GRADUATE THESIS PROPOSAL

EARTH SCIENCES 6300

STUDENT NAME: Masoud Aali

DEGREE PROGRAMME: PhD

SUPERVISOR: Mladen Nedimovic

PROPOSAL TITLE:

PREDICTING SEDIMENTARY PROPERTIES BY INTEGRATION OF ROCK PHYSICS MODELING AND QUANTITATIVE SEISMIC INTERPRETATION TO STUDY GLOBAL SEA-LEVEL CHANGES OFFSHORE NEW JERSEY

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SUMMARY OF PROPOSED RESEARCH: The New Jersey continental margin has been well recognized as the principal focus area for eustatic studies. At this rifted margin, due to very slow rate of subsidence since Triassic-Early Jurassic, relative sea-level change has been the leading driver for sedimentary processes and unconformities. Among the many questions regarding environmental factors affecting eustatic change that were formulated during the early investigations, two have been raised as particularly suitable for addressing offshore New Jersey: 1) what are the spatial and temporal near-shore processes that formed the paleo-shelf during eustatic cycles? 2) how do the sedimentological parameters (e.g. textural maturity, grain size, sorting)

vary spatially over the sedimentary units formed since mid-Oligocene? Improving our understanding of both sedimentary processes in the near-shore and variations in depositional environment were the main drivers for the recent studies on this margin that include drilling three IODP wells in 2009 and completing a 3D seismic survey in 2015. The key objective of this study is to use these newly collected data to predict sedimentological properties in shallow marine sediments at a significantly higher resolution (~5 m laterally) than previously achieved (~100s of m).This will be done by integrating sequence stratigraphy and rock physics within the 600 km2 study area covered by the 3D seismic survey. First, a practical rock physics model will be developed for shallow-marine unconsolidated sediments to determine the relationship between sedimentological parameters and elastic moduli in low-pressure conditions. The resulting rock physics model will be used for determining the spatial distribution of sedimentological properties within each stratigraphic sequence in the study area. This will be followed by a study of seismically imaged shelf channel system to determine spatial trends in sedimentological parameters within them. Characterizing the channelized sediments, especially those which formed during the eustatic changes, will help to: 1) understand the sedimentary processes involved in the evolution of the shoreline, 2) refine the existing estimates of the eustatic changes for the geological period investigated.

TIME TABLE:

ACTIVITY PLAN START (MONTH)

PLAN END (MONTH)

PERCENT COMPLETE

Phase I: Literature Review 1 36 41% Review rock physics modeling for unconsolidated sediments 3 13 50% Review the mechanism of se- level changes 4 12 25% Study the geological setting of the NJ margin 6 12 25% Attend required courses for Ph.D. degree 1 10 75% Submit research proposal 5 14 50% Gather raw and processed data from the previous studies 2 14 75% Prepare thesis background & introduction 12 24 25% Phase II: Project Development 1 43 13% Process seismic data for AVO analysis/inversion 4 28 10% Structural modeling and stratal reconstruction 5 11 0% Seismic inversion 8 24 0% Petrophysical & rock physics modeling 8 15 10% Phase III: Completion 28 43 0% Publish papers, assemble thesis, compile questions 28 40 0% Present at AGU/SEG 20 28 0% Thesis write-up and editing 38 44 0%

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1 BUDGET

BUDGET SUMMARY

Year 1 Year 2 Year 3 Year 4

A) Laboratory expenses $6,000 $0 $0 $1,700

B) Travel $1,624 $0 $1330 $8446

C) Other costs $3,000 $0 $0 $0

Total $22,100

A) LABORATORY EXPENSES. Computer hardware totaling $7700 will be needed during the 4 years. 40 TB of

solid-state drive ($6000) is needed to run the seismic data processing and interpretation. 20 TB of data

tape is needed ($1700) to back up the raw seismic data and final results at the end of the fourth year.

B) TRAVEL. Two trips are planned to meet with co-supervisor and collaborators at University of Kiel-

Germany and Rutgers University-United States respectively. Two trips are budgeted in the third and

fourth year to participate and present the final study results at the AGU (American Geophysical Union)

and SEG (Society of Exploration Geophysics) annual meetings in San Francisco and Dallas respectively.

