Samuel Gray

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Samuel Gray
Image gray.jpg
Latest company CGGVeritas
PhD Mathematics

Samuel (Sam) Gray received a PhD in Mathematics in 1978, and he joined the oil and gas industry in 1982 at Amoco's Research Lab in Tulsa, Oklahoma, where he worked on seismic imaging, amplitude analysis, and velocity estimation problems. He moved to Amoco Canada in 1994, where he was humbled by the near surface. He joined Veritas (now CGGVeritas) in 1999. Gray has published and presented widely, and has won awards for best paper in Geophysics and The Leading Edge, best presentation at SEG and CSEG meetings, and Honorable Mention for Best Paper in Geophysics. He has also served several times as an Associate Editor of Geophysics. In 2010, he received the SEG's Reginald Fessenden Award for his work on both the theoretical and practical sides of imaging. He won the SEG Maurice Ewing Medal in 2017. He is currently a chief scientist at CGGVeritas.

SEG Maurice Ewing Medal 2017

Samuel Gray’s work from an industry perspective is impressive, with major contributions in the areas of depth imaging, velocity estimation, and seismic modeling. In particular, he has pioneered and collaborated with others in the areas of turning wave imaging, antialiasing in Kirchhoff migration, true-amplitude imaging, beam migration, and wave-equation migration. Gray also excels as a great communicator. He not only has mastered conveying complicated mathematical formulas behind seismic imaging in simple, understandable language for fellow geologists and geophysicists who are not familiar with seismic imaging, he also has inspired newcomers to our industry to carry the torch to further advance imaging technology.

Biography citation for the Maurice Ewing Medal

by John Etgen[1]

Everyone who knows Samuel Gray describes him as energetic and engaging, astute and brilliant, practical and performance-driven, and most importantly humble and wise. Sam's mentors at the University of Denver were Norm Bleistein and Jack Cohen. There he found that he could always collaborate with one of those two eminent scientists to explain the more esoteric concepts proposed by the other. That ability to synthesize and improve the understanding of complex topics by reaching out to colleagues is one of Sam's great strengths. Sam did not start his post-PhD work in exploration seismology; instead he worked for the Naval Research Lab and then as an instructor at the General Motors Institute, now known as Kettering University. But he realized he had something important to give to the field of geophysics and joined Amoco Production Research Company in Tulsa, Oklahoma. There his colleagues, collaborators, and mentors were the likes of Ken Kelly, Sven Treitel, and Dan Whitmore. It was there at the Tulsa lab, “the house that Sven built,” that Sam began to make his mark on exploration geophysics.

Sam was the focal point of Amoco's efforts to develop 3D Kirchhoff prestack depth migration (PSDM) in the late 1980s/early 1990s. There were many scientific and engineering compromises in the design and implementation of that technology; during those days many of them were not fully explored. There were many times when he could have called the work “good enough” and just delivered what would have been improved images compared to what we had. That was not good enough for Sam, who has an amazing ability to create algorithms that are not only faster than you think possible, but also more accurate. The Kirchhoff 3D PSDM implementation that Sam helped create gave Amoco a pioneering capability in industry. It ran faster than what many believed even theoretically possible and, on top of that, was essentially true amplitude. We later coined the term “warp-drive” for the computational technique that Sam and the team developed, which allowed the Amoco 3D KPSDM to run so well. When Sam joined CGG in 1999 he immediately demonstrated the depth of his theoretical knowledge and his ability to translate theory into practical algorithms and efficient computer code, just like he did for Amoco.

Sam is also a key figure in the development of beam migration methods in general and CGG's development of controlled beam migration in particular. The R&D team sought to develop a variant of beam migration that is both better and faster than Kirchhoff migration and Gaussian beam migration. As one would expect for any project with such lofty goals, the team was stuck for months. Sam cracked the secret of migrating exactly which few percent of the data to produce images of high signal-to-noise ratio at lightning speed. Sam modestly considered his contribution to be trivial, and he graciously declined to share a CGG technical award with the R&D team. But of course this reminded everyone that Sam is one of the giants in seismic imaging who allows us to see and go further on his shoulders.

Sam skillfully presents complex technical ideas in a way that is both amusing and understandable. I've always profited from Sam's advice to “never have more than one and a half ideas” in a presentation. His conference presentations always draw huge crowds, and the audience is never disappointed. It is rumored that he doesn't even need slides. Sam once was giving an imaging presentation to a large, diverse audience. After the first couple of slides, the projection system malfunctioned, and all that remained was a white screen. There was growing concern from the event organizers, but Sam seemed completely unfazed by the complications. When it became evident that the projection system was not going to return, Sam had a suggestion: “Why don't I continue the presentation and just describe what you would be seeing if the slide was actually there.” He then proceeded to give the full presentation in that fashion.

