Maslov theory for surface wave propagation on a laterally heterogeneous earth

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.