Expenses

\ Destination

Rutgers University AGU-San Francisco SEG-Dallas Kiel University

Air Fare $850 $820 $760 $1250

Lodging $40*8 days $40*5 days $40*5 days $0

Meals $48 *8 days $48*5 days $48*5 days $48*122 days

Airport Transport $70 $70 $70 $70

Total $11,400

C) OTHER COSTS. $3000 is needed in total to order the necessary complimentary processing on the

seismic data from the consulting company. These results has not been budgeted in the preliminary

contract (signed in 2014) for processing the NJ seismic data. Part of this budget ($600) is for buying 5 TB

hard-disc drive to receive the deliverables.

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2 STATEMENT OF THE PROBLEM. With about 200 million people globally living within the coastal floodplain less than 1 meter above current sea-level, sea-level rise and its effect on the low-lying areas is a potential socio-economic hazard on a global scale that needs to be studied, particularly during the present period of accelerated ice-cover melting. The New Jersey (NJ) margin has for decades been recognized as the leading focus area for eustatic studies because, due to very slow rate of subsidence since Triassic-Early Jurassic at this rifted margin (Watts and Steckler, 1979; Greenlee et al., 1988), relative sea-level change has been the leading driver for sedimentary processes and development of unconformities between stratigraphic units (Miller et al., 2005). These early studies resulted in formulation of numerous questions related to environmental factors affecting eustatic change. Two key questions are particularly suitable for addressing offshore New Jersey: 1) what are the spatial and temporal near-shore processes that formed the paleo-shelf during the eustatic cycles? 2) how do the sedimentological parameters (e.g. textural maturity, grain size, sorting) vary spatially over the sedimentary units formed since mid-Oligocene? This thesis research will use the 2015 data collected offshore NJ by a 600 km2 hybrid multichannel seismic (MCS) survey and centered on three Integrated Ocean Drilling Programme (IODP) wells drilled in 2009, to directly address these questions by improving our understanding of the variations in the depositional environment and the near-shore sedimentary processes through prediction of rock properties in the shallow marine sediments at unprecedented resolution (~5 m laterally).

3 BACKGROUND

3.1 EUSTATIC CHANGE ON THE NEW JERSEY MARGIN Well-developed siliciclastic sequences displaying prominent clinoforms offshore the NJ margin have become one of the main targets for investigating the effects of eustatic change. The timing and amplitude of large (>100m) sea-level changes that typified the Pleistocene, which greatly affected sedimentation processes at that time, have been very well studied. However, because of limited access to direct samples and poor stratigraphic time constraints, their effects on continental margin sedimentation have been difficult to evaluate (Miller et al., 2012).The target area for this study on the NJ margin is bounded by the3D seismic dataset and includes the three IODP wells (Figure 1). The IODP cores and log data show two classes of sediments: (1) well-sorted silt and sand accumulated in offshore to shoreface environments; and (2) interbedded poorly sorted silt with layers of turbidite sands and silty clays deposited during intervals of clinoform slope degradation (Figure 2). The silt-rich sediments are dominant in all three wells and clay-sized deposits are absent across all ages (Mountain et al., 2010). IODP reports show no evidence of subaerial exposure at clinoform inflection points (Figure 2). However, periodic shallow-water facies along clinoform foresets and deep-water facies on topsets suggest large-amplitude changes in relative sea level (Mountain et al., 2010). Moreover, some uncertainties about whether or not sea-level falls caused subaerial exposure of clinoform topsets or whether they remained submerged are still matters of

Figure 1) Bathymetry of the New Jersey margin. Red, black and blue lines show the position of multichannel seismic data. The gray rectangle indicates the position of 3D seismic data. The onshore and offshore wells drilled by the Atlantic Margin Coring Program, Ocean Drilling Program (ODP), and Integrated Ocean Drilling Program (IODP). The thick blue line shows the location 2D seismic shown in Figure2. (Miller et al., 2013).

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controversy. Imaging the shallow stratigraphic sequences in 3D and providing a model to predict the sedimentary parameters spatially over the sedimentary units would greatly improve our understanding of the sedimentological and paleo-environmental effects of sea-level change from the mid-Oligocene on the NJ margin.

