First-order reflection/transmission coefficients for unconverted plane P waves in weakly anisotropic media

Abstract

SUMMARY We present approximate formulae for the plane-wave displacement reflection/transmission (R/T) coefficients for interfaces of arbitrary contrast, separating two homogeneous, weakly anisotropic media. They result from boundary conditions requiring continuity of displacement vector and traction, in which coupled S waves are considered as a single S wave and exact quantities are replaced by first-order quantities used in first-order ray tracing. Specifically, the phase velocities, slowness and polarization vectors of P and coupled S waves appearing in the boundary conditions are of the first-order with respect to the deviations of anisotropy from isotropy. Application of the derived R/T coefficients transforms the amplitude of an incident P wave into amplitudes of reflected/transmitted P or coupled S waves. Coefficients can be computed for any incidence angle between 0° and 90°, and for any azimuth. In this paper, we test the accuracy of the derived R/T coefficients of unconverted plane P waves. We show that, except for critical regions, first-order coefficients approximate the exact coefficients with accuracy comparable or better than accuracy of linearized weak-contrast coefficients, which are, however, applicable only in subcritical regions.