Accurate formulae for <i>P</i>-wave reflectivity and transmissivity for a non-welded contact interface with the effect of <i>in situ</i> vertical stress
Fubin Chen, Zhaoyun Zong, Xingyao Yin, Yanwen Feng
Abstract
SUMMARY A detailed knowledge of wave reflectivity parametrization for non-welded interface plays an important role in fracture characterization and reservoir prediction. However, the effect of in situ stress on reflectivity formulae for non-welded contact interface remains unclear. Here based on the linear-slip theory and acoustoelasticity theory, we propose the accurate P-wave reflectivity and transmissivity formulae for planar P wave incident upon the non-welded interface between two elastic half-spaces under the in situ vertical stress. The discontinuous boundary conditions coupled with vertical stress is used to represent the non-welded contact interface for the elastic and viscous cases. Then accurate formulae are derived by solving the boundary conditions. Numerical results show that the proposed formulae are frequency-dependent and the non-welded interface performs as high- and low-pass filters for reflected and transmittedP wave at low stress, respectively. Moreover, initial vertical stress can change the maximum amplitudes of reflection and transmission coefficients and the corresponding critical angles. Particularly, vertical stress weakens the fracture-induced anomalous seismic reflections in zones lack of significant impedance contrasts at low incidence angles. The sensitivity analysis suggests a non-welded interface transforms into a welded interface at normal compliance ${\Delta _N} \le 5 \times {10^{ - 11}}$ m Pa−1. The phases and amplitudes of the four coefficients reach the maximum values at the specific viscosity $\eta \approx {10^6}$ Pa·s m−1 for the case of P wave obliquely incident upon the viscous interface at incidence angle 30°. Finally, we describe a method for simulating seismic reflection at the interface of two elastic media with experimental measurement.