Eigenreverberations, eigenmodes and hybrid combinations: A new approach to propagation in layered multiwave media

Abstract

Coupling of wave species at interfaces and boundaries in a medium composed of plane multiwave layers creates a proliferation of ray fields even after relatively few multiple reflections. This inhibits a ray treatment of propagation from source to observer. The difficulty may be overcome by diagonalizing, in a plane wave spectral representation of the Green's function, the reverberation matrix F descriptive of the boundary coupling. The resulting eigenvectors of F represent combinations of the original Q wave species, to be referred to as eigenrays, which, except for multiplication by the eigenvalue λ q , q = 1 … Q, remain unaltered after one complete reverberation. Thus, eigenrays may be traced through successive reverberations like ordinary rays in a single-wave medium. This feature also permits the original multiwave Q × Q matrix problem to be decoupled into a sequence of scalar problems. Conventional eigenmodes are generated from eigenrays by imposing self-consistency ( λ q = 1) after one reverberation. Alternative representations for the multiwave Green's function by use of these new concepts include plane wave spectral integrals, normal and leaky modes, ray expansions, and hybrid ray-mode expansions. The latter are based on the formulation of an eigenray-eigenmode equivalent. After comparing the new representation with the conventional one, P-SV coupling in an elastic three-layer medium is treated as a special example.