Stability analysis of the Biot/squirt models for wave propagation in saturated porous media

Abstract

This work is concerned with the Biot/squirt (BISQ) models for wave propagation in saturated porous media. We show that the models allow exponentially exploding solutions, as time goes to infinity, when the characteristic squirt-flow coefficient is negative or has a non-zero imaginary part. We also show that the squirt-flow coefficient does have non-zero imaginary parts for some experimental parameters. Because the models are linear, the existence of such exploding solutions indicates instability of the BISQ models. This result calls on a reconsideration of the widely used BISQ theory. Furthermore, we demonstrate that the 3D isotropic BISQ model is stable when the squirt-flow coefficient is positive. In particular, the original Biot model is unconditionally stable where the squirt-flow coefficient is 1.