Higher order linearized approximations of the phase velocities for the quasi – compressional (qP) and two quasi – shear wave types, qS 1 and qS 2 , in a weakly anisotropic orthorhombic medium are presented. Some manipulation of the formulae obtained by standard linearization techniques is done so that the phase velocities are in the form consisting of the most degenerate cases phase velocities (ellipsoids) of an orthorhombic medium plus correction terms to compensate for the deviation from the degenerate orthorhombic case. This is analogous to the ellipsoidal case in a transversely isotropic medium. The quantities in the formulae for the phase velocities all have physical interpretations, that is, they can all be associated with some physically realizable quantity. Further, obtaining the related approximations for group velocities of the three wave propagation types is considerably simplified.
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