Abstract

Insight into wave propagation in prestressed media is of importance to geophysical applications such as monitoring changes in geopressure and tectonic stress. This issue can be approached by the theory of acoustoelasticity that accounts for nonlinear strain responses due to stresses of finite magnitude. In this study, a rotated staggered-grid finite-difference (RSG-FD) method with an unsplit convolutional perfectly matched layer (CPML) absorbing boundary is used to solve the relevant acoustoelastic equations with third-order elastic constants for elastic wave propagation in prestressed media. Numerical acoustoelasticity simulations for wave propagation in single- and double-layer models are performed under four states of prestresses, confining, uniaxial, pure-shear, and simple-shear. The results display the effective anisotropy of elastic wave propagation in acoustoelastic media, illustrating that the prestress-induced velocity anisotropy is of orthotropic features that are strongly related to the orientation of prestresses. These examples demonstrate the significant impact of prestress conditions on seismic responses in both phase and amplitude.

Introduction

The impact of prestressed zones on seismic waves is an important issue that affects the interpretation of the results by seismic imaging and inversion. It is well known that acoustic velocities in rocks are sensitive to prestresses. The theory of acoustoelasticity, as an extension of the classical theory of elasticity, is set up under the framework of hyperelasticity (Shams et al., 2011). The theory relates elastic moduli to prestresses (or residual stresses) in solids (Pao and Gamer, 1985), resulting in an effective anisotropy for wave propagation in acoustoelastic media. It has been used to account for stress-induced velocity variations in rocks (Johnson and Shankland, 1989), therefore perhaps providing the potential to understand the acoustic response to in-situ stresses (Sinha and Kostek, 1996; Huang et al., 2001) and, in turn, to monitor changes in geopressure and tectonic stress. Theoretical and experimental investigations of acoustoelasticity for wave propagation in prestressed rocks have made great signs of progress, but with limited literature on numerical simulations for acoustoelastic wave propagation. As a useful complement to the theoretical solutions of acoustoelastic equations, numerical acoustoelasticity simulations are thought to provide further insights into the stress-induced variations in velocity and anisotropy.

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