### Abstract

The usual JWKB ray‐theoretical description of Love and Rayleigh surface wave propagation on a smooth, laterally heterogeneous earth model breaks down in the vicinity of caustics, near the source and its antipode. In this paper we use Maslov theory to obtain a representation of the wavefield that is valid everywhere, even in the presence of caustics. The surface wave trajectories lie on a 3‐D manifold in 4‐D phase space (θ, φ, k_{θ}, k_{φ}), where θ is the colatitude, φ is the longitude, and k_{θ} and k_{φ} are the covariant components of the wave vector. There are no caustics in phase space; it is only when the rays are projected onto configuration space (θ, φ), the mixed spaces (k_{θ}, φ) and (θ, k_{φ}), or momentum space (k_{θ}, k_{φ}), that caustics occur. The essential strategy is to employ a mixed‐space or momentum‐space representation in the vicinity of configuration‐space caustics, where the (θ, φ) representation fails. By this means we obtain a uniformly valid Green's tensor and an explicit asymptotic expression for the surface wave response to a moment tensor source.

Original language | English (US) |
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Pages (from-to) | 512-528 |

Number of pages | 17 |

Journal | Geophysical Journal International |

Volume | 115 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 1993 |

### All Science Journal Classification (ASJC) codes

- Geophysics
- Geochemistry and Petrology

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## Cite this

*Geophysical Journal International*,

*115*(2), 512-528. https://doi.org/10.1111/j.1365-246X.1993.tb01203.x