Decoupled acoustoelasticity equations and stable FD modeling for wave propagation in prestressed media

Abstract

Seismic exploration of deep oil/gas reservoirs involves wave propagation in high-pressure media. Acoustoelasticity with the third-order elastic constants can account for nonlinear strain responses due to stresses of finite magnitude. Since current seismic exploration depends primarily on P waves, further development in prospecting technology to handle deep reflection data will benefit from the ability to decouple the elastic waves from high-pressure deep formations. We decouple the first-order velocity-stress acoustoelasticity equations for wave propagation under isotropic (confining) and anisotropic (uniaxial and pure shear) prestress conditions. A rotated staggered-grid finite-difference (RSG-FD) method is used to solve the decoupled acoustoelasticity equations with an unsplit convolutional perfectly matched layer (CPML) absorbing boundary. Numerical examples demonstrate the significant impact of prestressed conditions on seismic responses in both phase and amplitude. The stress-induced seismic anisotropy with orthotropic characteristics is strongly related to the orientation of prestresses. We compare the coupled and the decoupled wavefields to validate the proposed decoupling method. Investigation of the influence of prestresses on the acoustoelastic decoupling illustrates that the isotropic prestress does not affect the decoupling, but the anisotropic prestresses significantly affect the decoupling accuracy.