Wednesday, September 2, 2015

General relativity @ 100

November 2015 marks the 100th anniversary of Einstein's theory of general relativity (GR). Actually, he published four papers on the subject in November of 1915. Remarkable. The first two papers lead to the field equations of GR while the other two lay out vital consequences of the theory, including the anomalous precession of the perihelion of Mercury (unexplained since 1859) and the gravitational bending of light. The latter phenomenon was famously confirmed by Eddington's 1919 observation of a total solar eclipse and the shift of apparent position for stars whose light passed very near the sun. Einstein, already famous, became a household name -- an early 20th century super star.

While Einstein's 1905 theory of special relativity dealt with constant velocity frames of reference, GR  dealt with accelerating reference frames. Fond of thought experiments, for special relativity Einstein imagined an elevator in space moving at constant velocity when a horizontal light beam entered from one side. As the light progresses across the small space, the elevator is moving up so that the light appears to exit on the other side below where it entered. But since the velocity is constant, the beam is still straight, just inclined to the floor.

For GR, the same thought experiment gives a different result. Because the elevator is accelerating upward, if we were able to track progress of the light beam across the elevator in equal time intervals the early intervals would show little movement toward the floor, while later ones would have more shift as the elevator speeds up. In other words, the light would appear to bend down toward the floor. Since the only known force that can accelerate everything equally is gravity, this little experiment leads to the idea that light bends in a gravitational field. The bending is small, unless the gravity is due to a very massive body leading to large acceleration.

What connection, you may ask, can GR possibly have to exploration geophysics? Well, there are several. For one thing, the GR field equations are tensor equations as are the field equations of elasticity. Also in both, the equations are so difficult that exact, analytic solutions are few. For elastic, this is basically limited to a point source in unbounded constant velocity media (Stokes, 1849) or near a plane interface (Caniard, 1939) or some ungeologic shape like a sphere or cylinder. For GR, the first (and most useful) is the field around a chargeless, non-rotating spherical object  (Schwarzschild, 1916) which introduced the concept of what we now call a black hole.

But a more interesting similarity resides in the concept of gravitational lensing. This relates to the bending of light by massive objects that lie between us and distant stars. Gravitational lensing can distort the light from stars and galaxies into a bestiary of curiously-shaped (and named) objects: Einstein crosses, rings, arcs and arclets.

While those of us in seismology are at ease with the idea of rays bending in 3D, this kind of distortion is unfamiliar. In the summer of 2004 I visited Stanford University at the invitation of Jon Claerbout. One day I was looking at some gravitational lensing images online when Jon stopped by and mentioned that the same thing must happen with seismic waves in the near surface of the earth. Specifically, the low velocity layer can act as a distorting lens, focussing and defocusing deep reflection energy as it passes upward toward surface receivers. If the effect were big enough we would see it as time shits that we call statics. But more subtle velocity features would only show up as amplitude anomalies created by focusing and defocusing seismic wavefront energy.

Jon pointed me to pages 154-8 of his wonderful 1985 book Imaging the Earths Interior. In that section he discusses Einar Kjartansson's 1979 PhD thesis, part of which was work along these lines. Einar studied 2D data from the Gulf of Mexico and showed that anomalous pods of material in the earth would show up in the data differently if they were shallow, intermediate or deep; just as gravitational lensing depends on the relative location of source, distorting object, and observer.

That was 1979 and in 2004 Jon looked at me and said that if someone could understand gravitational lensing and bring that to the seismic problem, we would know a lot more about the near surface than we do now. Who knows, maybe he hoped that I would be able to do it. Alas, my abilities fall far short of this formidable problem.

But maybe, just maybe, someone reading this will know enough of both worlds to take on the challenge. I think young Einstein would have jumped on it.

References cited:

Stokes, G.G., 1849. On the dynamical theory of diffraction, Trans. Camb. Phil. Soc., 9, 1-62. 

