Weak‐contrast reflection–transmission coefficients in a generally anisotropic background

Abstract

Explicit equations for approximate linearized reflection–transmission coefficients at a generally oriented weak‐contrast interface separating two generally and independently anisotropic media are presented. The equations are derived also for all singular directions and are thus valid in degenerate cases (e.g., in an isotropic background). The equations are expressed in general Cartesian coordinates, with arbitrary orientation of the interface. The explicit equations for linearized reflection–transmission coefficients have a very simple form—much simpler than the equations published previously. The equations for all reflection–transmission coefficients, with the exception of the unconverted transmitted wave, have a common form. The form of the equations is very suitable for inversion and for analyzing the sensitivity of seismic data to discontinuities in individual elastic moduli. The factors of proportionality of the contrasts of elastic moduli and density are expressed in terms of the slowness and polarization vectors of the corresponding generated wave and incidentwave.