Variational principles for surface wave propagation on a laterally heterogeneous Earth—II. Frequency‐domain JWKB theory

Jeroen Tromp, F. A. Dahlen

Research output: Contribution to journalArticle

71 Scopus citations

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 languageEnglish (US)
Pages (from-to)599-619
Number of pages21
JournalGeophysical Journal International
Volume109
Issue number3
DOIs
StatePublished - Jun 1992

All Science Journal Classification (ASJC) codes

  • Geophysics
  • Geochemistry and Petrology

Keywords

  • JWKB theory
  • lateral heterogeneity
  • surface waves
  • variational principles

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