## Properties of weak contrast PP reflection/transmission
coefficients for weakly anisotropic elastic media

**Ivan Psencik** ** & **
**Jorge Leonardo Martins**
### Summary

Approximate formulae for PP reflection/transmission
(R/T) displacement
coefficients for weak contrast interfaces separating
weakly anisotropic media of an arbitrary
symmetry are presented. The coefficients have
a form of a sum of a well-known approximate PP
reflection/transmission coefficient for a weak
contrast interface separating two background
isotropic halfspaces and a correction due to weak
anisotropy. The correction is controlled, linearly,
by the so-called weak anisotropy (WA) parameters.
The coefficients are defined with respect to an
arbitrary isotropic background. The formulae
are convenient for description of coefficients of
reflection and transmission in low symmetry
weakly anisotropic media as well as in media with
higher symmetry (orthorhombic, hexagonal) with
arbitrarily oriented axes of symmetry. For
anisotropies of higher symmetry, for which
approximate formulae of other authors exist, we discuss
the differences between these and our formulae
and effects of these differences on the accuracy of
approximate coefficients. Performance of the
approximate formulae for R_{PP} coefficients is tested on
models with weak anisotropy and weak contrast
interfaces as well as on models whose anisotropy
and velocity contrast are in no way weak.
Even in the latter case, the formulae yield satisfactory
results. Accuracy of the approximate R_{PP} coefficient
depending on the choice of the background is
then investigated. It is shown that the R_{PP}
coefficient can be described, approximately, by
a formula, whose correction term due to anisotropy
is independent of the S-wave background
velocity and depends only slightly on the choice
of the P-wave background velocity. The formulae
for the R_{PP} coefficients commonly used in literature
for higher symmetry anisotropies are obtained
by linearization of the above mentioned formula.
Linearization leads to the dependence of the R_{PP}
coefficient on the choice of the S-wave background
velocity and, generally, to a slight decrease of
accuracy. Presented formulae are convenient
for solving an inverse problem: determination of
contrasts of parameters of anisotropic media
surrounding an interface. Sensitivity of the
approximate R_{PP} coefficient to basic weak anisotropy
parameters is presented.

### Whole paper

The reprint is available in
PDF (2355 kB !).

*Stud. geophys. geod.*, **45** (2001), 176-199.

SW3D
- main page of consortium ** Seismic Waves in Complex 3-D Structures **.