Open AccessSymmetry of the wave equation and excitation of body waves
Author(s) -
Chapman C. H.,
Woodhouse J. H.
Publication year - 1981
Publication title -
geophysical journal of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0016-8009
DOI - 10.1111/j.1365-246x.1981.tb04883.x
Subject(s) - propagator , physics , symmetry (geometry) , excitation , classical mechanics , vibration , matrix (chemical analysis) , differential equation , viscoelasticity , plane symmetry , mathematical analysis , mathematics , geometry , quantum mechanics , materials science , composite material , thermodynamics
Summary. The symmetry of the differential system for elastic waves, previously noted for plane geometry, is extended to any linear differential system and, in particular, the elastic‐gravitational vibrations in a spherical earth. The result remains valid in a linearly viscoelastic medium. The symmetry allows the inverse of the propagator matrix to be obtained by simply ‘transposing’ the elements of the propagator. With this result, it is shown how the source excitation using a particular integral can be put in a more instructive form, comparable with the result for the excitation of normal modes.