3.2 SEISMIC SEQUENCE STRATIGRAPHY Reflection seismic data are widely used in sequence stratigraphy to interpret subsurface structure. The principal idea behind using such data for sequence stratigraphy is that, within the resolution of the reflection method, the contrast between acoustic impedance at the interface of two layers causes part of the seismic energy to bounce back. At this interface, sedimentological parameters such as textural maturity (sorting, grain shape), sand/shale ratio, and type of clay dispersion (within the layer and inside the pore structure) can affect the acoustic properties of the interface (Murphy, 1982; Han; 1986; Nur et al., 1991; Mavko and Jizba; 1991; Marion 1990; Yin 1992; Marion et al., 1992; Nur et al., 1995; Avseth et al., 2000; Gutierrez, 2001). Such a large number of variables can make any interpretation of seismic amplitude non-unique. To minimize this non-uniqueness, principles of seismic sequence stratigraphy will be applied to separate the seismic section into sedimentary units with similar sedimentological properties. This method will limit the number of variables that can affect the acoustic response of the sediments within each sedimentary unit. However, gathering detailed information about the variation of a specific sedimentological parameter among the sedimentary units (e.g. variation of porosity within a sedimentary unit or between them) requires very dense sampling from the depositional environment. Alternatively, a comprehensive rock physics model can be used to predict the sedimentary parameters along the stratigraphic horizons.

3.3 ROCK PHYSICS MODELING OF UNCONSOLIDATED SEDIMENTS In the rock physics domain, we determine the mathematical relationship between the elastic properties influencing the acoustic impedance of the rock and sedimentological parameters such as mineralogy, textural maturity, pore fluids and pore pressures (Dutta, 2009). In a well location, the model simulate the amplitude response to variation of different parameters such as lithology, porosity, and elastic properties. Then, the calibrated model is used to interpret and explain observed seismic amplitude variations in terms of underlying sedimentological parameters away from the wells (Dutta, 2009). Many studies have modeled the elastic properties of different rock frameworks by applying different kinds of constraints on sedimentological parameters or physical conditions (Avseth et al., 2010; Walton, 1987; Dvorkin and Nur 1996; Berryman, 1980; Dutta, 2009). However, since shallow sediments have rarely been considered as a target for hydrocarbon exploration, little work has been done to improve rock physics models for these sediments. Furthermore, the discrepancy between measured values and results from the available theoretical models for shallow sediments is still noticeable.

Among the available rock physics models, the Hertz-Mindlin theoretical model of elasticity (Mindlin, 1949) is widely used for deep marine unconsolidated sediments. This model calculates the normal and shear stiffness of two elastic spherical grains in contact. Then, the average contact forces distributed over all grain contacts are

Figure 2) 2D seismic profile indicated by a thick blue line in Figure 1.Travel time has been converted to depth below sea level (Mountain and Monteverde, 2012). Key Oligocene-Miocene sequence boundaries shown in red have been labeled based on their age (“o” for Oligocene and “m” for Miocene). The gamma logs are shown at the position of wells. Red lines indicate the boundary of major seismic sequences. Inset at lower left is a generalized clinoform model (after Miller et al., 2013b). TS—Transgressive Surface; TST—Transgressive Systems Tract; LST—Lowstand Systems Tract; HST—Highstand Systems Tract; MFS—Maximum Flooding Surface; SB—Sequence Boundary (Miller et al., 2013).

0 10km

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used to determine the effective elastic moduli of the media. This procedure, often referred to as an effective-medium approximation (EMA), assume homogeneous strain over the studied sample. However, laboratory experiments demonstrate that the measured dynamic bulk and shear moduli vary with isotropic confining pressure more than predicted by the Hertz-Mindlin effective medium model (figure 3A). Moreover, the observed Vp/Vs ratios from the lab measurements are noticeably higher than those predicted by most of the effective medium models (Figure 3B). Deficiencies in existing models require a fresh approach to measuring and predicting the seismic properties of unconsolidated sediments.

