### 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.

Original language | English (US) |
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Pages (from-to) | 435-457 |

Number of pages | 23 |

Journal | Wave Motion |

Volume | 6 |

Issue number | 5 |

DOIs | |

State | Published - Sep 1984 |

### ASJC Scopus subject areas

- Modeling and Simulation
- Physics and Astronomy(all)
- Computational Mathematics
- Applied Mathematics

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## Cite this

*Wave Motion*,

*6*(5), 435-457. https://doi.org/10.1016/0165-2125(84)90001-5