Interpretation of Shear Wave Birefringence

We present an original method for estimating local shear wave birefringence properties for 3D surface P to S converted waves. To accomplish this we approach the problem using reverse VSP (RVSP). The method works in the pre-stack domain and uses the P waves converted to S as shear wave sources. We solve the transmission problem using the propagator matrix method. The importance of this method is that it does not require information about layering above the zone of interest and is accurate for estimating the anisotropy parameters. The method involves solving a non-linear problem in the frequency domain where Simulated Annealing is used as the global minimization technique. The procedure allows estimation of the propagator matrix related to the target zone, assuming plane wave propagation allows its diagonalization by pure rotations. This matrix diagonalization ends up with an estimation of the natural eigen directions of the medium when the range of offset angles does not exceed 35*. The proposed method is validated with synthetic RVSP data for two models with different densities of vertical fractures. Results show good accuracy in the estimation of the angle of the fractures for the whole range of offsets. The study also extends to show the dependence on the frequency and on the offset. Thesis supervisor: M. Nafi Toksdz Title: Professor of Geophysics Acknowledgments I would like to thank my adviser Prof. Nafi Toksoz for his guidance, encouragement and help during the time I spent at MIT. I benefited greatly from his philosophy in approaching the geophysical problems. My thanks go to Dr. John Queen for helping me with the theoretical aspects of the Propagator Matrix method and its applications over seismic data, and also for reviewing this thesis. His guidance and encouragement are also greatly appreciated. I wish to thank Dr. Rama Rao for discussing many aspects of the implementation of the Simulated Annealing technique and for reviewing Chapter 2 of this thesis. I would like to express my gratitude to Prof Dale Morgan, Prof. Michel Bouchon, Dr. Bill Rodi, Dr. Dan Bums, Dr. Matthias Imhof and Dr. Beltran Nolte for sharing their knowledge and for helpful discussions during classes. My special thanks go to my officemate and good friend Dr. Feng Shen for so many fruitful and valuable discussions about fractured reservoir characterization and seismic wave propagation. Her encouragement and friendship are also appreciated. Many thanks to my good friend, coworker and classmate Franklin Ruiz who experienced with me all this exciting and fruitful time at MIT. Only he and I know how hard is to be an MIT student and the head of a family at the same time. Thanks to my good friends Jonathan Kane and Wei Chen. We shared good and bad times during classes. Many thanks to all the fellow students and visiting scientists at ERL for sharing many things at MIT: Shirley Rieven, Dr. John Sogade, Hafiz Alshammery, Xiaojun Huang, AlDajani Abdulfattah, Mary Krasovec, Nancy Romero and Phil Reppert. Special thanks to Dr. Oleg Mikhailov and Dr. Bob Greaves for their encouragement. Thanks to Jane Maloof for helping with the computational facilities at ERL and for those many times I had to bother her asking for assistance. I am so grateful with Sue Turbak, Liz Henderson and Sara Brydges for always being there to help me. Special thanks go to Kate Jesdale who reviewed the technical writing of the thesis. These people make ERL a friendly and enjoyable place to work. I would like to thank my friends and coworkers Antonio De Lilla, Maria Perez and Reinaldo Michelena who helped me with many things from Venezuela. I really appreciate their friendship. Thanks to my friend Elias Ata and his family for all their help, encouragement and friendship that made the stay of my family less traumatic in this foreign country. Very special thanks to my lovely wife Maria Raquel for her understanding, encouragement and patience every day of my time at MIT and for taking care of our son Gabriel. Thanks Gabriel for your patience for all those times I could not be with you when you asked me for. You will understand when you grow up. Many thanks go to the whole of our family, especially my Mom, Reina, and Dad, Jesus, and to my in-laws Ecio and Raquel for their continued encouragement and support. I am very grateful to Intevep, S.A. for its financial support of my studies at MIT. Finally I greatly thank God for the health and strength I needed to succeed in my studies at MIT and throughout my life.