Acoustic signature of impermeable barriers in porous media

Abstract

SUMMARY Impermeable barriers are abundant in rock formations and their delineation via seismic reflections are of prime importance. However, such barriers have received little attention in the poroelasticity literature. For this reason, we revisit the reflection–transmission problem for two porous half-spaces which are in welded contact and across which no fluid exchange is possible. We carry out this analysis in the poroelastic theory initiated by de la Cruz and Spanos (1985), which describes four waves: the fast P, fast S-, slow P and slow S waves. The fast P and S waves account for the in-phase motion in compression and shear nature, whereas the slow P and S waves are the out-of-phase motion. We find that the often times suggested notion of effective elastic scattering is not quite correct because of the generation of slow waves at the impermeable contact. The energy flux the slow waves carry is negligibly small at low frequencies when the fluid is viscously coupled to the solid frame. In contrast, slow waves carry substantial energy flux at high frequencies when the fluid is viscously decoupled. Moreover, the reflection–transmission behaviour at an impermeable contact is distinctively different when compared to that of a permeable contact, which means that, in principle, amplitudes of scattered waves can be used to identify the kind of contact. A seemingly unnoted but important result is the strong conversion scattering from a fast S wave into the slow P wave at high frequencies, which may be an alternative way to observe slow P waves in the laboratory as well as a means to characterize impermeable contacts.