Abstract
We present a JWKB theory for the propagation of monochromatic Love and Rayleigh waves on a smooth, laterally heterogeneous Earth model. The analysis is based upon a slowly varying Lagrangian which yields local Love and Rayleigh eigenfunctions, local dispersion relations, and transport equations which determine the variation in surface wave amplitude along a ray. The amplitude of a monochromatic Love or Rayleigh wave varies only as a result of geometrical spreading; the amplitude diverges and the phase is shifted by /2 each time the wave passes through a caustic singularity, where the width of the ray tube vanishes. We obtain the JWKB surface wave Green's tensor and derive an explicit expression for the JWKB response to a moment tensor source. The theory allows for slowly varying topography of the Earth's surface and any internal discontinuities, and incorporates the effect of self‐gravitation and slight anelasticity on surface wave propagation.
Original language | English (US) |
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Pages (from-to) | 599-619 |
Number of pages | 21 |
Journal | Geophysical Journal International |
Volume | 109 |
Issue number | 3 |
DOIs | |
State | Published - Jun 1992 |
All Science Journal Classification (ASJC) codes
- Geophysics
- Geochemistry and Petrology
Keywords
- JWKB theory
- lateral heterogeneity
- surface waves
- variational principles