Stress-Dependent PP-Wave Reflection Coefficient for Fourier-Coefficients-Based Seismic Inversion in Horizontally Stressed Vertical Transversely Isotropic Media

The subsurface in situ stress fields significantly influence the elastic and anisotropic properties of rocks, yet traditional linear elastic theories often overlook the impact of stress on seismic response characteristics. Nonlinear acoustoelastic theory integrates third-order elastic constants (TOECs) to elucidate the influence of stress on changes in elastic and anisotropic properties of stressed rocks. A comprehensive examination of recent scholarly investigations on nonlinear acoustoelastic phenomena precedes the introduction of an innovative stress-dependent equation for the PP-wave reflection coefficient. This equation delineates the dependence of azimuthal seismic response on horizontal uniaxial stress in inherently vertical transversely isotropic (VTI) media, or those VTI formations induced by a single set of horizontal aligned fractures. Emphasis is placed on delineating stress-induced anisotropy and elucidating azimuthal PP-wave reflection characteristics in horizontally uniaxially stressed VTI media. Additionally, this discourse extends to more intricate scenarios involving horizontally biaxially and triaxially stressed VTI media, as delineated by nonlinear acoustoelastic theory. Subsequently, the reflection coefficient of horizontally uniaxially stressed VTI media is expressed in terms of azimuthal Fourier coefficients (FCs), revealing that the unstressed VTI background exhibits heightened sensitivity to zeroth-order FC, while the stress-induced anisotropy manifests greater sensitivity to second-order FC. Through the application of azimuthal FCs-based amplitude versus offset and azimuth (AVOAz) inversion method to both synthetic and field datasets, the proposed model and approach offer promising avenues for reservoir characterization in VTI media subject to horizontal uniaxial stress conditions.