## PP-wave reflection coefficients in weakly anisotropic elastic media

**Vaclav Vavrycuk** **&**
**Ivan Psencik**
### Summary

Approximate PP-wave reflection coefficients for weak contrast interfaces
separating elastic, weakly transversely isotropic media have been derived
recently by several authors. Application of these coefficients is
limited because the axis of symmetry of transversely isotropic 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 consists of a sum of
the PP-wave reflection coefficient for a weak contrast interface separating
two background isotropic half-spaces and a perturbation attributable to
the deviation of anisotropic half-spaces from their isotropic backgrounds.
The coefficient depends linearly on differences of weak anisotropy parameters
across the interface. This simplifies studies of sensitivity of such
coefficients to the parameters of the surrounding structure, which represent
a basic part of the amplitude-versus-offset (AVO) or amplitude-versus-azimuth
(AVA) analysis. The reflection coefficient is reciprocal. In the same way,
the formula for the PP-wave transmission coefficient can be derived.
The generalization of the procedure presented for the derivation
of coefficients of converted waves is also possible although slightly more
complicated. Dependence of the reflection coefficient on the angle of
incidence is expressed in terms of three factors, as in isotropic media.
The first factor alone describes normal incidence reflection. The second
yields the low-order angular variations. All three factors describe
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 formulas presented 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
half-space from a half-space 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.

### Whole paper

The reprint is available in
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*Geophysics*, **63** (1998), 2129-2141.

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