Alternative linearized expressions for qP, qS1 and qS2 phase velocities in a weakly anisotropic orthorhombic medium
P. F. Daley, Edward S. Krebes
Alternative linearized approximations of the phase velocities for the quasi-compressional, qP, and two quasi-shear wave types, qS1 and qS2, in an orthorhombic medium are presented. Algebraic manipulation of the formulae obtained from the standard linearization technique is done so that the phase velocities are in the form consisting of the most degenerate cases of phase velocities in an orthorhombic medium (ellipsoids) plus anellipsoidal correction (perturbation) terms to compensate for the deviation from the degenerate orthorhombic case. The quantities in the formulae for the phase velocities all have physical interpretations, that is, they can all be associated with some physically realizable and measurable quantity. After obtaining these intermediate linearized expressions for the qP, qS1 and qS2 phase velocities, further approximations are made to obtain the equivalent of what are termed fully linearized formulae. This includes the introduction of an isotropic background velocity, , for the qP and in the qS1 and qS2 equations. A comparison of the intermediate linearized approximations for the phase velocities with the exact formulae are presented in a series of figures.