Seismic attenuation in a heterogeneous porous rock

Abstract

I study the attenuation of an elastic wave propagating in a macroscopic heterogeneous poroelastic medium due to the scattering (conversion) of the passing wave's energy into the highly attenuative Biot's slow wave. This is done by studying two particular geometrical configurations: (1) a thinly-layered porous medium and (2) porous saturated medium with ellipsoidal inclusions. The frequency dependence of the so-called mode-conversion attenuation has the form of a relaxation peak, with the maximum of the dimensionless attenuation (inverse quality factor) at a frequency at which the wavelength of the Biot's slow wave is approximately equal to the characteristic length of the medium (layer thickness or size of the inclusion). The width and the precise shape of this relaxation peak depend on the particular geometrical configuration. Physically, the mode-conversion attenuation is associated with wave-induced flow of the pore fluid across the interfaces between the host medium and the inclusions. The results of our study demonstrate how the local flow (or squirt) attenuation can be effectively modeled within the context of Biot's theory of poroelasticity.