Finite Difference Based Wave Simulation in Fractured Porous Rocks

Abstract

Biot's theory provides a framework for computing seismic wavefields in fluid saturated porous media. Here we implement a velocity-stress staggered grid 2D finite difference algorithm to model the wave-propagation in poroelastic media. The Biot's equation of motion are formulated using a finite difference algorithm with fourth order accuracy in space and second order accuracy in time. Seismic wave propagation in reservoir rocks is also strongly affected by fractures and faults. We next derive the equivalent media model for fractured porous rocks using the linear slip model and perform numerical simulations in the presence of fractured interfaces. As predicted by Biot's theory a slow compressional wave is 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. We finally conclude by commenting on the major details of our results.