Rocks in the upper mantle are extensively subjected to initial stress. The rock exhibits elastic anisotropy under the deviatoric stress, which affects the seismic response of underground structures. This paper aims to study the effect of stress‐induced anisotropy on the seismic source. The seismic moment tensor generated by a shear faulting in a homogeneous isotropic medium with initial stress is derived by using the motion description in the intermediate configuration, the constitutive relation of third‐order elasticity, and the boundary condition considering the effect of initial stress. Then the seismic moment tensor is decomposed to investigate seismic source characters quantitatively. Our results show that shear faulting in a stress‐induced anisotropic medium can produce significant non‐double‐couple (non‐DC) mechanisms, including compensated linear vector dipole (CLVD) and isotropic (ISO) components. ISO and CLVD components vary linearly with the initial shear stress on faults. In addition, stress‐induced anisotropy causes the double‐couple (DC) to deviate from the plane defined by the fault normal and slip direction. The initial stress not only affects the source intensity but also affects the propagation of seismic waves. The radiation patterns of longitudinal waves have non‐uniform lobes, which shows the characteristic of anisotropy. Stress‐induced anisotropic parameters are smaller than intrinsic anisotropy at high‐stress levels and a nearly linear function of the increased initial stress. These results underscore the importance of considering stress‐induced anisotropy in the inversion of focal mechanisms and provide a new perspective for monitoring underground stress.

Summary The reflection and transmission of elastic waves are of great significance for predicting reservoir physical properties, interpreting seismic data, and detecting crustal structures. Most studies only consider the initial vertical stress state when studying the reflection and transmission of elastic waves at imperfectly bonded interfaces, but few studies consider the influence of initial stress on boundary conditions. Moreover, the effect of initial stress on the energy distribution of elastic waves at imperfectly bonded interfaces has rarely been investigated. We propose a unified method to calculate the energy reflection and transmission coefficients for different incident waves at welded or imperfectly bonded interfaces in stressed media. The effects of initial stress on the equation of motion, the elastic properties of the medium, and the boundary conditions at the interface are considered. The elastic properties of rocks under initial stress are described by acoustoelasticity theory. In addition, we define a new stress tensor to modify the linear-slip model for describing boundary conditions at the imperfectly bonded interface in the presence of initial stress. Numerical results show that the energy reflection and transmission coefficients at the non-welded interface in stressed media depend on the elastic properties of the incident and transmitted media, the initial stress, the type and magnitude of the interfacial compliance, and the frequency and propagation direction of the incident wave. The initial vertical and horizontal stresses dominate the reflection and transmission coefficients at small and large angles, respectively. The discontinuity in displacement across the imperfectly bonded boundary results in the frequency dependence of the reflection and transmission coefficients. Imperfect bonding enhances P-wave and SV-wave energy reflection and weakens P-wave energy transmission. However, imperfect bonding can enhance the energy transmission of the SV wave for the imperfectly bonded interface with high contrast between tangential and normal compliance, and a resonance peak appears at a specific frequency. We also notice that imperfectly bonded interfaces with interfacial compliance less than $1.0 \times {10}^{ - 11}$ m/Pa can be regarded as welded interfaces in the seismic frequency band (lower than 100 Hz). In addition, the initial stress greatly influences the reflection coefficient at high frequencies and the transmission coefficient at low frequencies. The initial vertical stress can reduce the energy transmission of SV waves at imperfectly bonded interfaces. In contrast, the initial horizontal stress can significantly increase the energy transmission of low-frequency SV waves and may lead to the disappearance of the resonant peak in the transmission coefficient.