For those who have worked closely with him, Sam is particularly famous for his dry wit and sense of humor. His best witticisms are usually reserved for those who need their complacency challenged, and through the years he has had a few Yogi Berra moments. On one particular occasion, someone was glowing about how good we had become in seismic imaging and turned to Sam for corroboration. Sam thought for a moment and gently said, “You don't have to be good to be the best; you just have to be the best.” The recipient didn't quite understand what Sam meant and changed the subject. From that point on, “you don't have to be good to be the best” became the reality check for those of us trying to imitate Sam's ethos of excellence. We are reminded over and over again that being the best is not always good enough in seismic imaging. Sam's many cleverly honest quotes continually tell us that we can always improve what we do in seismic imaging.

Biography citation for the Reginald Fessenden Award

Contributed by Judy Armstrong, Norm Bleistein, and Sven Treitel

Sam received his Ph.D. in mathematics at the University of Denver in 1978. Sam’s style was established from the get-go: cut-off shorts, wrinkled tees, long hair, tennis with a wood racket at the local park, and a bike with too few gears and a steep frame. He was a fine colleague to his fellow graduate students; a source of humor and camaraderie. During this time, he met his wife Julie and they married at the Evans Memorial Chapel on the campus of the University of Denver. Sam and Julie have two children, Christopher and Catherine.

Sam’s career in exploration geophysics began in 1982 when he joined Amoco. He was among the last in a cohort of gifted scientists hired by Amoco’s Tulsa Geophysical Research Division. Here he first became interested in the 1D seismic inverse problem, a topic made popular by earlier work of Geza Kunetz at CGG in France. After some time, he became increasingly attracted to a seismic imaging project conducted by Dan Whitmore in a group run by Ken Kelly. Here Sam’s deep mathematical insights began to bear fruit: early work with poststack Kirchhoff time migration was successively followed by Kirchhoff poststack depth migration, and these already established techniques then led him to their prestack counterparts.

Next Sam tackled a problem that had defied the efforts of the best imagers in the trade: to map not only the steepest portion of a salt dome flank, but also to obtain pictures of the salt overhang from below. He was among the first, if not the first, who managed to achieve this impressive feat by the use of turning rays, whose computer implementation he achieved by remarkably clever programming trickery. Sam’s earliest imaging work at Amoco soon found widespread application within the company because of a close collaboration with Davis Ratcliff, who was then working in Amoco’s Houston office. While Sam developed the ideas and the software, Davis became its masterful salesman; the two made quite a team.

A clever contribution of Sam’s was his solution of the operator aliasing problem in Kirchhoff migration. It arises when the migration swings events out to very steep dips; the high-frequency components become under-sampled on the migration grid, and a noisy image results. Use of sampling theory led to a migration operator that produced cleaner images. This trick is now universally applied to Kirchhoff migration.

By 1994 it became clear that Amoco’s Research Center had entered a period of decline; Sam requested a transfer to Amoco Canada in Calgary, where he continued his imaging research until Amoco was merged into BP.

Sam joined Veritas, now part of CGGVeritas, in Calgary in 1999, where he has remained ever since. He continued his work in depth imaging, velocity estimation and seismic modeling, both in classic acoustic models and in anisotropic elastic models of the Earth. He is also part of a group in the company who are intent on introducing “true-amplitude” adjustments in a ray-theoretic sense to various migration techniques, including Gaussian beam and reverse time migration. He is much in demand for expository presentations and papers, sharing his insights on the imaging aspects of seismic data processing in which he is a recognized expert. A paper he co-authored received a Best Paper award in Geophysics (1999), with two others cited for honorable mention, and he received an award for Best Paper presented at the SEG Annual Meeting in 2004. He also co-authored a paper that received a Best Paper Award in The Leading Edge this year. Sam remains active in research and development of modeling and migration methods, collaborating with colleagues both in and outside of CGGVeritas. The variety of his co-authors is an indication of the breadth of his interests and capabilities. His current title is Chief Scientist, a clear indication of his stature within the company, and more broadly within the industry.

