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.

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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