Approximate PP-wave reflection coefficients for weak contrast interfaces se
parating elastic, weakly transversely isotropic media have been derived rec
ently by several authors. Application of these coefficients is limited beca
use the axis of symmetry of transversely isotropic media must be either per
pendicular or parallel to the reflector. In this paper, we remove this limi
tation by deriving a formula for the PP-wave reflection coefficient for wea
k contrast interfaces separating two weakly but arbitrarily anisotropic med
ia. The formula is obtained by applying the first-order perturbation theory
. The approximate coefficient consists of a sum of the PP-wave reflection c
oefficient for a weak contrast interface separating two background isotropi
c half-spaces and a perturbation attributable to the deviation of anisotrop
ic half-spaces from their isotropic backgrounds. The coefficient depends li
nearly on differences of weak anisotropy parameters across the interface. T
his simplifies studies of sensitivity of such coefficients to the parameter
s of the surrounding structure, which represent a basic part of the amplitu
de-versus-offset (AVO) or amplitude-versus-azimuth (AVA) analysis. The refl
ection coefficient is reciprocal. In the same way, the formula for the PP-w
ave transmission coefficient can be derived. The generalization of the proc
edure presented for the derivation of coefficients of converted waves is al
so possible although slightly more complicated. Dependence of the reflectio
n coefficient on the angle of incidence is expressed in terms of three fact
ors, as in isotropic media. The first factor alone describes normal inciden
ce reflection. The second yields the low-order anular variations. All three
factors describe the coefficient in the whole region, in which the approxi
mate formula is valid. In symmetry planes of weakly anisotropic media of hi
gher symmetry, the approximate formula reduces to the formulas presented by
other authors. The accuracy of the approximate formula for the PP reflecti
on coefficient is illustrated on the model with an interface separating an
isotropic half-space from a half-space filled by a transversely isotropic m
aterial with a horizontal axis of symmetry. The results show a very good fi
t with results of the exact formula, even in cases of strong anisotropy and
strong velocity contrast.