Calculation of Wave Parameters for Weakly Anisotropic Media

Summary To compute the phase velocities in the weakly anisotropic media, we propose to transform the Christoffel matrix into an adapted coordinate system, and, then, apply the perturbation theory to the resulting matrix. The diagonal elements of the resulting matrix are initial approximations of the phase velocities squared. To refine them, it is proposed to use either iterative schemes or Taylor series expansions. To approximate the phase velocities of the S1 and S2 waves, a stable method is proposed based on solving a quadratic equation with the coefficients being expressed in terms of the matrix elements and the precomputed value of the qP wave phase velocity squared. The computational accuracy is demonstrated for the standard orthorhombic model.