Using a linearized approximation of the phase velocity related to quasi-compressional (qP) wave propagation in a weakly general 21 parameter anisotropic medium, an approximate eikonal equation is constructed. The corresponding expression for the related group velocity is then derived. The degenerate (ellipsoidal) case of (qP) wave propagation in an anisotropic medium is explored and an exact group velocity expression obtained, together with the exact expressions for the slowness vector components, for this reduced case. This ellipsoidal group velocity is taken as the reference or background velocity surface. Slowness vector components are in terms of the group velocity vector angles. This result is employed as a trial solution in the approximate eikonal equation, where the related group velocity surface is taken to be a perturbed ellipsoid. The group velocity expressions, both approximate and exact, are numerically compared for an anisotropic model that may be classified as weakly anisotropic or, possibly more accurately, weakly anellipsoidal, as the background group velocity surface used is an ellipsoid.
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