Numerical Models of Converted Slow P-wave Modes in Porous Media

Abstract

Biot theory has predicted a second P-wave that can propagate in a fluid saturated porous material. This wave can be regarded as a propagating wave predominantly through the fluid saturating the medium. For this wave, the fluid moves opposite to the solid and is highly attenuated. Consequently, it is hard to detect and has only been observed in laboratory experiments so far. Several boundary conditions for the reflection and transmission of plane waves at plane interfaces separating media involving porous rocks have been proposed since the Biot theory was introduced in the 1950’s. However there is a controversy on which set of boundary conditions should be employed for such media. Only experimental tests can warrant a definitive answer to this controversy. In this contribution, forward numerical models for the reflection-transmission in porous media will be presented at both high and low frequencies. These models are based on wave propagation using Biot theory and various sets of boundary conditions. Converted waves from and to a slow P-wave mode will be given a particular attention. Models, obtained at an interface between a water-saturated porous rock and water using the open boundary conditions, show converted slow P-waves with moderate amplitudes. However models derived from boundary conditions that restrict relative fluid movement with respect to the solid, such as those used in the case of a porous-solid interface, lead to weak converted slow P-waves. This confirms that the slow P-wave is predominantly a flow process. However, recent reflectivity experiments from a porous-solid interface exhibit converted slow P-waves with significant amplitudes that cannot be explained by the closed boundary conditions. The modeling also shows that the slow P-wave can convert to both a fast P-wave and to an S-wave (or vice versa) with relatively significant amount of energy when the relative fluid-solid motion is not restricted at the interface.