Stress-dependent reflection and transmission of elastic waves under confining, uniaxial, and pure shear prestresses

Abstract

Insights into the reflection and transmission (R/T) of waves at a prestressed interface are important in geophysical applications, such as evaluating the angle-dependent elastic properties for monitoring geopressure and tectonic stress using sonic logging data or seismic data. Although many studies deal with wave propagation in prestressed media, the angle-dependent R/T of waves at an interface subject to different prestress loading modes remains largely unaddressed. We address this issue by applying the theory of acoustoelasticity with third-order acoustoelastic constants to study the R/T coefficients at the interface between two prestressed media. Stress-induced elastic deformations are assumed to be locally homogeneous without boundary dislocations caused by stress concentration so that the static boundary conditions can be applied. We consider three typical prestress modes (confining, uniaxial, and pure shear), each of which takes into account the incidence of upgoing and downgoing P and S waves. The Knott equations under different types of prestresses are derived, followed by the estimation of angle-dependent R/T coefficients. The energy conservation at the interface and the acoustoelastic finite-difference simulation of predicted P and S modes verify the correctness of the angle-dependent R/T coefficients under confining prestress. Comparisons with the elastic case (prestress $\sigma =0\mathrm{MPa}$) indicate the important influence of prestresses on the energy distribution of reflected and transmitted waves, including stress-dependent critical angles, converted waves, and R/T energy ratios. Such acoustoelastic effects mainly occur around/after the critical angle. For small-angle incidence, prestresses mainly affect the gradient of R/T coefficients. The type and magnitude of prestress are closely related to the angle-dependent R/T coefficients and must be considered for amplitude-variation-with-offset analysis in prestressed media.