A study of a nonwelded contact interface: Exact and approximate formulas for P-SV reflection and transmission coefficients, and frequency domain raytracing

The sixteen exact mathematical formulas for the P-SV particle displacement refection and transmission coefficients for elastic plane waves incident upon a nonwelded contact interface separating two solid half-spaces, and approximations to these formulas for small amounts of nonwelded contact, small incidence angles, etc., are presented. The nonwelded contact at the interface is represented by displacement discontinuity boundary conditions. The characteristics of these conditions are that the traction is continuous across the interface but the displacement is not. The displacement discontinuity components are proportional to the corresponding stress components—the constants of proportionality are called specific compliances. The exact formulas for the coefficients are obtained by algebraically solving the displacement discontinuity boundary conditions for each possible incident wave in the P-SV case. The formulas are expressed in the form of the coefficients for the welded contact case plus additional terms due to the presence of nonwelded contact. The formulas show that the existence of nonwelded contact makes the coefficients frequency-dependent.; For the specific case in which the media above and below the interface are the same (e.g., a fault, joint or fracture in a homogeneous medium), reflected waves exist, and there are phase changes in the transmitted wave, unlike the case for a perfect welded contact interface between two identical media, in which there are no reflected waves due to the lack of an impedance contrast. Numerical computations of the coefficients also confirm, in this case, that the nonwelded contact interface acts like a low-pass filter (Pyrak-Nolte et al., 1990b), i.e., more of the incident energy is transmitted through the interface at lower frequencies than at higher ones.; Ray-synthetic seismograms are also computed for media containing nonwelded interfaces. Due to the frequency dependence of the coefficients, the synthetic seismograms are generated by frequency domain raytracing to include the full effect of nonwelded contact for all considered frequency ranges. The generated seismograms show the change in both amplitude and phase over a nonwelded contact interface. Even for small values of the specific compliances, the phase change is significant.