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\title{Joint Inversion of Reflectivity and \\
            Background subsurface components}
\dept{Geophysics}
\author{Alejandro Cabrales Vargas}
\principaladviser{Biondo Biondi}
\firstreader{Robert Clapp}
\secondreader{Jerry Harris}
\submitdate{August 2020}
%\thirdreader{Jane Supernumerary} %if needed
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\beforepreface
\prefacesection{Abstract}
\input{Chapters/Abstract}

\prefacesection{Preface}
\input{preface}

\prefacesection{Acknowledgments}

This section is perhaps the most difficult one of this dissertation for me to write. Although whatever flaw found in my research is solely my responsibility, the opposite is the truth; whatever contribution written here constitutes a learning experience I embarked on, and I owe gratitude toward many people. The problem is having someone out by accident or not honoring someone properly. I apologize beforehand for these people. If that happens, it is unintentional and merely a by-product of my non-brilliant mind.

I am deeply grateful to Biondo Biondi, who accepted me as a member of the prestigious SEP group and guided me throughout my Ph. D. journey. I am not exactly the kind of smart person he was surely expecting (as virtually all the SEPers are and have been). For that reason, I am also immensely grateful for his patience in my slow learning. Similarly, I also thank Robert ``Bob" Clapp for his invaluable help in almost everything. Is there something about seismic imaging that he ignores? Is there a piece of code that still resists his attacks to maximize the performance? I still have no answer to these questions.

I want to thank the other committee members, Jenny Suckale, Gary Mavko, and Jerry Harris. I did my second project with Jenny, and thereby I contributed on a tiny scale to rescue our planet (by understanding ice dynamics in Antarctica). Thanks to her merciless reviews, I improved my writing skills when it comes to redacting scientific papers. Gary was part of my committees until he retired, and then Jerry generously agreed to take the vacant place. I am very grateful to both of them.

Of course, I have special gratitude toward Jon Claerbout, not only because he is the reason SEP exists. My inspiration for getting into seismic imaging was reading Imaging the Earth's Interior. I reproduced his Ratfor codes in languages that I could use. After discarding Matlab, I tried C++ and then Fortran... just to come back to C++ when Bob declared the ``death" of Fortran. I think of him as a forever young man who never gets tired of sparking new ideas.

I thank Stewart Levin for his assistance in understanding the 3-D data that I used in this work, and in general, his help to all of us, the students.

I am in debt with the SEP crew for having, directly and indirectly, supported me. Each of their contributions was so important that the order in which I mention the people is irrelevant. Something important that they gave me as a group was the sense of humbleness, something that I need to cherish and transmit to the highly arrogant oil \& gas world in Mexico. Rather than monotonically thanking each SEPer, I implicitly thank them by describing my relationship and perception of each one of them. I do not wish to omit that my intrinsic personality, that of an introvert, always afraid of saying B.S., unfortunately, was the stumbling block that did not allow me to be closer to them (or to other people in the department for that matters). 

Yi Shen was my office-mate, and still is my ever-smiling friend that was always there to make me feel good when the ``pre-quals" stress manifested.

Huy Le is an introvert person, almost like myself. However, he is the anisotropy expert, and a dangerous player of the GPU computing game (and also the soccer game!). From him, I learned that, despite starting a project being utterly ignorant about something (in this case, seismic imaging), one could become an expert with enough hard work and dedication.

The Ettore-Guillaume duet has helped most students, and I am very grateful to them for the excellent solver that saved me one year of work. Ettore is always smart and enthusiastic at explaining and sharing his vast knowledge. As for Guillaume, I have admired his tenacity and persistence about thoroughly understanding whatever topic. That is more amazing considering his advanced age (at least in appearance!)

Rahul Sarkar is undoubtedly the group's expert in inverse theory (and more recently in quantum computing). Thanks to Rahul, I understood why the method that I humbly propose in this dissertation had no hope to work within the linear regime. Unfortunately, I could not stay longer at Stanford to work with him. I have to say that I was fortunate enough to have the opportunity to know him better during the period that we worked together when he accepted the challenge of suffering my slow learning. 

Our most recent post-doc, Ariel Lellouch, is also my friend and a person full of sense of humor. I admire his leadership (something I am still not good at) and his fast thinking, so he is prone to produce rapid and pertinent opinions about research works, even when he is an expert on a particular topic.

Stuart ``The Young" Farris (to be distinguished from Stewart ``The Wise" Levin), among the other young people of the group, taught me the valuable lesson that one should listen to and learn from everybody, notwithstanding that he or she is younger by more than one decade. Stuart constitutes an epitome of a person that can be smart, young, and mature at the same time.

