3D acoustoelastic FD modeling of elastic wave propagation in prestressed solid media

Abstract

Seismic exploration of deep oil/gas reservoirs involves the propagation of seismic waves in high-pressure media. Traditional elastic wave equations are not suitable for describing such media. The theory of acoustoelasticity establishes the dynamic equation of wave propagating in prestressed media through constitutive relation using third-order elastic constants. Many studies have been carried out on numerical simulations for acoustoelastic waves, but mainly are limited to 2D cases. A standard staggered-grid (SSG) finite difference (FD) approach and the perfectly matched layer (PML) absorbing boundary are combined to solve 3D first-order velocity-stress equations of acoustoelasticity to simulate wave propagating in 3D prestressed solid medium. Our numerical results are partially validated by plane wave analytical solution through the comparison of calculated and theoretical P-/S-wave velocities as a function of confining prestress. We perform numerical simulations of acoustoelastic waves under confining, uniaxial, and pure shear prestressed conditions. The results show the stress-induced velocity anisotropy in acoustoelastic media, which is closely related to the direction of prestresses. Comparisons to seismic simulations based on the theory of elasticity illustrate the limitation of conventional elastic simulations for prestressed media. Numerical simulations prove the significant effect of prestressed conditions on seismic responses.

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.…”

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.…”

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.…”