4 OBJECTIVES The key objective of this study is to improve the prediction of sedimentary properties in shallow marine sediments by integrating sequence stratigraphy and rock physics modeling techniques, which will improve mapping of the temporal and spatial variation of these properties on the offshore NJ margin. I will start by studying the trends of sedimentary parameters in difference eustatic sequences. Then, I will develop a practical rock physics model for unconsolidated sediments to compute their elastic properties in the shallow marine environment. The resulting rock physics model should reproduce the real measurements from the IODP sites. Next, I will use the resulting rock physics model and elastic properties derived from the seismic data to determine the probable spatial trend of sedimentological properties (e.g., textural maturity, grain size, sorting) for each sequence. This model results in a more accurate estimate for the amplitude of sea-level changes offshore the NJ margin over the geological time investigated. Finally, we estimate the spatial trends of sedimentological parameters in channelized sediments to provide information about sedimentary environment, especially during the Pleistocene sea-level changes in the area.

5 METHODOLOGY 5.1 STEP 1: TRENDS IN SEDIMENTOLOGICAL PROPERTIES CAUSED BY EUSTATIC CHANGES. In shallow marine depositional environments where sediments are mainly deposited at or near sea-level, the trends of sedimentological properties (e.g., textural maturity, sorting, grain size, sand/shale ratio and bioturbation) are robust and sensitive to the variation of sea-level. In this environment, sea-level transgression and regression make systematic changes in sedimentological properties (Van Wagoner et al., 1990). The trends of changes in these parameters are opposite for marine transgression and regression. During transgression, the depositional energy diminishes as a function of time and results in a decrease of the sand/shale ratio, grain size, sorting, and an increase in bioturbation. Transgression also causes a retrogrational stacking pattern. In contrast, regression causes progradational stacking, brings progressively higher depositional energy to the environment, improves sorting, increases sand/shale ratio, and decreases bioturbation (Figure 4). Each of the above sedimentological properties can be considered as an attribute providing information about sea level at the time of sediment deposition. If the sediments are further from the source, we usually expect grains to be better

Figure 3) A: VP/VS ratio vs. pressure, and B: velocities vs. pressure of dry unconsolidated sandstone of Pomponio beach, California (Zimmer, 2003). The solid lines represent the predictions of velocities by the Hertz-Mindlin contact model. The model over-predicts VS (b), and under-predicts VP/VS ratio (a) (Zhang and Brown, 2001).

Model

Data

Data

Model

Model

Data

Pressure, MPa

Pressure, MPa

VP/V

S V

elo

city

(m

/s)

A

B

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sorted, less angular, and to have better textural maturity. These sedimentological parameters also control the elastic stiffness of the rock, and consequently the amplitude of the reflected seismic waves.

5.2 STEP 2: SPATIAL GRADIENTS IN SEDIMENTOLOGICAL PROPERTIES Gradients of sedimentological parameters follow two trends: 1) along the chronostratigraphic unit, and 2) perpendicular to it. The surface between two chronostratigraphic units represents a gap in the sedimentation record, which may be due to erosion or lack of deposition. These gaps, usually accompanied by contrasts in acoustic impedance of adjacent layers in the form of a step function, are a source of seismic wave reflections (Tipper, 1993). In contrast to the vertical gradient, the gradient of sedimentary parameters along the chronostratigraphic units is continuous, smooth, and follows the shape of the chronostratigraphic unit. Therefore, the changes in sedimentological properties are abrupt across the unit and gradual along it (Dutta, 2009).

Properties such as paleo-water depth of deposition, rate of deposition, and transition between eustatic cycles are among factors that control lateral gradients of sedimentological properties. Estimating these lateral gradient for each sedimentological property requires dense sampling of the subsurface. A rock physics model can be used to infer the deterministic relationship between these properties and elastic moduli of the sediment derived from seismic inversion and prestack seismic data. Therefore, elastic moduli derived from seismic data can integrated with rock physics modeling results to generalize the parameters measured inside the wells to the whole area covered by seismic data. As a result, it will be possible to predict the above sedimentological properties at each point within the sedimentary units.

