Robert H. Stolt is an American geophysicist and the inventor of (f,k) migration.
Early years and education
Robert H. Stolt earned a B.S. in mathematics and physics from Wyoming University in 1966 and a Ph.D. in theoretical physics from the University of Colorado in 1970. He also served as a post doctoral fellow at CU for a year before joining Conoco in 1971.
Dr. Stolt has contributed much to the geophysical technologies that Conoco and the industry have used and continue to use today.
SEG 2019 Maurice Ewing Medal Award 
Robert Stolt was awarded the Reginald Fessenden Award for his pioneering landmark contribution to seismic migration in the Fourier domain. One of his subsequent major contributions was the extension of his original f-k migration algorithm to provide the only comprehensive, inclusive and effective method for imaging and inverting specular and non-specular reflectors. He has been and remains the epitome, the lodestone, and the main engine of direct seismic migration and inversion methods that are based on well-founded physics with clear derivations that make both the strengths and the limitations and assumptions behind his new methods and algorithms transparent and abundantly clear. He has been a leader in extending and merging two previously disjointed and unconnected activities into one framework with migration-inversion.
Biography Citation for the 2019 SEG Maurice Ewing Medal Award
Robert H. Stolt earned his PhD in physics at the University of Colorado, in the research area of parastatistics, mentored by professor John Taylor, followed by a postdoctoral fellowship with professor Wes Britain in many-body theory. Bob entered the petroleum industry and joined Conoco Research in Ponca City, Oklahoma, in 1971. At Conoco, Bob flourished in a positive and enlightened Conoco research culture, moving to a technical leadership position and inheriting the mantle of preeminent researchers like Pierre Goupillaud and Jerry Ware.
In 1980, Bob received the SEG Reginald Fessenden Award for his pioneering work on f-k migration. His contribution is known worldwide as Stolt f-k migration. In 1998, Bob received the SEG Honorary Membership Award, recognizing his landmark contributions to seismic migration and inversion. In this citation, I will describe Bob’s substantive and impactful contribution since 1998 that goes far beyond his earlier landmark contribution to f-k migration. Wave theory methods for migration were introduced in the 1970s. These migration methods consisted of two ingredients — a wave propagation model and an imaging principle — and three distinct imaging principles were introduced. The imaging principle behind f-k migration involved using surface-recorded reflection data to predict a source and receiver reflection experiment at a coincident point in the subsurface and asking for the time-equals-zero value of that experiment. That imaging principle has tremendous conceptual and practical advantages in terms of clarity, meaning, and physical interpretability when compared to the other two original imaging principles.
Bob made two major conceptual and practical extensions to the most effective of the original imaging principles that resides behind f-k migration. The f-k migration result outputs a data-like scalar point function, a structure map, and image. Bob realized that to output more than a number at each point on the structure map — to provide, for example, an angle-dependent function (for amplitude analysis) at every point on the structure — the original and at that time most effective imaging principle behind f-k migration was too rigid and restrictive. He recognized that the original f-k migration result produced a highly localized band-limited singular function at every point on the structure, and within the character of that singular function resided information on the angle-dependent information needed to go beyond a structure map to amplitude analysis. Bob responded to that challenge and introduced a new imaging principle, by relaxing the coincident source and receiver condition of the original f-k migration. He examined the resulting offset dependence of the original f-k migration imaging principle in the Fourier conjugate to offset domain. The latter dependence provided angle-dependent amplitude information, and subsequent analysis, at every point on the structure map. Bob’s advance from migration to migration-inversion can be viewed as a (naturally and much more complicated) multidimensional extension and generalization of the earlier one-dimensional NMO-stack evolving to NMO-AVO. The second part of his new and extended imaging principle introduces the concept of a point reflectivity that automatically accommodates specular and non-specular reflectors. To realize those advances, Bob connected with and extended linear inverse scattering methods to prestack seismic data and multiparameter acoustic and elastic 2D and 3D earth models. That allowed the original wave theoretic migration and imaging principle behind Bob's f-k migration to provide a fundamentally new and quantitatively interpretable imaging principle for migration. Rather than seen as the end product, this new migration is now a preprocessing intermediate step and stage for first locating where any subsurface physical property changed (a reflector) and then to determine what specifically has changed and by what amount. Migration evolved into migration-inversion, determining first where something changed (migration) before using that new extended form of f-k migration to determine what specifically changed and by what amount (inversion). That contribution provided a new framework that superseded the conventional view that these were two (i.e., migration and inversion) entirely unrelated topics. Prior to Bob’s advancement, those who practiced migration and those who practiced amplitude analysis (for example, trace integration, model-matching and AVO) basically ignored each other (at best) and their inconsistent and contrary views of the world. Bob extended the imaging principle to allow for both structure and amplitude analysis in a multidimensional subsurface, that with one algorithm automatically accommodates planar, curved, undulating, and diffractive reflectors and pinch-outs. At that time, the seismic world was separated into two camps: migration and amplitude analysis. The migration community cared about “where” in a multidimensional subsurface, but didn’t care about “what” changed, while the amplitude analysis people assumed a one-dimensional subsurface and cared about what changed but didn’t care about where. In many research labs, these two groups were kept physically separated and often were located on different floors.
