Characteristics of orthorhombic anisotropic seismic response induced by horizontal in situ stress in vertical transversely isotropic media

Sedimentary strata typically exhibit the characteristics of transverse isotropy (VTI) with a vertical axis of symmetry. However, fractures in sedimentary strata tend to produce anisotropic closure due to horizontal in situ stress, resulting in pronounced orthorhombic anisotropy in VTI media under such stress conditions and influencing the propagation behavior of seismic waves. Previous studies have primarily focused on the elastic wave velocity anisotropy induced by applied stress in isotropic background media, neglecting the impact of VTI background media on the anisotropy induced by horizontal in situ stress and the response characteristics of seismic wave propagation. To address these gaps, we first establish the effective elastic stiffness tensor of VTI media under horizontal in situ stress using nonlinear acoustoelastic theory. Then, we derive the accurate and linearized approximate equations for P-wave seismic reflectivity of VTI media under horizontal in situ stress, based on wave equations and scattering theory, respectively. Finally, we compare and analyze the characteristics of orthorhombic anisotropic seismic response induced by horizontal in situ stress at various types of elastic reflection interfaces. Our results demonstrate that the linearized approximation of the seismic reflection response characteristics closely aligns with the accurate equations under conditions of small stress below 10 MPa, effectively capturing the azimuth-dependent orthorhombic anisotropy induced by horizontal in situ stress in VTI media. The results of this study also provide a novel theoretical approach and valuable insights into the seismic prediction of in situ stress.