## Sensitivity of qP waves to elastic parameters
of arbitrary weakly anisotropic media

**Ivan Psencik** ** & **
**Dirk Gajewski**
### Summary

Approximate formulae for the qP wave phase velocity, polarization
vector and normal moveout in an arbitrary weakly anisotropic medium
are presented. They are all expressed in terms of parameters, which
represent a natural generalization of parameters introduced by
Thomsen (1986). The formulae and the parameters have properties of
Thomsen's (1986) formulae and parameters: (i) the approximate
equations are considerably simpler than exact equations for *qP*
waves; (ii) the generalized parameters are nondimensional quantities;
(iii) in the limiting case of weakly anisotropic media, in isotropic
media, the generalized parameters reduce to zero and the corresponding
equations reduce to equations for isotropic media; (iv) the
generalized parameters are linearly related to the density normalized
elastic parameters. For the case of transverse isotropy, the
equations and the generalized parameters reduce to equations and
parameters of Thomsen (1986). Accuracy of presented formulae is
illustrated on two examples of a hexagonally symmetric material with
a horizontal axis of symmetry, one with qP wave anisotropy less than
1%, the other one with anisotropy of about 20%. Even for the latter
material, satisfactory results are obtained.

In: Seismic Waves in Complex 3-D Structures, Report 4, pp. 93-128,
Dep. Geophys., Charles Univ., Prague 1996.