Cagniard, L., 1962, Reflection and refraction of progressive seismic waves, McGraw-Hill. Translated from Cagniard (1939).   

Schwarzschild, K., 1916,  Über das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie. Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften 7: 189-196. (Title translation: About the gravitational field of a mass point in Einstein's theory)

Claerbout, J. F., 1985, Imaging the Earth's Interior, Blackwell Scientific Publications.

Wednesday, August 19, 2015

Opening of SEG building GRC2

Speech given August 20, 2015 by SEG President Christopher Liner at Grand Opening of GRC2. Original draft by Steve Brown (SEG Staff) with edits by C. Liner and D. Proubasta

During speech in lobby of GRC2 with Mayer Bartlett (left) and Councilman Lakin (right) listening.

Good afternoon. Thank you for coming out on such a historic day for the SEG AND the city of Tulsa. As SEG President and a Tulsa native, I am honored to preside over the dedication of this new building — the Geophysical Resource Center 2.

If you will indulge me for a few minutes, I’d like to provide some historical context for our celebration today.

Founded in 1930, the Society of Exploration Geophysicists is a non-profit organization in its 85th year. The SEG mission is one of connecting, inspiring, and propelling the people and the science of geophysics. 

Our members apply the science of geophysics to energy exploration … to mineral exploration … to environmental and engineering problems … to archaeology and mitigating earth hazards. SEG currently has nearly 33,000 members in 125 countries, with offices in Dubai and Beijing. But SEG is proud to call TULSA home.

The building just to our South — you can see it through those windows — was dedicated 30 years ago during a ceremony much like this one. We built that building, the Geophysical Resource Center’s Cecil and Ida Green Tower to serve as headquarters for SEG’s growing staff and assure stability of our Society by diversifying revenue. 

When we broke ground on this 11-acre campus back in 1983, it was an oil boom. SEG AND the city of Tulsa were riding high.

Even as SEG President Red Olander dedicated that first building, a dramatic downturn in the oil industry began. Within year oil prices fell by half and oil companies began to slash expenses.  Our Society’s membership fell that year, and it would continue to shrink for almost a decade.

Both SEG and Tulsa were going through dire straights.

What about now?

Here we are, 30 years later, in the midst of another severe downturn of the oil and gas industry dedicating another new building in Tulsa — GRC…two!  There will always be hard times and opportunities. We seize the opportunity.

The fact is that our SEG staff of about 100 occupies just ONE floor of GRC1. The rest is leased to other Tulsa businesses. Our 1980s investment in that building served its purpose. It provided much-needed office space for SEG and others in the Tulsa community and helped SEG through some tough economic times.

GRC2 -- a $20 million, 80,000-square-foot, Class-A office building — is currently almost 70% leased and we expect 85% lease by mid-September.

Our Society’s investment in real estate enhanced SEG’s ability to serve a global membership during difficult times and will continue to do so with first class tenants. 

Important companies already calling this building home include CCK Strategies, Kinder Morgan and, very soon, Central National Bank. And we have room for a few more. 

GRC2 initiated under the leadership of former SEG President Dave Monk, SEG Board Members, and the SEG Real Estate Board lead by Bob Wyckoff.  GH2 Architects, Manhattan Construction, Program Management Group and Newmark Grub took our vision and turned it into this impressive structure and campus. When we look at what’s been built here, everyone involved can take pride in knowing they did a fantastic job.

A special thank you as well to the tenants of GRC1 who have put up with all the inconvenience of construction. To our new GRC2 tenants: we couldn’t be happier to have you here.

As a significant addition to the SEG AND the city of Tulsa, I hereby dedicate and officially open the Geophysical Resource Center 2. 

Thank you.

Tulsa World article detail:

Tulsa World article full page:

Tulsa World article page one

Tulsa World article page two

Thursday, August 13, 2015

Book Review: Treatise on Geophysics 2nd Edition

As a sitting SEG President I have to be somewhat selective accepting new commitments. You might think a book review is the last thing I would step into, after all I am barely keeping up a few Seismos columns per year in the Leading Edge.

