to

To

time

time

D/P

rat

io

measuredD/P ratio

Modified from Dodson (1973)




D(t) = D(0)e�t/⌧

Dodson’s effective closure temperature

• Dodson (1973) introduced a method for calculating the closure temperature of a thermochronological system based on the observed diffusion parameters and the rock/mineral cooling rate

• If we assume that once a rock enters the partial retention zone, the temperature will vary as the inverse of time (%∝1/!), it is possible to find an approximate solution to the temperature-dependent diffusion equation with a diffusivity where , is is the time taken for the diffusivity to decrease by a factor of 1/e

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Tc =Ea

R ln(A⌧D0/a2)

⌧ = �RT 2

EaT


• After some mathematical manipulation we can solve for , and findwhere Ṫ is the cooling rate (negative by convention)

• Dodson’s closure temperature equation iswhere - is a geometry factor (25 for a sphere, 27 for a cylinder and 8.7 for a plane sheet)

• We can find the closure temperature as a function of cooling rate by assuming %=%c in the equation for , and iterating

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Pseudo-code for solving Dodson’s equation

• Define constants

• Define initial “guess” for value of ,

• Loop over some range to iterate on values of , and %c

• Calculate new %c with current value of ,

• Calculate new value of , for new %c value

• Check to see how much value of %c has changed since last iteration

• If value has not changed more than some very small number, exit loop and output calculated ‘final’ %c value

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• The effective closure temperature %c increases significantly at higher cooling rates

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Chapter 2: Basics of Thermochronology - Figure 3

Cooling rate (oC Myr-1)

1 10 100

Clo

sure

te

mp

era

ture

(oC

)

55

60

65

70

75

80

85

90

95



Estimated %c for apatite (U-Th)/He


From age to process

• Using Dodson’s equations, we’re able to calculate closure temperatures as a function of cooling rate

• This does not provide any information about the depth of the closure temperature in the Earth

• There are several possibilities for determining the depth (or position) of %c, such as assuming a constant geothermal gradient

• As quantitative geologists, we can do better…

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Recap

• What is the basic idea for thermochronology?

• What is an effective closure temperature and how does it relate to the rate of cooling of a mineral sample?

35


Recap

• What is the basic idea for thermochronology?

• What is an effective closure temperature and how does it relate to the rate of cooling of a mineral sample?

36


References

Braun, J., der Beek, van, P., & Batt, G. E. (2006). Quantitative Thermochronology. Cambridge University Press.

Reiners, P. W., and M. T. Brandon (2006), Using Thermochronology to Understand Orogenic Erosion, Annual Review of Earth and Planetary Sciences, 34, 419–466.

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