PP wave reflection coefficients in weakly anisotropic elastic media

Vaclav Vavrycuk & Ivan Psencik


Approximate PP wave reflection coefficients for weak contrast interfaces separating elastic, weakly transversely isotropic (TI) media have been derived recently by several authors. Applicability of these coefficients is limited by the fact that the axis of symmetry of TI media must be either perpendicular or parallel to the reflector. In this paper, we remove this limitation by deriving a formula for the PP wave reflection coefficient for weak contrast interfaces separating two weakly but arbitrarily anisotropic media. The formula is obtained by applying the first-order perturbation theory. The approximate coefficient is found as a sum of the corresponding PP wave reflection coefficient for a weak contrast interface separating two isotropic media and its perturbation. The coefficient depends linearly on differences of weak anisotropy (WA) parameters across the interface. This makes studies of sensitivity of such coefficients to the parameters of the surrounding structure, which represent a basic part of the amplitude-versus-offset or amplitude-versus-azimuth analyses, an easy task. The reflection coefficient is reciprocal. In the same way as for the PP wave reflection coefficient, the formula for the PP wave transmission coefficient can be derived. The generalization of the presented procedure for the derivation of coefficients of converted waves is also possible although slightly more complicated. The dependence of the reflection coefficient on the angle of incidence is expressed in terms of three factors, as in isotropic media. The first alone describes normal incidence reflection. All three factors describe then the coefficient in the whole region, in which the approximate formula is valid. In symmetry planes of weakly anisotropic media of higher symmetry, the approximate formula reduces to the formulae presented earlier by other authors. The accuracy of the approximate formula for the PP reflection coefficient is illustrated on the model with an interface separating an isotropic halfspace from a halfspace filled by a transversely isotropic material with a horizontal axis of symmetry. The results show a very good fit with results of the exact formula even in cases of strong anisotropy and strong velocity contrast.

Revised version

Vavrycuk, V. & Psencik, I.: PP wave reflection coefficients in weakly anisotropic elastic media. Geophysics, 63 (1998), 2129-2141.

In: Seismic Waves in Complex 3-D Structures, Report 6, pp. 217-239, Dep. Geophys., Charles Univ., Prague, 1997.
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