Exact P-wave reflection and transmission coefficients for horizontal transversely isotropic media at an imperfectly welded contact interface under in-situ horizontal stress

A comprehensive understanding of exact seismic P-wave reflection and transmission (R/T) coefficients at imperfectly welded or non-welded contact interfaces holds paramount importance in the realm of seismic exploration. Nonetheless, scant attention has been devoted in previous literature to the investigation of stress-dependent exact R/T coefficients in horizontal transversely isotropic (HTI) media, characterized by a horizontal symmetry axis, at such interfaces. Addressing this scholarly gap, we present exact R/T coefficient formulations specifically tailored to an imperfectly welded contact interface separating two HTI media under the influence of in-situ horizontal stress. We begin by deriving the equation of motion for a stressed HTI medium, utilizing the theoretical framework of acoustoelasticity to examine the impact of in-situ horizontal stress on the overarching elastic properties of HTI media. Precise boundary conditions are then established at the imperfectly welded contact interface by applying generalized stress-strain relationships and linear-slip theory, with the influence of in-situ horizontal stress on the interface further explored through the linear-slip model. By integrating these elements with the seismic wave displacement equation, we derive exact R/T coefficient formulations applicable to an imperfectly welded contact interface between two HTI media. Numerical analyses are conducted to elucidate the effects of in-situ horizontal stress on critical parameters such as rock density, seismic wave velocity, Thomsen-type anisotropy parameters, R/T coefficients, and seismic reflection responses at the imperfectly welded contact interface. Furthermore, the proposed formulations are frequency-dependent, with the imperfectly welded contact interface acting as a frequency-selective filter for both reflected and transmitted waves. Notably, under conditions of sufficiently large incident angles, the sensitivity of R/T coefficients to key influencing factors increases significantly. The derived R/T coefficient formulations and the accompanying numerical results offer valuable insights for fracture characterization, stress-dependent parameter inversion, and in-situ stress detection.