My decision to follow Gassmann's model is heuristic. I expect successful simulation and inversion of time-lapse data to justify the formulation. Ultimately, the careful study of the sensitivity and resolvability of reservoir parameters will have to decide the most feasible approach.

The wave equation governs the seismic experiment. It can be formulated for a wide variety of problems and materials. The literature offers simpler and more complex alternatives to Gassmann's formulation. Biot 1962, for example, offers a comprehensive theory that includes Gassmann as a special low-frequency case. Terzaghi offers an alternative approximation that is popular in geomechanic applications. Geerstma and Smit approximate Biot's frequency dependent velocity expressions by a combination of a zero frequency and infinite frequency term. Mindlin 1949 approximates macro elastic modulo for porous rock from pore-scale considerations of dry dense random pack of identical spherical grains. Wyllies 1956, on the other hand, offers a simple velocity averaging scheme that is popular in well logging.

The list of available models of wave propagation in fluid filled porous rocks is long and I restrict my discussions to Gassmann (above), Biot, Terzaghi, and Wyllie. What follows are not mathematical derivations, but an overview and motivation of various formulations.

3/9/1999