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