Coupled P and SV waves propagating in spherical elastic layers: Exact solution and interpretation

We study the propagation of coupled P and SV waves emitted by a source point placed outside a given finite set of concentric elastic spherical layers. We show that the system of boundary conditions of this pattern is a linear combination of the boundary conditions of the simpler problem of reflectionrefraction phenomenon of a wave at a spherical surface. From this result the exact solution follows for all regions of the multilayered structure without using Cramer's technique. This solution is written as a series of which each element is interpreted directly in terms of multiple reflection-refraction. It gives a simple explanation for triggering of resonance phenomena. The solution contains many particular bases of which several are investigated.