The Biot-Gassmann equation

This talk will discuss the derivation and analysis of the Biot-Gassmann equation. I doubt if many mathematicians have ever heard of this equation, but it is fundamental to the science of rock physics. Looking at how this equation was derived will help us understand some interesting differences between mathematics and physics or, to put it another way, the different ways that physicists (more specifically, geophysicists) and mathematicians look at a problem. For one thing, the Biot-Gassmann equation is a fairly simple algebraic equation, so would have very little inherent interest to a research mathematician. Also, there are no formal proofs associated with the equation. It was derived in a heuristic fashion from basic physical principles. However, there are some aspects of the equation that will be of interest to mathematicians, notably its manipulation into different forms and the fact that Biot and Gassmann derived it in such fundamentally different ways. In fact, the Biot approach involved the inversion of a seven by seven matrix, by hand! This feat alone should amaze anybody with a mathematics background. I have tailored this talk to a mathematical audience, and will be focusing on the equation itself rather than its applications. However, I would hope that the talk would also be of interest to my geophysical colleagues.

Biography:  Dr. Brian Russell holds a B.Sc. in physics and geophysics from theUniversity of Saskatchewan, a M.Sc. in geophysics from DurhamUniversity, U.K., and a Ph.D. in geophysics from the University of Calgary. He worked for Chevron as an exploration geophysicist before co-founding Hampson-Russell Software Ltd. with Dan Hampson in 1987. In 2002 Hampson-Russell became a wholly-owned subsidiary of VeritasDGCInc, subsequently CGGVeritas, where he is now Vice President. Dr. Russell is also an Adjunct Professor in the Department of Geoscience at the University of Calgary and is registered as a Professional Geophysicist (P.Geoph.) in the Province of Alberta.

Dr. Russell’s research interests include rock physics, seismic inversion and seismic attribute analysis and he is also a widely known continuing education speaker. He is a Past-President of both the Canadian SEG (CSEG) and international SEG (Society of Exploration Geophysicists) and has received Honorary Membership from both societies. Brian is currently Chairman of the CSEG Foundation Board and also Chairman of the Board of PIMS, the Pacific Institute for the Mathematical Sciences.