Velocity-stress finite-difference modeling of poroelastic wave propagation

Shahin Moradi, Donald C. Lawton

A velocity-stress staggered-grid 2D finite difference algorithm was developed in Mat-lab to model the wave propagation in poroelastic media. The Biot's equations of motion were formulated using a finite difference algorithm with fourth order accuracy in space and second order accuracy in time. We examined two examples, where the first was a single layer sandstone saturated with brine and C O2 and second, a two-layered sandstone model with same matrix properties in both layers, but with different fluid content. As predicted by Biot's theory a slow compressional wave was observed in the particle velocity snapshots. In the layered model, at the boundary, the slow P-wave converts to a P-wave that travels faster than the slow P-wave. The results showed that our algorithm handles the layered model perfectly and should be examined for more complicated models. In the future, this finite difference algorithm could be used for inversion to obtain the properties of the porous media, such as saturation.