Linearized inversion frameworks toward high-resolution seismic imaging By Ali Aldawood In Partial Fulfillment of the Requirements of Doctor of Philosophy Earth Sciences and Engineering Department Physical Sciences and Engineering Division King Abdullah University of Science and Technology, Thuwal, Kingdom of Saudi Arabia September, 2016 2 The thesis of Ali Aldawood is approved by the examination committee Committee Chairperson: Ibrahim Hoteit Committee Member: Tariq Alkhalifah Committee Member: George Turkiyyah Committee Member: Abdullatif Al-Shuhail Committee Member: Mohammed Alfaraj 3 Copyright ©2016 Ali Aldawood All Rights Reserved 4 ABSTRACT Linearized Inversion Frameworks toward High-resolution Seismic Imaging Ali Aldawood Seismicexplorationutilizescontrolledsources,whichemitseismicwavesthatprop- agatethroughtheearthsubsurfaceandgetreflectedoffsubsurfaceinterfacesandscat- terers. The reflected and scattered waves are recorded by recording stations installed along the earth surface or down boreholes. Seismic imaging is a powerful tool to map these reflected and scattered energy back to their subsurface scattering or reflection points. Seismic imaging is conventionally based on the single-scattering assumption, where only energy that bounces once off a subsurface scatterer and recorded by a re- ceiver is projected back to its subsurface position. The internally multiply scattered seismic energy is considered as unwanted noise and is usually suppressed or removed from the recorded data. Conventional seismic imaging techniques yield subsurface images that suffer from low spatial resolution, migration artifacts, and acquisition fingerprint due to the limited acquisition aperture, number of sources and receivers, and bandwidth of the source wavelet. Hydrocarbon traps are becoming more chal- lenging and considerable reserves are trapped in stratigraphic and pinch-out traps, which require highly resolved seismic images to delineate them. This thesis focuses on developing and implementing new advanced cost-effective seis- mic imaging techniques aiming at enhancing the resolution of the migrated images by 5 exploiting the sparseness of the subsurface reflectivity distribution and utilizing the multiples that are usually neglected when imaging seismic data. I first formulate the seismic imaging problem as a Basis pursuit denoise problem, which I solve using an L1-minimization algorithm to obtain the sparsest migrated image corresponding to the recorded data. Imaging multiples may illuminate subsurface zones, which are not easily illuminated by conventional seismic imaging using primary reflections only. I then develop an L2-norm (i.e. least-squares) inversion technique to image internally multiply scattered seismic waves to obtain highly resolved images delineating vertical faults that are otherwise not easily imaged by primaries. Seismic interferometry is conventionally based on the cross-correlation and convo- lution of seismic traces to transform seismic data from one acquisition geometry to another. The conventional interferometric transformation yields virtual data that suffers from low temporal resolution, wavelet distortion, and correlation/convolution artifacts. I therefore incorporate a least-squares datuming technique to interferomet- rically transform vertical-seismic-profile surface-related multiples to surface-seismic- profile primaries. This yields redatumed data with high temporal resolution and less artifacts, which are subsequently imaged to obtain highly resolved subsurface images. Tests on synthetic examples demonstrate the efficiency of the proposed techniques, yielding highly resolved migrated sections compared with images obtained by imaging conventionally redatumed data. I further advance the recently developed cost-effective Generalized Interferometric Multiple Imaging procedure, which aims to not only image first but also higher-order multiples as well. I formulate this procedure as a linearized inversion framework and solve it as a least-squares problem. Tests of the least-squares Generalized Inter- ferometric Multiple imaging framework on synthetic datasets and demonstrat that it could provide highly resolved migrated images and delineate vertical fault planes compared with the standard procedure. The results support the assertion that this 6 linearized inversion framework can illuminate subsurface zones that are mainly illu- minated by internally scattered energy. 7 ACKNOWLEDGEMENTS “No duty is more urgent than that of returning thanks.” ∼ James Allen To my supervisor, Prof. Ibrahim Hoteit, to you I express my sincere thanks. I would never forget his warm welcome on my first day when I first joined his data assimilation group. His guidance and high expectations never seized to motivate and push me to work harder. His wide knowledge on many geophysical data inversion problems continued to enlighten me and really assisted me in finding solutions. I am grateful for his personal involvement and support with my business travel so I can present my work at prominent international conferences in Europe, United States, and the Middle East. I hope that our scientific collaboration continues for many years to come during my professional career. My thanks are also extended to my sponsoring company, Saudi Aramco, for its solid commitments to develop its employee through higher education and training. Heartfelt gratitude goes to my dissertation committee members, Prof. Tariq Alkhali- fah and Prof. George Turkiyyah. Dr. Alkhalifah’s deep knowledge and understanding of wave-propagation physics and seismic imaging and inversion helped me pursue my desired research direction whereas Dr. Turkiyyah’s computational and optimization knowledge helped me execute my proposed solutions and be more efficient in the op- timal direction of research. I would also like to take the opportunity to thank my external collaborators, Prof. Abdullatif Alshuhail and Dr. Mohammed Alfaraj. Their personal and technical advises helped me strengthen my research base and overcome many obstacles. I am thankful to my teachers, friends, cousins, and KAUST colleagues; namely Mo- 8 hammad Zuberi whose earlier work has become the base of my thesis dissertation topic. “A happy family is but an earlier heaven.” John Bowring. To my parents, all my achievements and successes would not have been possible with- out my parents’ love, prayers and endless support. I can never thank them enough. I dedicate this dissertation and my success to them. 9 TABLE OF CONTENTS Examination Committee Approval 2 Copyright 3 Abstract 4 Acknowledgements 7 List of Abbreviations 10 List of Figures 11 1 Introduction 12 1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.2 Thesis Objectives and Contributions . . . . . . . . . . . . . . . . . . 17 2 The Possibilities of Compressed-sensing based Kirchhoff pre-stack Migration 20 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.2 Least-square migration . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.3 Compressed sensing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.4 Single scatterer example . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.5 Horizontal layers example . . . . . . . . . . . . . . . . . . . . . . . . 29 2.6 Fault model example . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.7 Robustness to Observation Noise . . . . . . . . . . . . . . . . . . . . 32 2.8 Robustness to Velocity Error . . . . . . . . . . . . . . . . . . . . . . . 33 2.9 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3 The Possibilities of Least-squares Migration of Internally Scattered Seismic Energy 43 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 3.2 Single-scattering modeling and inversion . . . . . . . . . . . . . . . . 46 10 3.3 Double-scattering modeling and inversion . . . . . . . . . . . . . . . . 49 3.4 Imaging vertical fault planes . . . . . . . . . . . . . . . . . . . . . . . 52 3.5 Robustness to Observation Noise . . . . . . . . . . . . . . . . . . . . 53 3.6 Robustness to Velocity Error . . . . . . . . . . . . . . . . . . . . . . . 54 3.7 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 4 Least-squares Datuming of VSP Multiples 67 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 4.2 Least-squares datuming . . . . . . . . . . . . . . . . . . . . . . . . . 70 4.3 Numerical Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 4.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 5 Least-squares generalized interferometric multiple imaging 84 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 5.2 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 5.3 Numerical Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 5.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 6 Concluding Remarks and Future Work 100 6.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 6.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 References 104 Appendices 114 4