PP-wave reflection coefficient in stress-induced anisotropic media and amplitude variation with incident angle and azimuth inversion

Abstract

The PP-wave reflection coefficient (i.e., the ratio of the amplitude of reflected P wave to the amplitude of incident P wave) has crucial practical applications in many field scenarios, such as seismic inversion and in-situ stress monitoring. However, the effect of biaxial stress, frequently encountered in the earth’s interior, on the PP-wave reflection coefficient is seldom studied. To fill this gap, we first formulate the P- and S-wave moduli and density in a biaxial-stress-induced anisotropic medium based on the acoustoelasticity theory. Then, the stress-dependent anisotropy parameters and normal/tangential rock weaknesses are proposed in the context of the stress-induced anisotropy model to obtain the corresponding effective elastic stiffness tensor and its spatial perturbation. Two stress-induced anisotropy factors (SIAF) are established to quantify the magnitude of anisotropy in a stress-induced anisotropic medium. The media with large SIAF tend to demonstrate strong anisotropy when stressed and tend to be more easily fractured from the perspective of engineering application. Furthermore, an approximate formula for the PP-wave reflection coefficient for biaxial-stress-induced anisotropic media is developed with the scattering theory. Numerical results illustrate how the reflection coefficients are affected by horizontal biaxial stress and demonstrate the feasibility and accuracy of our formula. Modeled and field inversion examples illustrate that SIAF can be reasonably inverted with our amplitude variation with incident angle and azimuth inversion method from azimuthal seismic data. Our results help to better understand the effect of biaxial stress on anisotropy and wave propagation in stress-induced anisotropic media.