Open AccessVariational principles for surface wave propagation on a laterally heterogeneous Earth—I. Time‐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.tb00119.x
Subject(s) - classification of discontinuities , rayleigh wave , surface wave , dispersion (optics) , eigenfunction , surface (topology) , wave propagation , dispersion relation , amplitude , classical mechanics , geophysics , internal wave , geology , physics , geometry , mechanics , mathematical analysis , mathematics , optics , quantum mechanics , eigenvalues and eigenvectors
SUMMARY We present a JWKB theory that describes the propagation of well‐dispersed Love and Rayleigh wavegroups on a smooth, laterally heterogeneous Earth model. The analysis is based upon an averaged Lagrangian which yields local Love and Rayleigh eigenfunctions, local dispersion relations, and conservation laws for the surface wave energy. The local dispersion relations determine the surface wave trajectories, and the energy equations determine the surface wave amplitudes. The amplitude of a surface wavegroup varies in time as a result of both dispersion and geometrical spreading. The theory allows for smooth topography on the Earth's surface and any internal discontinuities, and incorporates the effect of self‐gravitation.