As with all major new ideas in the history of science, Bob’s idea of “where before what,” or migration-inversion in a multidimensional subsurface, faced tremendous headwinds and resistance from both the migration and the AVO communities and practitioners. Bob and his colleagues held steady, kept moving forward, and eventually persevered.
Bob was the concept and idea generator, the point man and driving force in the development of migration-inversion, a major advance in seismic data processing. That development was inspired and influenced by scattering theory concepts. Bob’s extended source and receiver experiment at depth imaging principle was the most comprehensive, capable, and interpretable imaging theory for migration at that time, and remains that today. The M-OSRP group at the University of Houston has recently advanced Bob’s extension of his original f-k migration method to allow for discontinuous rapidly varying and smoothly varying heterogeneous media, producing the first migration method for a heterogeneous subsurface that avoids high frequency approximations, in both the imaging condition and the wave propagation model. That migration is equally effective for all frequencies at the target, with practical advantages for structural resolution, illumination, and target identification. Bob's contribution to the theory of migration ultimately entered inverse scattering series (ISS) multiple removal methods that he helped pioneer and collaborated on, producing methods that allowed multiples to be removed that were generated by specular or nonspecular reflections, without needing to know, estimate, or ever determine anything about the subsurface or the reflectors that generated the multiples. Those multiple removal methods are the most capable methods available today and are offered by all the major oil service companies, (among them PGS, Western-Geco Schlumberger, BGP, CGG, and TGS) with innumerable published references from both industry and academia that document the worldwide usage and impact on both offshore and onshore plays. In addition to being the only methods for free surface and internal multiple removal that require no subsurface information, another reason the ISS internal multiple attenuation and elimination algorithms are so effective is the ISS internal multiple algorithms incorporate the prestack form of extended f-k migration that Bob pioneered and delivered, the only form of migration (the most capable and effective migration method at that earlier time, and currently) that within the context of multiple prediction automatically accommodates both specular and nonspecular multiple generators, including pinch-out generators and head-waves as subevents of the multiple to be removed. The most popular form of migration today, reverse time migration, in all its various extensions and incarnations, derives from a separate and intrinsically less capable choice among the three original imaging principles, and they are unable to match that set of standalone imaging, resolution, illumination, and inversion strengths and capabilities. Over the years, the direct inversion methods that were derived as distinct isolated task inverse scattering subseries (for free surface and internal multiple removal, depth imaging, parameter estimation, and Q compensation, each without any subsurface information known, estimated or determined) would run into either theoretical, practical, or political obstacles with no shortage of naysayers at every step of the way. Bob was the one individual in our leadership team always ready with a positive word of optimism, encouragement, and support, and always available at a darkest moment when needed most. Bob has played and continues to play a key role in that success and continuing campaign and delivery. I will always remember and will forever be grateful and appreciative. During the 1980s, Bob was developing computer processing algorithms for dip moveout and amplitude-preserving prestack cascading time migration. Bob's work in migration and inversion culminated in coauthorship (with Al Benson) of a classic migration textbook published in 1986. In 2012, Bob and I published the first of a two-volume graduate text for Cambridge University Press, Seismic Imaging and Inversion: Application of Linear Inverse Theory. The second volume, Seismic Imaging and Inversion: Application of Direct Non-Linear Inverse Theory, is currently underway and being written. Volume two provides a first single comprehensive framework and platform that derives both the direct linear seismic methods for imaging and inversion that require a velocity model (volume one) and the direct non-linear methods for all seismic processing objectives that do not require or need a velocity model or any subsurface information (volume two) with the former derived as a special and limiting case of the latter. Those two volumes describe what Bob, his coauthor, their colleagues, and their students have pioneered, developed, and continue to deliver, along with open issues. During 1979–1980, Bob served as a consulting professor and acting director of the Stanford Exploration Project. He helped that prestigious group in developing breakthroughs in inversion and multiple attenuation. Bob has served SEG in a number of capacities including as associate editor and then editor of Geophysics, Chairman of the Publications Committee, Technical Program Chairman of the 1994 Annual Meeting, and as a member of the Research Committee since 1991. He is an Honorary Member of the Geophysical Society of Tulsa. Bob was selected to receive the DuPont Lavoisier Medal, an award recognizing great technical and creative accomplishments and contributions over many years that resulted in a measurable business impact of enduring significance. The winners represent the best scientists and engineers in DuPont's history, and Bob is one of the few recipients who was an active employee at the time of his award. In 2017, Bob was inducted into the Offshore Energy Center Hall of Fame.
