## Polarization, phase velocity and NMO velocity
of qP waves in arbitrary weakly anisotropic media

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

Approximate formulae for the qP wave phase velocity, polarization
vector and normal moveout velocity in an arbitrary weakly anisotropic medium
obtained with the first order perturbation theory are presented. All the
mentioned quantities are expressed in terms of weak anisotropy (WA)
parameters, which represent a natural generalization of parameters
introduced by Thomsen (1986). The presented formulae and the WA 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 WA parameters are non-dimensional quantities;
(iii) in isotropic media, the WA parameters are zero and the corresponding
equations reduce to equations for isotropic media.
In contrast to Thomsen's (1986) parameters, the WA parameters are linearly
related to the density normalized elastic parameters. For the transversely
isotropic media with vertical axis of symmetry, the
presented equations and the WA parameters reduce to equations and linearized
parameters of Thomsen (1986). Accuracy of presented formulae is tested on
two examples of anisotropic media with relatively strong anisotropy:
on a transversely isotropic medium with the horizontal axis of symmetry
and on a medium with triclinic anisotropy. Although anisotropy is rather
strong, the presented approximate formulae yield satisfactory results.

### Whole paper

The paper is available in
PostScript (862 kB)
and GZIPped PostScript (237 kB).

### Revised version

Psencik, I. & Gajewski, D.:
Polarization, phase velocity and NMO velocity
of qP waves in arbitrary weakly anisotropic media.
Geophysics, **63** (1998), 1754-1766.

In: Seismic Waves in Complex 3-D Structures, Report 6,
pp. 183-215, Dep. Geophys., Charles Univ., Prague, 1997.

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