The coupling ray theory provides a continuous transition between the isotropic and anisotropic ray theories, and is particularly important at degrees of anisotropy and frequencies typical in seismic exploration and structural seismology on all scales. In the anisotropic–common–ray approximation of the coupling ray theory, the coupling equation is solved along a single common reference ray, which is traced using the average Hamiltonian of both anisotropic–ray–theory S waves