Open AccessVariational principles for surface wave propagation on a laterally heterogeneous Earth—II. Frequency‐domain JWKB theory
Author(s) -
Tromp Jeroen,
Dahlen F. A.
Publication year - 1992
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1111/j.1365-246x.1992.tb00120.x
Subject(s) - surface wave , physics , wave propagation , rayleigh wave , classification of discontinuities , caustic (mathematics) , amplitude , classical mechanics , eigenfunction , optics , quantum mechanics , mathematical analysis , mathematics , mathematical physics , eigenvalues and eigenvectors
SUMMARY 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.