Joseph Jennings, ``mi amigo Joe", always helped me to practice my Spanish. Seriously, he helped me better understand the 3-D dataset that I use for Chapter 5 and to understand the adjoint method better. He is also an excellent friend that always was there to listen to my weird stories. I will miss him so much!

Taylor Dahlke and I started a friendship soon after we began interacting, almost by chance at the beginning. He happened to be working with the same 3D dataset that I used in Chapter 5 and helped me understand the OBC acquisition. Moreover, he performed most of the processing that made the data ready for imaging, which was invaluable for saving time and relaxing my tight deadline. I will also miss him!

Mademoiselle Fantine Hout is a polyglot lady that speaks many languages, including Machine Learning, every day more ubiquitous in the Geophysics community (Some people say that even Guillaume would be learning it soon). Always prone to give away a warm and charming smile, among other things, she assisted me when I started working in the cluster with the now famous (and thoroughly undecipherable) Yang's code. She also played the role of my adopted daughter when we mischievously visited Disneyland during the SEG Annual Meeting in Anaheim.

Yinbin Ma has been quite an enigmatic character. He helped me understand a lot of useful stuff during the implementation of my codes, including the violation of causality that prevented my Born operator from passing the dot-product test. He also wrote the code that I (and some other people) use to compute the random boundary condition. However, I have the feeling that sometimes he does not appreciate his skills. Therefore, I want to publicly manifest that he is an expert in inverse theory and computation sciences, besides an excellent friend.

Rustam Akhmadiev and Siyuan Yuan spent quite a long time with me when they join the group. Siyuan was my office-mate (until I decided to work outdoors). Rustam has contagious enthusiasm and mastery in muscle-ups. He also taught me that you could do it when you want to learn something (for instance, Spanish!)

Milad Bader helped me during my TAship, in a very particular way. He was taking the courses. The other student in the class has a hyperactive and inquiring mind, and his questions quite often went beyond my knowledge. Milad came to assist me in answering such questions. I arguably learned more stuff than that that I helped to teach during such periods. Thanks to both of them!

Now it is the turn of my friend Julio Frigerio, who unfortunately joined the group too close to my departure. If I felt that my situation was desperate, having five years to achieve graduation in SEP, he came with the consign to finish in only three and a half! Nevertheless, he shows an untamed spirit and such a badass attitude that I cannot but admire. Moreover, I certainly cannot hide my awe at someone who understands Einstein's General Relativity.

Special thanks to Kurt Marfurt, my masters' advisor in Oklahoma. He encouraged me to work in the least-squares Kirchhoff time migration. It was the moment when I jumped from seismic interpretation to seismic imaging.  

Speaking of the Mexican crew, I am very thankful to my mentor, Sergio Ch{\'a}vez, who, since our encounter in his class (which I was merely auditing at that time), has never run out of advice. I also thank him for having made me moved from water to oil \& gas exploration. Also, thanks to the Pemex crew: My current boss, Humberto Salazar; my short-time boss, Carlos Caraveo; my colleagues, Alfredo V{\'a}zquez, Israel Ronz{\'on}, Rub{\'e}n Ponce, Sergio Romahn, Karen Hern{\'a}ndez, Alejandra M{\'e}ndez, Silvino Dom{\'i}nguez, Jorge Chagolla, Madai Galero, and Juan N{\'a}jera. Special thanks to my former boss, Marco V{\'a}zquez, who firmly pushed me to apply for Stanford when I was reluctant about that. Thanks to my everlasting friends Javier ``Oso" S{\'a}nchez, {\'O}scar ``Cyranus" Boni, and Vicente ``Rayita" Hern{\'a}ndez, with whom I took my first steps toward the steep and thorny road of geophysics. Last but not least, thanks to my colleagues Humberto Ar{\'e}valo, Mois{\'e}s Hern{\'a}ndez, and their families, who faced the challenge of being a graduate student at Stanford before me.

Of course, I dedicate this work to the loves of my life: my wife Patricia, and my daughters, Zaira and Parisa. They endured with me a five-years life adventure at Stanford, far from our beloved ones. I also dedicate my work to my parents, Manolo and Lucha, my siblings, Manuel, Roberto, Lucy and Lupita, and all my relatives, who never lost faith in me!

{\it ``...when you have eliminated the impossible, whatever remains, however improbable, must be the truth."}
Sherlock Holmes to Dr. Watson in ``The sign of the four", by Arthur Conan Doyle.

\afterpreface

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%\chapter{Conclusions}

\appendix
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