Bob was the highest-ranking technical person in Conoco. In his role as senior research fellow, he made tremendous advances in imaging and in multiple attenuation. He continues to be extremely active and productive since his retirement from ConocoPhillips.
Bob is devoted and dedicated to his wife Donna, his family, and his community. He is a role model of quiet confidence, competence, and integrity. It has been my great good fortune to work with many brilliant, creative, and prolific scientists, and it is not the slightest exaggeration to say that Bob is in a separate highest tier and category by himself. It is my honor, privilege and pleasure to write this citation for the 2019 SEG Maurice Ewing Award for Robert H. Stolt.
Award Citation for Bob Stolt's 1998 Honorary Membership in SEG
Contributed by John R. Hopkins
I consider it an honor to write this citation for Bob Stolt's Honorary Membership in SEG.
I first met Bob Stolt in early 1974 while interviewing for a job at Conoco. I could tell right away that I was in the presence of an intellectual giant and hoped for a chance to work for a company that hired people like Bob. Being hired by Conoco was the beginning of my good luck. Bob's good luck started when he married Donna. He has a great sense of humor, although it's often so "dry" that only the most attentive listeners understand.
He earned a B.S. in mathematics and physics from Wyoming University in 1966 and a Ph.D. in theoretical physics from Colorado University in 1970. He also served as a post doctoral fellow at CU for a year before joining Conoco in 1971.
Bob has contributed much to the geophysical technologies that Conoco and the industry have used and continue to use today. Over the years, Bob has been a technical leader and a leader of people and often both. Under his managerial leadership, Conoco was able to remain competitive in the geophysical sciences during the "bust" years. When Bob assumed a supervisory position in 1977, he was still working on f-k migration. After publishing the landmark paper in 1978 on f-k migration, frequently referred to as "stolt migration," he started to also work in seismic inversion. This work led to another internationally recognized paper in 1981 with R. W. Clayton.
During the 1980s, Bob was developing computer processing algorithms for dip moveout and amplitude-preserving prestack cascading time migration. Bob's work in migration and inversion culminated in coauthorship (with Al Denson) of a classic textbook published in 1986.
Once more powerful computers were available, Bob began to develop new methods in inversion, partial migration, demigration, and multiple removal. He had such a unique understanding of the relationships between computing speed and his developments that he was able to focus on techniques that could be implemented cost-effectively on the available machines. This insight into the linkage between computers and geophysics is rare.
Bob received the Reginald Fessenden Award in 1980 for his pioneering work in f-k migration. During 1979-1980 he served as a consulting professor and acting director of the Stanford Exploration Project. He helped that prestigious group in developing breakthroughs in inversion and multiple attenuation. Bob has served SEG in a number of capacities including Associate Editor, then Editor of Geophysics, Chairman of the Publications Committee, Technical Program Chairman of the 1994 Annual Meeting, and as a member of the Research Committee since 1991. He is an Honorary Member of the Geophysical Society of Tulsa.
