Reflection coefficients for non-welded interface between orthorhombic half-spaces under initial stress

SUMMARY Complex oil and gas reservoirs represented by orthorhombic shale usually have the characteristics of strong anisotropy, wide distribution of non-welded interfaces (i.e. particular boundaries caused by horizontal bedding or fracture development), and ubiquitous initial stress effects. The knowledge of their seismic response characteristics plays an essential role in hydrocarbon exploration in stressed shale reservoirs. However, seismic wave reflection in the orthorhombic media under initial stress remains unclear. To address this issue, we used the theories of acoustoelasticity and elastic anisotropy to derive a stress-dependent effective elastic stiffness tensor. At the same time, we obtain the wave velocity and polarization characteristics directly by solving the Christoffel equation. According to the linear slip theory, we further constructed the exact reflection and transmission coefficient equations for the non-welded interface between isotropic and orthorhombic half-spaces under the initial stress. The effects of the non-welded interface on seismic wave velocity and reflection and transmission coefficients were systematically analysed. Meanwhile, we characterize the law of P-wave reflection coefficient effected by elastic coefficients. Our equations and results potentially lay an equation foundation for orthorhombic reservoirs in high-stress fields and are essential in orthorhombic reservoirs in high-stress geophysical exploration.