Poro-acoustoelasticity finite-difference simulation of elastic wave propagation in prestressed porous media

Abstract

Insights into wave propagation in prestressed porous media are important in geophysical applications, such as monitoring changes in geo-pressure. This can be addressed by poro-acoustoelasticity theory, which extends the classical acoustoelasticity of solids to porous media. The relevant poro-acoustoelasticity equations can be derived from anisotropic poroelasticity equations by replacing the poroelastic stiffness matrix with an acoustoelastic stiffness matrix consisting of second-order 2oeC and third-order 3oeC elastic constants. The theory considers the poroelasticity equations as nonlinear due to the cubic strain energy function with linear strains under ?nite-magnitude prestresses. In this study, a rotated staggered-grid finite-difference (RSG-FD) method with an unsplit convolutional perfectly matched layer (C-PML) absorbing boundary is used to solve a first-order velocity-stress formulation of poro-acoustoelasticity equations for elastic wave propagation in prestressed porous media. Numerical solutions were partially verified by computing the velocities of fast P-wave, slow P-wave and S-wave as a function of hydrostatic prestress and were compared with the exact values. Numerical simulations of wave propagation were carried out for the model of poro-acoustoelastic homogenous space under three states, prestress-confining (hydrostatic), uniaxial, and pure shear; and for the model of two poro-acoustoelastic homogenous half-spaces in the planar contact under confining (hydrostatic) prestress. The resulting wavefield snapshots show fast P-wave, slow P-wave and S-wave propagations in poro-acoustoelastic media under loading prestresses, which illustrates that the stress-induced velocity anisotropy is of orthotropy strongly related to the orientation of prestresses. These examples demonstrate the significant impact of prestressing conditions on seismic responses in both velocity and anisotropy.

A Compact High-Order Finite-Difference Method with Optimized Coefficients for 2D Acoustic Wave Equation

“…The source is located at (2300, 10) m, which is a Ricker wavelet with 30 Hz dominant frequency. A perfectly matched layer absorbing boundary [54,55] is used for wavefield extrapolation.…”

“…The source is located at (2300, 10) m, which is a Ricker wavelet with 30 Hz dominant frequency. A perfectly matched layer absorbing boundary [54,55] is used fo wavefield extrapolation. Figure 7 displays the wavefield snapshots at 0.9 s computed by the CFD4 (Figure 7a) and OCFD4 (Figure 7c-e) schemes.…”

Adaptive-Coefficient Finite Difference Frequency Domain Method for Solving Time-Fractional Cattaneo Equation with Absorbing Boundary Condition

“…A more accurate absorbing boundary algorithm, named complex-frequency-shifted (CFS) PML, improves conventional PML methods for grazing incidences (see [19,20]). The CFS PML has been generalized to the rotated staggeredgrid finite difference simulation (see [21]) for wave propagation in poroelastic (see [22,23]), acoustoelastic (see [24,25]), and thermoelastic (see [26,27]) media.…”

Padé a coustoporoelasticity for 3D wave propagation in prestressed porous rocks with inelastic deformations

“…Great progress has been made in both the theoretical and experimental aspects of acoustoelasticity and acoustoporoelasticity, but dedicated numerical simulations are rarely reported. Yang et al (2022aYang et al ( , 2022bYang et al ( , 2023 perform FD numerical simulations for elastic wave propagation in acoustoelastic and acoustoporoelastic media under confining, uniaxial, and pure shear prestresses, which demonstrates the significant impact of prestressing conditions on seismic responses in velocity and anisotropy. In this study, we apply the standard staggered-grid finite-difference (SSG-FD) to 3D Padé acoustoelasticity and acoustoporoelasticity equations for elastic wave propagation in fluid-saturated porous media subject to confining, uniaxial, and pure shear prestresses.…”

“…We first briefly introduce acoustoelasticity (Pao et al, 1985) and Padé acoustoelasticity (Fu and Fu, 2017) in Appendix A for wave propagation in prestressed media. We then extend the velocity-stress acoustoporoelastic formulation from 2D (Yang et al, 2022b) to 3D cases by incorporating the 3D acoustoelastic 3oeCs into the velocity-stress formulations of 3D poroelasticity equations. Velocity-stress formulation of 3D Padé acoustoporoelasticity equations is formulated by incorporating the 3D acoustoelastic 3oeCs into the velocity-stress formulations of 3D poroelasticity equations.…”