Spring 2012 SEG Distinguished Lecturer

A brief history of depth…and time seismic imaging

From the 1920s to the present, seismic imaging ("migration") has helped the oil and gas industry locate hydrocarbon traps inside the Earth. Migration has evolved and improved over the years, and it is now used routinely for structural imaging, seismic velocity estimation, and amplitude analysis, among other applications. It is applied to narrow- and wide-azimuth towed-streamer marine data, to marine data with multicomponent sensors placed on the sea floor, to land data from desert and mountainous areas, to data acquired in transition zones, to sparsely and densely acquired data, and even to blended data. Migration is applied in many different kinds of settings, and it comes in many different shapes and sizes.

Was migration in the 1920s anything like migration today? Perhaps surprisingly, the answer is yes. Even the most advanced current methods are based on principles that drove early innovators to exploit the nature of recorded seismic wavefields in mapping subsurface reflectors – sound waves bouncing off reflectors and sending localized packets of wiggle energy back toward recording devices. Of course, the details changed as, first, specialized machines replaced pencil and paper and, later, the digital revolution replaced analog devices and allowed the modeling of wavefields inside the computer. Some methods fell by the wayside and others emerged as computers became more powerful and allowed us to migrate more and more wiggles on more and more traces.

Is migration finished, or even mature? Mature, yes, but by no means finished. We now often apply a complete two-way wave equation when migrating seismic data, but the wave equation we use is almost always an acoustic one applied to waves propagating in an elastic Earth. This itself is a big approximation, and it affects our ability to estimate velocity and analyze amplitudes. Sometimes migration does not use a complete acoustic equation – the equation might not admit two-way propagation, or it might use an approximate ray-based solution. In fact, depending on the seismic acquisition, migrated images using an "incomplete" wave equation are often preferable to more theoretically correct images. So there is still a lot of work to do, both in improving the fidelity of our high-end methods and in refining our lower-end methods to accommodate less-than-ideal acquisition.

Additional Resource

A recording of the lecture is available.[2]

Pretour Preview

Seismic interpreters and processors, and occasionally exploration managers and even technology managers, have been known to ask in an exasperated tone, "Why are there so many seismic imaging methods?" The implication, of course, is that there are too many; maybe one is the preferred number. (Maybe developing all the others has been a wasted effort?) Indeed, I believe one is the preferred number, but after nearly a century of imaging, we still haven't gotten the actual number down to one. In fact, the preferred imaging method of 2012 is probably not the one we really want to end up with. To understand why there are so many, we need to take a look at how the technology developed over the years.

A lot of seismic imaging, or migration, was done before we had computers to do the imaging with. This meant that the earliest imaging methods had to be based on very simple physical principles. The simplest principle, embodied in the very first migrated images, was to estimate where in the Earth's subsurface a measured reflection event may have reflected from, given its source and receiver positions. Enough independent measurements from a reflecting surface allowed us to map the surface. Surprisingly, this principle is in common use today; it is the basis of one of today's most widely-used imaging methods, Kirchhoff migration. Although it is not the most advanced method, users understand what Kirchhoff migration does and can often interpret through the artifacts it tends to produce, which is not the case with other, more advanced, methods. A second principle, later known as beamforming, summed neighboring reflection events along various trajectories that correspond to angles of incidence at the Earth's surface. Mapping these beams into the Earth along the incidence directions provided an imaging method that eliminated the need to migrate all the individual traces. Necessity was the mother of invention.

The digital revolution took place in the 1960s, and seismic processing became serious business. We learned about digital signal processing and its implications for seismic traces that are discretely sampled in space and time. We also learned how to use computers to model the wave equation. Jon Claerbout was one of the first to do this, and he was the first to apply this modeling to seismic migration. However, Claerbout realized that modeling the "real" two-way acoustic wave equation would be prohibitively expensive on the computers of the day, so he developed an approximate wave equation that modeled wave propagation in a generally downward direction or a generally upward direction, but not both at once. This was the first wave-equation migration method, and others soon followed; the race was on to produce the fastest, most accurate imaging method possible. Unfortunately, the fastest was never the most accurate, so a wide spectrum of methods was developed – some that could image steep dips, others that were very efficient, and still others that were very accurate but perhaps could not image steep dips. And the rules kept changing. Faster computers made last year's method obsolete. Prestack migration changed the economics and the objectives of seismic imaging. Depth migration became more important, and 3D completely revolutionized seismic exploration.