5.3 STEP 3: ROCK PHYSICS MODELING Based on coring and logging results, the friable-sand model (Dvorkin and Nur, 1996; Mavko et al., 1998) is the closest rock physics model for relatively unconsolidated sands on the NJ margin. The friable-sand model, also known as the soft-sand model, describes how the velocity–porosity relationship changes as sorting deteriorates. The “well-sorted” end of the model is considered as a pack of similar grains with the same grain size, and whose elasticity at grain contacts determines their elastic properties. At the other end of the model, “poorly sorted” sands are considered as a pack of “well-sorted” grains modified with additional smaller grains deposited in the pore space (Figure 5). These additional grains slightly increase the rock stiffness, deteriorate sorting, and decrease the porosity. In this model, the elastic moduli of the soft sand are determined by the Hertz-Mindlin theory as follows:

Where KHM and GHM are the dry rock bulk and shear moduli, φ0 is

the critical porosity (~40 % for sandstone), C is the coordination

number (average number of grain contacts), G and ν are the

mineral shear modulus and Poisson’s ratio, respectively. Although this model is commonly used for unconsolidated sandstone,

Figure 5) Schematic description of the friable-sand model and its response to corresponding variation of rock properties (Figure modified from Dutta, 2009).

Well sorted sand

Poorly sorted sand

(1) (2)

Bed-thickness

Sand/shale ratio

Sorting

Textural Maturity

Less Bioturbation

Figure 4) The trend of sedimentological properties during marine transgression and regression ( Van Wagoner et al., 1990).

Deep

Transition

Zone

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laboratory experiments demonstrate that the measured dynamic bulk and shear moduli vary with isotropic confining pressure faster than the results of the Hertz-Mindlin effective medium model (Goddard, 1990;

Zimmer, 2003). Some other theoretical models have used the modified extended Walton theory (Walton, 1987) to determine a better correlation between the predicted elastic moduli and the laboratory measurements

(Jenkins et al., 2005; Dutta, 2009). These modifications of the extended Walton theory resulted in a better model for variation of shear wave velocity as a function of confining pressure. However, for shallow unconsolidated sands, the modeling results using the Hertz-Mindlin effective medium theory are in better

agreement with laboratory measurements (Figure 6). Whereas, at low confining pressures, the effect of pore fluid should be counted in determining the elastic moduli, the extended Walton theory considers the pores of unconsolidated sand to be free of fluid. This assumption increases the error in prediction of P-wave velocity which is sensitive to pore fluid, especially in low-pressure environments. Determining a hybrid model based on both extended Walton theory and Hertz-Mindlin theory can result in a better estimate of P-wave and S-wave velocities for unconsolidated shallow sediments in the low-pressure environments. Estimating the pressure interval, in which pore fluid affects the elastic properties of sediments, is necessary to find the transition point from one model to another. The deviation of each of these rock physics models from the measured data is the main criterion by which to determine the most precise model in each pressure interval.

5.4 STEP 4: SEISMIC INVERSION In seismic inversion the original reflectivity data, recorded during the seismic survey, are converted from an interface property (i.e., a reflection) to a rock property such as acoustic impedance or Vp/Vs ratio. In poststack seismic inversion, all reflections are considered to have been recorded at zero offset from the seismic source. This type of inversion converts seismic amplitude to acoustic impedance, which is the product of rock density and P-wave velocity. Unlike the amplitude of reflected seismic waves or the reflection coefficient (which are interface properties), acoustic impedance is a property of the rock itself. Prestack AVO inversion is a method that uses seismic data with multiple offsets or reflection angles as the inputs to data analysis. As the output, it deterministically solves the Zeopperitz equation to generate volumes of P-impedance, S-impedance, and Vp/Vs ratio. The resulting elastic moduli are real rock properties that help differentiate geologic features with similar P-impedance signatures.

5.5 SORTING TREND PREDICTION IN UNCONSOLIDATED SHALLOW MARINE SEDIMENTS Coring and logging results from the three IODP boreholes show that while the lateral lithology variation is negligible, grain size and sorting are the major sedimentary properties that vary proximally within the stratigraphic layers. Negligible lithology variation gives a very good control in rock physics modeling of the margin sediments, because variation of sorting is a strong function of paleo-water depth of deposition and distance from the shoreline. Since the volume of between-grain space is related only to the method of grain packing and sorting of the grains, grain size does not control the porosity. Therefore, sorting is the key factor that controls the variation of porosity within and between sequences. By computing synthetic seismographs for the boreholes, it is possible to calibrate the rock physics model for shallow unconsolidated sands, quantitatively model the variation of sorting as a function of acoustic impedance and Vp/Vs ratio, and use the seismic data to predict the variation of sorting over the area covered by the seismic survey.

