Padé acoustoporoelasticity finite-difference simulation of elastic wave propagation in prestressed porous media

Abstract

Abstract Acoustoelasticity has significant implications in seismic exploration, enabling the inference of geological structures and the properties of oil and gas reservoirs through rock physical acoustoelastic parameters, as well as elucidating the propagation of elastic waves in subsurface rocks. In traditional acoustoporoelastic numerical simulations, third-order elastic constants are derived from the Taylor expansion of the strain energy function. However, under conditions of high effective stress, the Taylor approximation can lead to divergent elastic wave velocities. To address this limitation, we propose employing the Padé approximation for the expansion of the strain energy function, as it provides superior accuracy compared to the Taylor approximation. By calibrating the Padécoefficients using experimental data for various rock types, the resultant acoustoelastic constants exhibit a reasonable theoretical limit on elastic wave velocities as effective stress increases. This method allows for a more precise characterization of velocity variations with stress, especially under high-pressure conditions. The acoustoporoelasticity numerical simulation is mainly limited to the 2D cases, so we consider confining prestressed mode in the 3D cases.