SOME ASPECTS OF ELASTIC WAVE PROPAGATION IN FLUID‐SATURATED POROUS SOLIDS

Abstract

Biot’s equations for the propagation of dilatational waves in fluid‐saturated porous solids in the low‐frequency range are analyzed for the purpose of application in geophysical research. The deformation constants of the system are unraveled in terms of compressibilities and porosity, and suitable approximate solutions for wave velocity and attenuation of the waves of both the first and the second kind are obtained. A saturated elastic porous solid is found to behave, as far as the wave of the first kind is concerned, approximately as a standard element. The wave of the second kind rapidly dies out with increasing distance from the source and consequently one might infer that in seismic studies only the wave of the first kind needs consideration. It is shown, however, that its presence has an effect upon the reflection and absorption at any interface between two different fluid‐saturated porous solids. At such an interface a wave of the second kind is again generated. General formulae for the reflection and absorption for normal incidence at the interface are obtained, which include the effect of second‐wave generation. Additional results of the investigation are the following: A rather simple formula for the speed of sound in sedimentary rocks (the wave of the first kind) is obtained, which has to replace the so‐called “time‐average relation” now sometimes used. A comparison between the results obtained here and published results on wave propagation in simpler fluid‐solid systems, such as, for instance, suspensions, showed some weak points in the older theories. Suggestions for possible improvements are given.