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

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

We present 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. All
these quantities are expressed in terms of weak anisotropy (WA) parameters,
which represent a natural generalization of parameters introduced by Thomsen.
The formulas presented and the WA parameters have properties of Thomsen's
formulas and parameters: (1) the approximate equations are considerably
simpler than exact equations for *qP* waves; (2) the WA parameters
are nondimensional quantities; (3) in isotropic media, the WA parameters
are zero and the corresponding equations reduce to equations for isotropic
media. In contrast to Thomsen's parameters, the WA parameters are related
linearly to the density normalized elastic parameters. For the transversely
isotropic media with vertical axis of symmetry, the equations
presented and the WA parameters reduce to the equations and linearized
parameters of Thomsen. The accuracy of the formulas presented 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 approximate formulas presented yield satisfactory results.

Geophysics, **63** (1998), 1754-1766.

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