Figure 6) Comparing the measured values of P-wave and S-wave velocity with modeling predictions using Hertz-Mindlin theory (Zimmer, 2003) and extended Walton theory (Dutta, 2009). Rock physics model based on extended Walton theory predicts S-wave velocity more accurately. However, in low pressure environments, the modeled trend based on Hertz-Mindlin theory better matches with measure values for P-wave velocity.

Extended Walton

Extended Walton

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By applying the concept of the spill-and-fill sequence stratigraphic model (Satterfield and Behrens, 1990) in a shallow marine depositional system and the rock physics model, it is expected that in a shelf fluvial/tidal channel, the sand/shale ratio and sorting will increase along the flow direction (Lerch et al., 2006). In order to quantify these spatial trends, it is necessary to do petrophysical analysis on available cores and well logs from the channelized sediments. These types of analysis are effective in estimating the sand/shale ratio, and porosity for different shale configurations within fluvial/tidal channels.The initial results from processing the 3D seismic data from offshore the NJ margin have confirmed the presence of shelf (clinoform topset) fluvial/tidal channel in the Miocene stratigraphic layers (Figure 7). The results of petrophysical analysis for the three IODP boreholes (Figure 1) will be used to calibrate the rock physics model parameters for channelized sediments. The calibrated models for variation of sand/shale ratio and sorting will then be used to interpret the inverted P-impedance (derived from acoustic inversion of seismic data) and Vp/Vs ratio (derived from AVO inversion of prestack seismic data) in terms of porosity and sand/shale ratio within these channels.

6 The uncertainty in rock physics modeling results During rock physics modeling, it is possible to decrease the error in the modeling process by comparing the real measurements with modeled values and by adjusting the model iteratively. However, these two values always misfit and should be reported as the model prediction error. Furthermore, the geological assumptions and sedimentological constraints applied to make the rock physics model are also erroneous. By applying these constraints and assumptions, an attempt is made to provide a quantitative paradigm for sedimentological variations in the most probable cases. Therefore, the predicted properties should be expressed by their probability density function (PDF) to reflect their uncertainty.

7 SIGNIFICANCE Some 200 million people live within the global coastal floodplain, less than 1 meter above current sea level. With the recent acceleration in global warming and ice-cover melting, sea-level rise and its effect on these low-lying areas have become a potential socio-economic hazard on a global scale. The NJ margin, with well-developed siliciclastic sequences of prominent clinoforms, has for decades been a focus area for investigating the effects of eustatic changes on sedimentary systems. The importance of improved understanding of coastal response to sea-level rise in this densely populated area was recently highlighted by 2012 Superstorm Sandy, the second costliest hurricane ($75B) in the US history that wreaked havoc on coastal NJ and New York. Large (>100m in the Pleistocene) sea-level changes have been occurring since the mid-Oligocene and have greatly affected sedimentation processes on this passive margin (Mountain et al. 2007). Although the timing and amplitudes of these eustatic changes are known, because of limited access to direct samples and poor time constraints, their effects on continental margin sedimentation have been difficult to evaluate (Miller et al., 2012). In 2015, a group of researchers (from Dalhousie University, University of Rutgers, and University of Texas at Austin) carried out an offshore 3D seismic survey on the NJ margin to provide high resolution imaging of the stratified sediments. The research proposed in here is the first to benefit from this newly acquired 3D seismic dataset to map paleo-sedimentological processes in the area. The 3D seismic imaging will be used to map and characterize nearshore features (e.g., meandering rivers, incised shelf valleys). Determining the sedimentological properties of these features and associated facies, that were developed during periods of known eustatic variations, is key to understanding the evolution of shorelines and quantifying timing and amplitude of the eustatic changes in each

Figure 7) Detecting some meander- like structures in the attribute analysis (spectral decomposition) of reflected seismic data from horizons m5.2 and m5.4 (Figure 2). A more advanced processing can increase the resolution of the result.

