Open AccessArchambeau's Elastodynamical Source‐Model Solution and Low‐Frequency Spectral Peaks in the Far‐Field Displacement Amplitude
Author(s) -
Snoke J. Arthur
Publication year - 1976
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.1976.tb00273.x
Subject(s) - classification of discontinuities , discontinuity (linguistics) , spurious relationship , boundary value problem , near and far field , mathematical analysis , exact solutions in general relativity , boundary (topology) , amplitude , field (mathematics) , displacement (psychology) , physics , relaxation (psychology) , mathematics , geometry , optics , psychology , psychotherapist , social psychology , statistics , pure mathematics
Summary An analysis of Archambeau's method for obtaining the elastodynamic source‐model solution for an instantaneous rupture leads to the following conclusions: (1) For most problems of interest Archambeau's method of solution is not exact because it neglects dynamical boundary conditions. (2) For calculating far‐field displacements, Archambeau's method of solution is equivalent to Randall's. (3) Archambeau's solution for a stress relaxation model gives a good approximation of the exact solutions for the far‐field displacements. (4) Solutions obtained by Archambeau's method have been presented and interpreted as initial‐value‐model solutions, but they can also be represented as boundary‐value‐model solutions. It is apparent from the boundary‐value‐model representation that all discontinuity surfaces in the elastic medium radiate simultaneously, whereas in this representation only the boundary should be a source of radiation. Anomalous spectral structure in models employing Archambeau's method of solution is found to result from radiation from discontinuities other than the rupture‐zone boundary and is therefore spurious.