To keep old knowledge warm and new makes the teacher.
— Confucius (551 B.C.-479 B.C.)
In the previous chapter, we found that a vertical velocity-transition zone results in a frequency-dependent reflection coefficient, a phenomenon that we call reflectivity dispersion. Now we approach the great problem of reflectivity dispersion arising from a poroelastic contact in the earth. This is of direct interest to hydrocarbon exploration because gas and petroleum reservoirs are described by an elastic frame composed of common minerals (quartz, calcite, and so forth) and pore space filled with gas, oil, and brine.
Theories of elastic wave propagation in porous solids begin with Gassmann (1951), who worked on sphere packs as a model for clean sandstone with nearly spherical grains. The seminal work in the field, however, is the derivation of equations of motion by Biot (1956a, 1956b). Biot's theory forms the headwater of a sizable literature on the physics of porous solids, including nonlinear theories (Berryman and Thigpen, 1985).
The fluid phase is connected; disconnected pores are treated as part of the solid matrix.
The porous medium is statistically isotropic so that a 2D slice of any orientation would show a constant ratio of pore space to solid frame.
Pore size is much smaller than seismic wavelength.
Wave motion induces only small deformation.
The solid matrix is elastic.
Gravity does not act on density fluctuations induced by wave motion.
Temperature changes caused by dissipation of wave energy are ignored.