70 Hz

80 Hz

90 Hz

N

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geological period. Furthermore, integrating the seismic amplitude with sedimentological parameters in the New Jersey passive margin requires an accurate rock physics model for shallow unconsolidated sediments. The current rock physics models available for unconsolidated sediments are not capable of predicting the trends of elastic properties at low compaction pressures. Therefore, the rock physics model developed as a result of this study can be used as a more accurate default model for future studies in similar conditions.

8 REFERENCES

(IODP Expedition 313. IODP progress report. Aminzadeh F., Shivaji N. Dasgupta. 2013. Elsevier. Avseth, P, T Mukerji, G Mavko, et al. 2010. Geophysics, 75: 7531–7547. Avseth, P. 2000. Ph.D. Diss., Stanford Uni. Avseth, P., T. Mukerji, and G. Mavko. 2005. Cambridge Uni. Press. Berryman, J. G. 1980. The J. Acoustical S. Amer., 68: 1820-1831. Castagna John P, Herbert W. Swan, and Douglas J. Foster. 1998. Geophysics, 63: 948–956. Dutta, N.C., Utech, R.W., Shelander, D. 2010. The Leading Edge, 29: 930-942. Dvorkin, J., and Nur, A. 1996. Geophysics, 61: 1363-1370. Flórez-Niño, J.M. 2005. Ph.D. Diss., Stanford Uni. Goddard, J.D. 1990. Proceedings of the R. S. London. Series A, Math. Phys. Sci. , 430: 105-131. Greenlee, S.M., W.J. Devlin, K.G. Miller, et al. 1992. GSA bulletin, 104: 1403-1411. Gutierrez, M. 2001. Ph. D. Diss., Stanford Uni. Han, D. 1986. Ph. D. Diss., Stanford Uni. Jenkins, J., D. Johnson, L. La. Ragione, et al. 2005. J. Mech. Phys. Solids, 53: 197- 225. Lerch, C., Strauss, M., Meibur, E., et al. 2006. AAPG Annual Convention, Search & Disc. Art. Marion, D. 1990. Ph. D. Diss., Stanford Uni. Marion, D., Nur, A., Yin, H., et al. 1992. Geophysics, 57: 554-563. Mavko, G., and Jizba, D. 1991. Geophysics, 56: 1155-1164. Miller, K.G., Browning, J.V., Kominz, M.A., et al. 1996. Geol. S. Amer., Abst. with Programs. pp. A-62. Miller, K.G., Browning, J.V., Mountain, G.S., et al. 2013. Geosphere, 9: 1257-1285. Miller, K.G., Kominz, M.A., Browning, J.V., et al. 2005. Science, 310: 1293–1298. Miller, K.G., Sugarman, P.J., Browning, J.V., et al. 2012. Geosphere, 9: 1-22. Mindlin, R. D. 1949. J. App. Mech., 16: 259- 268. Mountain, G., and Monteverde, D. 2012. AGU Fall Meeting, Abst. Mountain, G.S., Proust, J.-N., McInroy, D., et al. 2010. IODP Management Inter. Inc. Murphy, W. F., III. 1982. Ph. D. Diss., Stanford Uni. NFS Collaborative Research proposal, 2014. [Online]. Nur, A., Marion, D., and Yin, H. 1991. Kluwer Academic Publishers, the Netherlands. pp. 131-140. Nur, A., Mavko, G., Dvorkin, J., et al. 1995. In Proceedings of the 65th An. Int. Meeting, SEG. p. 878. Oberkampf, W. L., S. M. DeLand, B. M. Rutherford, et al. 2000. Tech. report, Sandia Nat. Labs. Satterfield, W.M., and Behrens, E.W. 1990. Mar. Geol., 92:51–67. Van Wagoner JC, Mitchum RM, Campion KM, et al. 1990. AAPG. Meth. Exp. Series, 2: 55. Walton, K. 1987. J. Mech. Phys. Solids, 35: 213-226. Wang, Z. and Nur, A. 1992. SEG. Watts, A.B., and M.S. Steckler. 1979. AGU Maurice Ewing series, 3: 218-234. Yin, H. 1992. Ph. D. Diss., Stanford Uni. Zimmer, M. 2003. Ph.D. Diss., Stanford Uni.