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

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.