Now at: Department of Earth and Planetary Sciences, Harvard University, Cambridge, Massachusetts 02138, USA.
Maslov theory for surface wave propagation on a laterally heterogeneous earth
Article first published online: 2 APR 2007
Geophysical Journal International
Volume 115, Issue 2, pages 512–528, November 1993
How to Cite
Tromp, J. and Dahlen, F. A. (1993), Maslov theory for surface wave propagation on a laterally heterogeneous earth. Geophysical Journal International, 115: 512–528. doi: 10.1111/j.1365-246X.1993.tb01203.x
- Issue published online: 2 APR 2007
- Article first published online: 2 APR 2007
- Accepted 1993 April 23. Received 1993 February 15; in original form 1992 April 3
- JWKB theory;
- lateral heterogeneity;
- Maslov theory;
- surface waves
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, kθ, kφ), where θ is the colatitude, φ is the longitude, and kθ and kφ 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 (kθ, φ) and (θ, kφ), or momentum space (kθ, kφ), 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.