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Seismic Anisotropy: Geological Causes and Its Implications to Reservoir Geophysics

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Seismic Anisotropy: Geological Causes and Its Implications to Reservoir Geophysics SEISMIC ANISOTROPY: GEOLOGICAL CAUSES AND ITS IMPLICATIONS TO RESERVOIR GEOPHYSICS A DISSERTATION SUBMITTED TO THE DEPARTMENT OF GEOPHYSICS AND THE COMMITTEE ON GRADUATE STUDIES OF STANFORD UNIVERSITY IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY Kaushik Bandyopadhyay August 2009 © Copyright by Kaushik Bandyopadhyay 2009 All Rights Reserved ii I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. ___________________________ Gary Mavko (Principal Adviser) I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. ___________________________ Biondo Biondi I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. ___________________________ Tapan Mukerji I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. ___________________________ Jack Dvorkin Approved for the University Committee on Graduate Studies iii iv Abstract The primary focus of this dissertation is to improve the applicability of rock physics models for elastic anisotropy through useful approximations, empirical relations, and practical workflows considering the geological origins of rock anisotropy. Anisotropy arises from aligned heterogeneities at scales smaller than the scale of measurement. Ignoring elastic anisotropy may lead to poor seismic imaging, inaccurate well-ties, and incorrect interpretation of seismic data. Directional dependency of seismic wave propagation has become even more important with the routine acquisition of long offset, wide azimuth P-wave, S-wave and converted wave seismic data. The mathematics of rock anisotropy is far more advanced than what we can apply in practice. This is because we do not make enough measurements to completely characterize all of the input parameters necessary for anisotropic rock physics modeling. The main objective of this dissertation is to improve the applicability of anisotropic rock physics models considering the geological origin of elastic anisotropy. We present simplified linearization of the anisotropic models, provide empirical constraints on the input parameters and present practical workflows to model elastic anisotropy considering their geological cause. We consider three important geological origins of elastic anisotropy in sedimentary rocks: (a) anisotropy due to shale, (b) anisotropy due to stress and fractures, and (c) anisotropy due to fine laminations. Additionally, we explore the effect of fluids in modifying the anisotropy resulting from these causes. First, we present rock-physics modeling strategies for elastic anisotropy in (a) organic-rich source rocks and (b) shallow compacting shales. Our laboratory v measurements on compacted pure clay minerals show increasing velocity anisotropy with increasing compaction. However, our experiments suggest that a simple compaction- dependent clay orientation model may not always be valid. A compilation of ultrasonic velocity measurements was used to obtain useful links between the anisotropy parameters and commonly measured vertical velocities. Furthermore, we present simplified equations linking textural orientation in shale to anisotropic Thomsen’s parameters. Second, we present a method to compute the third order elastic coefficients from isotropic measurements, combining a compliant-porosity based stress-induced anisotropy model with the third order elasticity formalism. In addition, we invert the third order elastic coefficients from our compiled database on shale anisotropy. The third order coefficients in shale do not show any apparent inter-relationships. However, we show that in highly anisotropic organic shales, the third order coefficients increase with increasing thermal maturity of source rock. Third, we derive simplified equations for Walton’s contact-based model for stress- induced anisotropy in unconsolidated sandstones. Such simplifications make the application of the anisotropic model simpler and computationally more efficient. We extend this granular, contact-based model to sandstones with pressure solution. Finally, we derive an approximate form of the Gassmann’s anisotropic fluid substitution equations for vertical velocities, and present the fluid substitution equations in terms of the Thomsen’s parameters. Our approximation enables one to perform anisotropic fluid substitution for vertical velocities with fewer anisotropy parameters. It reveals that, in a VTI medium, it is the Thomsen’s parameter, δ , that controls the anisotropic contribution to the vertical velocity during fluid substitution. vi Acknowledgments Last five years at Stanford is one of the most important, exciting and enjoyable phase in my life. There are many people who made this journey a unique experience. First of all, I would like to extend my deepest gratitude to my adviser, Gary Mavko. This dissertation was inspired by Gary, and was enriched by his ideas and insights. Endless scientific discussions with him have always been a great pleasure for me. I feel honored and privileged to be one of his students. I thank Tapan Mukerji for his teachings, feedbacks, and encouragements. This dissertation would not be possible without his advice on many of the technical details. I find his guidance on writing and on presentations extremely valuable. I thank my other committee members, Biondo Biondi and Jack Dvorkin for their constructive comments and excellent suggestions. I thank Dave Pollard for agreeing to chair my dissertation defense. Thanks also to Fuad Nijim, for taking care of all the administrative details. I thank Tiziana Vanorio for teaching me how to measure ultrasonic velocities in the laboratory. She initiated our collaboration with Rudy Wenk, at University of California, Barkeley. I thank Rudy Wenk and Marco Voltolini for their collaborations. I would like to thank SRB and its industrial affiliates for financial support. Thanks also to Charlie West, Fersheed Mody and Mike Payne for showing the practical aspects of my research during my summer internships. My colleagues and friends at Stanford made sure that I always had a nice time. I thank all the members of the SRB group whom I had the pleasure of knowing and vii working with - Carmen, Cinzia, Danica, Ezequiel, Franklin, Kevin, Kyle, Pinar, Piyapa, Ramil, Richa, Stéphanie, and Youngseuk. Thanks you all for your discussions and criticisms during our group seminars. I thank Jeetendra Gulati for teaching me driving and for his great advices about the Bay Area. Thanks to Whitney Trainor for showing me a little piece of the real America. A special thanks to my office-mate Ratna for all the discussions we had on Mitchell Patio during our numerous breaks, for all the nice food he cooked for us and for all his great company during our drives to Houston. Finally I thank my best friend, Tanima, who is also my wife, colleague and critic. I dedicate this dissertation to my parents, Kalpana and Kashinath Bandyopadhyay, Tanima, and our son, Anik. viii Contents Abstract….....……………………………………………………………………………...v Acknowledgements….…………………………………………………………...............vii Contents……………………………………………………………………………...…...ix List of Tables..……...…………………………………………………………...............xiii List of Figures.……...…………………………………………………………................xv Chapter 1 Introduction.....................................................................................................1 1.1 Motivation and objectives................................................................................... 1 1.2 Chapter Descriptions........................................................................................... 2 1.3 References........................................................................................................... 4 Chapter 2 Elastic Anisotropy in Shale ............................................................................7 2.1. Abstract............................................................................................................... 7 2.2. Introduction......................................................................................................... 9 2.3. Origin of Anisotropy in Shale........................................................................... 11 2.3.1. Fabric due to Depositional Setting............................................................ 12 2.3.2. Fabric due to Biological Activities ........................................................... 13 2.3.3. Fabric due to Mechanical Compaction ..................................................... 13 2.3.4. Fabric due to Silt Content ......................................................................... 15 2.4. Rock Physics Models for Elastic Anisotropy in Shale ..................................... 18 2.4.1. Anisotropic Self Consistent Approximation (SCA) ................................. 18 2.4.2. Anisotropic Differential Effective Medium Model .................................. 20 2.4.3. Thomsen’s Parameters.............................................................................. 21 2.4.4. Compaction-dependent Grain Orientation................................................ 22 2.4.5. Layered Medium: Backus Average .........................................................
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