Gaussian beams in inhomogeneous anisotropic layered structures

Gaussian beams, approximate solutions of elastodynamic equation concentrated close to rays of high-frequency seismic body waves, propagating in inhomogeneous anisotropic layered structures, are studied. They have Gaussian amplitude distribution along any straightline profile intersecting the ray. At any point of the ray, the Gaussian distribution of amplitudes is controlled by the 2 × 2 complex-valued symmetric matrix M of the second derivatives of the traveltime field with respect to ray-centred coordinates. Matrix M can be simply determined along the ray if the ray propagator matrix is known and if the value of M is specified at a selected point of the ray. The ray propagator matrix can be calculated along the ray by solving the dynamic ray tracing system twice: once for the real-valued initial plane-wave conditions and once for the real-valued initial point-source conditions.