Coupled anisotropic shear-wave ray tracing in situations where associated slowness sheets are almost tangent

For shear waves in anisotropic media a frequency-dependent transport equation is derived, which involves coupling of both shear modes if the slowness vector points in a direction for which the associated slowness surfaces are (almost) tangent. This is achieved by averaging the Hamiltonians for both uncoupled shear modes. No assumption on weak anisotropy is made, and the shear polarisation is perpendicular to the P-wave polarisation for the actual slowness direction instead of an isotropically approximated P-wave polarisation. These are the main differences compared with the so-called zero-order quasi-isotropic approach.