Wave propagation in partially saturated porous media: simulation of a second slow wave

We simulate wave propagation in a partially saturated porous medium, where the novel feature is the presence of a second slow wave due to capillary forces. The pores are filled with a wetting fluid and a non-wetting fluid, and the model, based on a Biot-type three-phase theory, predicts three compressional waves and one shear wave. Moreover, the theory models the realistic attenuation levels observed in rocks. Attenuation is modeled with exponential relaxation functions which allow a differential formulation based on memory variables. The wavefield is obtained with a grid method based on the Fourier differential operator and a Runge–Kutta time-integration algorithm. Since the presence of slow quasi-static modes makes the differential equations stiff, a time-splitting integration algorithm is used to solve the stiff part analytically. The modeling is second-order accurate in the time discretization and has spectral accuracy in the calculation of the spatial derivatives. Surface-tension effects in the fluids, which are not considered in the classical Biot theory, cause the presence of a second slow wave, which is faster than the classical Biot slow wave. The present modeling algorithm can be used to study the conditions for which this new wave can be detected in laboratory experiments. © 2003 Elsevier B.V. All rights reserved.