Exact elastic P/SV impedance

Abstract

Several extensions of the concept of acoustic impedance (AI) to oblique incidence exist and are known as elastic impedances (EI). These quantities are constructed by heuristic integrations of reflectivity series but still involve approximations and do not represent a unique medium property. Nevertheless, for unambiguous interpretation, it is desirable to have an EI that would (1) be a mechanical property of the medium and (2) yield exact reflection coefficients at all angles of incidence. Here, such a definition is given for P- and/or SV-wave propagation in an arbitrary isotropic medium. The exact elastic P/SV impedance is a matrix quantity and represents the differential operator relating the stress and strain boundary conditions. With the use of the matrix form of the reflectivity problem, no approximations are required for accurate modeling of reflection (P/P and SV/SV) and mode-conversion (P/SV and SV/P) coefficients at all angles and for any contrasts in elastic properties. The matrix EI can be computed from real well logs and inverted from ray-parameter-dependent seismic reflectivity. Known limiting cases of P- and S-wave acoustic impedances are accurately reproduced and the approach also allows the extension of the concept of impedance to an attenuative medium. The matrix impedance readily lends itself to inversion with uncertainties typical of the standard acoustic-impedance inversion problem.