Wave reflection and transmission coefficients for layered transversely isotropic media with vertical symmetry axis under initial stress

Abstract

SUMMARYThe stress-dependent wave reflection and transmission (R/T) coefficients for the layered transversely isotropic media with a vertical symmetry axis (VTI) are seldom investigated in the published literature. To fill this gap, we propose the exact formulas for the plane wave R/T coefficients on the welded and non-welded boundaries between two distinct VTI half-spaces under the effect of initial stress. The theory of acoustoelasticity is used to describe the influence of initial applied stress on the overall elastic properties of VTI media and to represent two different boundary conditions. The normal and tangential compliances are used to characterize the discontinuity of non-welded boundary based on the linear-slip model, and their stress dependences are ideally considered according to the effect of stress on fracture aperture. Then the plane-wave displacement equations are substituted into the boundary conditions to yield the analytic formulas for frequency-independent R/T coefficients for the welded interface and frequency-dependent R/T coefficients for the non-welded interface. The stress-dependent wave slowness vector and polarization vector embedded in R/T coefficients can be directly computed with the Christoffel equation given by the acoustoelastic equation. Modelling results graphically show the effects of initial stress on the angle-dependent wave velocities, Thomsen elastic anisotropy parameters, fracture compliances, the R/T coefficients and seismic reflection responses for welded and non-welded interfaces in detail. The R/T coefficients are more sensitive to initial stress at relatively large incidence angles for the designed two-layer model with welded or non-welded boundary. The proposed R/T coefficient formulas and modelling results are relevant to in situ stress detection, fracture characterization, and exploration for oil and gas in shale reservoirs in high-stress fields.