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

Veronique Farra and Ivan Psencik


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. In deriving them, we use first-order quantities, with which we work when using first-order ray tracing (FORT) for inhomogeneous anisotropic media. Specifically, the phase velocities, slowness and polarization vectors used are of the first-order with respect to the deviations of anisotropy from isotropy. The derived R/T coefficients transform an incident P wave into a reflected/transmitted P or coupled S wave. Coefficients can be computed for any incidence angle between 00 and 900, 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 acceptable accuracy.

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In: Seismic Waves in Complex 3-D Structures, Report 20, pp. 77-102, Dep. Geophys., Charles Univ., Prague, 2010.