Padé Acoustoporoelasticity for 3-D Wave Propagation in Prestressed Porous Rocks With Inelastic Deformations

Insights into wave propagation in prestressed porous rocks have great interest in geophysical applications, such as remote monitoring in situ stresses. Wave-induced small dynamic fields superposed onto statically deformed objects can be addressed traditionally by acoustoporoelastic theory that extends the classical acoustoelasticity of solids to porous media by incorporating Biot's theory. Stress-induced deformations in porous rocks are of a progressively scaling feature with increasing prestress, undergoing linear elastic, hyperelastic (nonlinearly elastic), and inelastic deformations prior to mechanical failure. Conventional acoustoporoelastic theory is based on the Taylor expansion for the cubic strain-energy function with linear strains under finite-magnitude prestress. The theory with third-order elastic constants (3oeCs) only accounts for stress-induced hyperelasticity, insufficient to handle inelastic deformations with nonlinear strains of compliant microstructures. We replace the Taylor expansion with the Padé approximation to the strain energy function, leading to Padé acoustoporoelastic equations for inelastic deformations under large-magnitude prestress. Theoretical results from plane-wave analyses agree well with the laboratory measurements of fluid-saturated Portland sandstones under confining and uniaxial prestresses. Finite-difference simulations are implemented to solve the first-order velocity-stress formulation of Padé acoustoporoelastic equations for elastic wave propagation in prestressed porous media under isotropic (confining) and anisotropic (uniaxial and pure shear) prestresses. The resulting wavefield snapshots show the propagation of fast-P and slow-P and slow-S waves in acoustoporoelastic media, illustrating stress-induced velocity orthotropies, strongly related to the direction of prestress. Comparisons with conventional acoustoporoelastic simulations provide a framework to estimate stress-induced inelastic strains from seismic responses in velocity and anisotropy.