That is the answer to the question "Why so many?" In the meantime, the job of seismic imaging changed. At first, it was used to find structural targets such as anticlines and salt flanks. Gradually, careful attention to the wave equation enabled seismic imaging to become a tool for seeing through amplitude and phase distortions present in unmigrated data, and therefore to delineate more subtle stratigraphic traps like pinch outs. From there it was a natural step to investigate migrated amplitudes to see whether the lithology is associated with gas or oil. In a different direction, imaging became a tool to estimate seismic velocity inside the Earth. Gradually, imaging became part of a loop (sometimes seemingly endless) where prestack migration is used to estimate velocity that, in turn, is used to migrate some more. In fact, velocity has become such a crucial part of the imaging process that sometimes the estimated velocity is more important than the migrated image, as when we use velocity to estimate pore pressure. Meanwhile, the demands of structural imaging intensified, taking us from "Where is the flank?" to "Where is the base?" to "Where are the hydrocarbons beneath the base?" These demands have led the industry to develop accurate migration methods that can image very steep dips while handling extreme lateral velocity variations. At the high end, where the success of the most expensive wells depends in part on the quality of the seismic image, the emphasis is now on accuracy more than efficiency. Use of the full two-way wave equation (reverse-time migration) is common; however, we must remember that the acoustic wave equation is still an approximation to the true behavior of seismic waves in the Earth.

Seismic imaging continues to evolve today to satisfy the evolving requirements of seismic data analysis. Sparse acquisition of data from some land areas produces such poor-quality, noisy data that conventional migration typically fails to produce satisfactory images; some efforts at specialized stacking techniques before migration have enabled much better imaging. Unconventional resources, such as shale gas and shale oil, promise to make new demands on all of seismic processing, including imaging. In particular, determining sub-wavelength features such as fracture fields from migrated data will require amplitude-preserving imaging to appear relative early in specialized workflows. Generally, the trend toward analysis of migrated amplitudes will result both in better final images and more detailed estimation of lithology in moderately complex geology. Finally, the realization that the Earth is a lossy elastic medium will force us to keep working on even our most advanced imaging methods.

Sam Gray, CGGVeritas, Calgary, November 2011


Please tell us a little bit about yourself (e.g., your educational and work experience, why you became geophysicist, etc.). I decided at a very early age that I would be a mathematician, so I majored in math in college and got my PhD in math from the University of Denver many, many years ago. Along the way, I had an epiphany: I found out that applied math is more "fun" than pure math, more of a social math, if you can call any kind of math fun.

My graduate work (applied math) was related to seismic imaging, so the jump into geophysics was very natural. As a geophysicist, I have found out that math is an important tool in solving geophysical problems, but it is not the only tool. (It helps to know some geology, for example.) I have also found out that geophysicists are amazingly opportunistic, willingly picking up whatever tools are needed to solve geophysical problems. I haven't exactly sat still mathematically, but I know some geophysicists with less formal mathematical training than mine who are far better mathematicians than I am. So I am kind of a mathematician, but kind of a geophysicist too.

Would you like to mention anything about your personal attributes that helped you achieve the professional status you enjoy today? I had a lot of self-belief when I was younger, which was not really a bad thing: if you don't believe in yourself, how are you ever going to accomplish anything? So, even though I might not be as smart as I thought I was, I thought I could get things done. And I did get a few things done, but it was as much based on advice from two mentors as anything that came from myself.

My first mentor was Norm Bleistein, who was my PhD thesis advisor. Norm told me two things. First, careful mathematical analysis of a physical problem can lead to fast, elegant solutions. He said that in the context of one of his fields, asymptotic analysis. (Actually, as I developed geophysically, I turned that principle around, and used physics to guide the math - but it was the same general principle. This often works well for thinking about seismic waves, but sometimes it backfires.)

Second, you can only work so many productive hours in a day. Sometimes I would use this advice as an excuse to take the rest of the day off, but Norm really meant that you need to pace yourself over the course of a career, which is a lot of years.

My second mentor was Sven Treitel, who is a mentor for all petroleum geophysicists. Sven told me that personal life is more important than work. I needed to be told that! Even though I was pretty lazy and could be counted on not to work too many hours, Sven's words taught me to keep my priorities straight. Another thing Sven taught us is that, even if we are giants, we are standing on the shoulders of even bigger giants.

Why did you choose this lecture topic? Why is it important? When I was asked to be DL, without hesitation I chose my topic to be the history of seismic imaging. My choice was "instinctive," based on no reflection at all. At first, I thought my job would not be too hard because I knew as much about the history as just about anybody. Then I came to realize that, while I might know as much as anybody, I still did not know very much. So I've done a lot of learning over the last several months, and I've had great discussions with some of the giants in our field. I'm especially thankful to Bee Bednar, Jon Claerbout, and John Sherwood. The more I learn about the history of imaging, the more I think I made a good choice of topic.

