Analytical expressions for the exact 2x2 one--way propagator matrix of a plane S wave, propagating along the axis of spirality in the simple 1-D anisotropic "simplified twisted crystal" model, are presented. The analytical equations are useful in testing the applicability and accuracy of various approximate wavefield modelling methods, especially of the coupling ray theory and of its various quasi-isotropic approximations and various numerical implementations.
In addition to the exact analytical solution of the elastodynamic equation in the "simplified twisted crystal" model, the analytical solutions of the equations of the four ray methods are given. The ray methods are (a) the coupling ray theory, (b) the coupling ray theory with the quasi-isotropic perturbation of travel times, (c) the anisotropic ray theory, (d) the isotropic ray theory. These four approximate solutions of the elastodynamic equation are roughly compared with the exact solution. Both the exact analytical solution and the analytical ray-theory solutions in the "simplified twisted crystal" model are also helpful in debugging computer codes for various approximate wavefield modelling methods, especially for the coupling ray theory.
Anisotropy, S-wave coupling, polarization, elastic waves, exact solution.
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