But this is no ordinary book. Treatise on Geophysics 2nd Edition (TOG2) is an 11 volume tour de force, a broad and sprawling effort to capture the current state of knowledge in geophysics. From the outset that presents a problem. Geophysics is a vast collection of disciplines, specialties, topics, methods and so on. The full scope of geophysics cannot be captured even in 11 thick volumes (length varies from 907 page volume 1 to 302 page volume 9). But it is a majestic undertaking, well worth the effort. To paraphrase Robert A. Heinlein, such a book stitches the patches of the universe together into one garment for us.

The general scope of this laudable Elsevier project can be gathered from the volume titles: (1) Deep Earth Seismology, (2) Mineral Physics, (3) Geodesy, (4) Earthquake Seismology, (5) Geomagnetism, (6) Crustal and Lithosphere Dynamics, (7) Mantle Dynamics, (8) Core Dynamics, (9) Evolution of the Earth, (10) Physics of Terrestrial Planets and Moons, (11) Resources in the Near-Surface Earth.

How does one approach reviewing an 11-volume book? Based on education, I feel qualified to comment on volumes 1, 4, 5, 8 and 10. My entire working life, however, is within the scope of just volume 11.The last individual that is thought to known all of science was either Thomas Young (d. 1839) or Hermann Von Helmholtz (d. 1894), depending which historian you believe.  If we narrow the discussion to just geophysics, someone likely understood it all in the early 1960's (who?), before the subsequent explosion of applied science. It is the nature of a composite science like modern geophysics, that no one person can possibly be an expert in all aspects of the subject.

But that is precisely why magnificent projects like TOG2 are undertaken with an army of editors and contributors. The editor-in-chief of TOG2 is Gerald Schubert of UCLA, member of the National Academy of Sciences and famous as co-author with Donald Turcotte of the standard textbook Geodynamics. Each volume has one or two editors and individual chapters have one or more authors, so TOG2 runs the risk of being science by committee or, worse yet, a tired compilation of previously published papers presented as chapters. Yet, TOG2 compulsively and completely fights this temptation, creating instead a masterful collection of chapters by first-class authors rewarding the reader with a stroll right up to the dizzying height of current knowledge in literally hundreds of subject areas. In volume 1 alone, the list of chapter authors reads like a who's who, even if you are not in the field of Deep Earth Seismology: Dziewonski, Virieux, Cormier, Tromp, Levander, Zelt, Symes and Keller to name a subjective few.

The typical SEG reader will notice that TOG2 is not intended to span the applied geophysical subjects associated with fossil fuel and mineral exploration, although volume 11 (Resources in the Near-Surface Earth) is a good, self-contained overview. Rather, it deals with the fundamental science behind applied geophysics (particularly seismology) and its application to understanding the earth and planets. To give one example, Theory and Observations: Forward Modeling: Synthetic Body Wave Seismograms (vol. 1, ch. 6) is a panoramic discussion of seismic modeling algorithms, parameterization, and a broad view of heterogeneity, attenuation and anisotropy. One can easily forgive two colons in the chapter title considering the authoritative depth and breadth of the text. A picky reader might notice that constant Q theory is given as an approximation (that violates causality) without reference to the exact theory of Kjartansson, and anisotropy without mention of Thomsen. The former omission is particularly curious since Kjartansson's work appeared the prestigious  Journal of Geophysical Research. But these are quibbles that detract nothing from a strong authoritative text.

In my opinion, Treatise on Geophysics 2nd Edition is a splendid, ambitious encyclopedia of the fundamental geophysical sciences. As such, it would be a welcome addition to any working library in pure or applied geophysics. It's publisher, editors and authors are to be commended for undertaking and so finely executing such a task. One wishes that the major applied scientific societies (SEG, AAPG, SPE) would collaborate on a similar scale to create a treatise that would as adequately capture the current knowledge of applied geophysics.