Recently, Bob was selected to receive the DuPont Lavoisier Medal, an award recognizing great technical and creative accomplishments and contributions over many years which resulted in a measurable business impact of enduring significance. The winners represent the best scientists and engineers in DuPont's history, and Bob is one of the few recipients who were active employees at the time of their award.
Bob is now the highest ranking technical person in Conoco. In his new role as senior research fellow, he has resumed his brilliant work in multiple attenuation, and I expect that SEG members will see more breakthroughs from his "leading edge" work in years to come.
Once again, it's an honor for me to write this citation for Bob Stolt, and it's been fun and a great privilege to have interacted with this principle-centered man for 24+ years.
Award citation for the SEG Reginald Fessenden Award, 1980
This award, designated the SEG Medal Award at its inception in 1961, was renamed in 1977 to recognize Reginald Fessenden for his role as the originator of the concept of reflection and refraction surveying in 1917. It is awarded to a person who has made a specific technical contribution to exploration geophysics, such as an invention or a theoretical or conceptual advancement, which, in the opinion of the Honors and Awards Committee and the Executive Committee, merits special recognition.
R. H. (Bob) Stolt was selected for the Reginald Fessenden Award because of his work in wave equation migration and his F-K migration paper, "Migration by Fourier Transform." Bob's F-K migration makes use of Fourier transforms in both space and time, resulting in an algorithm which is both computationally efficient and accurate for steeply dipping events. Once the two-dimensional Fourier transform was taken, Bob made use of the fact that the tangent of the apparent dip angle is equal to the sine of the true dip angle. Migration in F-K space then becomes a matter of frequency shifting determined by this simple geometrical relation. The migrated section in space and time is then obtained by an inverse transform. The algorithm becomes, with a little physical insight, a clean and efficient work of art and not a clumsy, brute force approach consisting of many Fourier transforms.
The paper was received by the Editor of GEOPHYSICS in September 1976, presented to the Stanford Exploration Project (SEP) in May 1977, and finally published in February 1978. However, because of the release through SEP, the results were widely known and used much earlier than the publication date by purchase of software based on Bob's analysis. As a result of this work, Bob was asked to direct the SEP for the 1979-1980 academic year while Jon Claerbout was on sabbatical. In a characteristic manner, Bob decided to accept this new challenge leaving behind almost all of his old books, old problems, and old ideas, with some concept of interacting with the students at Stanford and examining anew the ideas of scattering theory. This new venture and interaction was very successful, and the exciting new results may force us all to learn more about scattering theory, Gelfand-Levitan algorithms, and even Dirac notation!
Bob Stolt is one of those quietly competent physicists who enjoys his family, religion, science, and fellowship with others in rarely balanced fashion. His contentment with himself and his confidence in his own abilities allows him to face the outside world with an open mind and an unpretentious manner. These qualities, coupled with such a warm personality and willingness to help others, makes his advice constantly sought after from his peers, since seldom can one obtain such valued advice and counsel so painlessly. With the possible exception of Einstein, he holds no one in too high esteem and, similarly, holds contempt for no man. His sense of humor makes him a pleasure to work with and often allows him to become the "soft shoe" act in any sequence of presentations. It is impossible to sleep through one of his talks for fear you might miss one of his subtle jokes, a tricky bit of mathematical physics, or his physical insight which suddenly explains the entire phenomenon.
It is hoped that Bob Stolt's new work on scattering and inverse scattering theory will be as useful and applicable to geophysics as his work on F-K migration.
- Honors and Awards, The Leading Edge Volume 38, Issue 11.
- Whaley, J., 2017, Oil in the Heart of South America, https://www.geoexpro.com/articles/2017/10/oil-in-the-heart-of-south-america], accessed November 15, 2021.
- Wiens, F., 1995, Phanerozoic Tectonics and Sedimentation of The Chaco Basin, Paraguay. Its Hydrocarbon Potential: Geoconsultores, 2-27, accessed November 15, 2021; https://www.researchgate.net/publication/281348744_Phanerozoic_tectonics_and_sedimentation_in_the_Chaco_Basin_of_Paraguay_with_comments_on_hydrocarbon_potential
- Alfredo, Carlos, and Clebsch Kuhn. “The Geological Evolution of the Paraguayan Chaco.” TTU DSpace Home. Texas Tech University, August 1, 1991. https://ttu-ir.tdl.org/handle/2346/9214?show=full.