Imaging has been the culmination of seismic processing for so long that we tend to forget where it came from; we just hit the button, look at the image, and interpret the results. But seismic imaging is based on some very fundamental principles of classical physics that should be ingrained in our very souls as geophysicists. Anyone who interprets or processes seismic data really needs to understand the physical principles that are ultimately responsible for producing the image. That way, she can understand what is wrong with the image, and what is less wrong. (It's never right, only less wrong.) A lot of this comes through in studying the history, and that is what I hope to get across to the audience. Of course, there are a lot of details, and there have been a lot of stopgap solutions to problems of the day (caused by slow computers, etc.), but even these are interesting because they show how much amazing ingenuity people have applied to get an image that, while not perfect, is a little or a lot better than before.

What do you hope people will have learned after they attend your lecture? How is it different from other lectures? My lecture is different from most, because it is about the history of our field. I think geophysicists are not a particularly introspective group, given to thinking about the past very much. But we have a past, and it is exciting and illustrious; it is also deeply entwined with the history of oil and gas exploration. I hope people who see my lecture will come away with some appreciation of the technical accomplishments they are a part of, and of the technical challenges that lie ahead.

You have quite a busy year ahead. Do you enjoy traveling? Will it be difficult to balance the tour with your work? I hope I enjoy traveling! Or, to put it differently, I enjoy traveling up to now. This will be different from the usual isolated business trip. But I will get to see some places I haven't seen, and revisit many places that I enjoy. I'm looking forward to the opportunity. Balancing the tour with work won't be a particular problem, since CGGVeritas has very generously allowed me to concentrate on the tour. But I hope to keep my hand in at work at least to some degree.

Would you share with us one or two of your most exciting successes? Not long after I received my PhD, I was dissatisfied with my main result, which had to do with a toy (one-dimensional) version of seismic migration. In the approximation I was making, the norm of the error was too big. So I was fiddling around with some equations and tried a slightly different formulation. Still an approximation, but the norm of the error was much smaller! It was slightly embarrassing that my PhD thesis was suddenly obsolete, but exciting nonetheless. This gave me a lot of confidence.

Later, in the early days of depth migration, I was writing a Kirchhoff migration program. I was trying to figure out an accurate way to compute traveltimes to build diffraction curves that would not take longer than the Kirchhoff summation. Believe it or not, this was a challenging problem. After many sleepless nights, it suddenly occurred to me that I needed to turn the problem upside down from the standard way of looking at it. When I did this, the pieces all fell into place.

It turns out, neither of these "successes" was the breakthrough I thought they were at the time. Other people had figured them out already, or were about to. That's all right: they were reasonably clever, they were advances, and they were not in common use at the time.

How about a couple of disappointments? I'm disappointed that I didn't work hard enough on some of the numerical aspects of wave-equation migration. I thought, "Why should I work hard on building a migration operator with one degree more dip when I can already do steep-dip Kirchhoff migration?" That attitude was shortsighted. Most of the exciting work on seismic imaging has been on wave-equation migration, which is very accurate beneath complex overburden. With my background in math, I've been able to understand this work, but I've had to watch from the sidelines. I should have jumped in and helped out when I first had the chance.

I'm also disappointed that I haven't learned more geophysics. I know a lot about seismic processing and a little about interpretation, but there is far more to geophysics than those subjects, complicated as they are.

What advice would you give to geophysics students and professionals just starting out in the industry? I'm not really full of wise advice, but I think you need to follow your instincts, try to find good mentors, and work on easy, important problems. (And hope that your instincts are good!)

SEG Best Paper in Geophysics Award 1999

Gary E. Murphy and Samuel H. Gray received the 1999 SEG Best Paper in Geophysics Award for their paper Manual seismic reflection tomography[3]

Honorable Mention (Geophysics) 1998

Jinming Zhu, Larry R. Lines, and Samuel H. Gray received 1998 Honorable Mention (Geophysics) for their paper Smiles and frowns in migration velocity analysis.[4]


  1. (2017). ”Honors and Awards.” The Leading Edge, 36(10), 806–819.
  3. Gray, S. H. and G. E. Murphy (1999), Manual seismic reflection tomography, Geophysics 64(5):1546.
  4. Zhu, J., L. R. Lines, and S. H. Gray (1998) Smiles and frowns in migration velocity analysis, GEOPHYSICS 63(4):1200.

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