Physics
Scientific paper
Nov 1982
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982pepi...30..214d&link_type=abstract
Physics of the Earth and Planetary Interiors, Volume 30, Issue 2-3, p. 214-227.
Physics
9
Scientific paper
When the source spectrum is expanded in powers of frequency, the coefficient of the nth power is a linear function of the nth moment tensor. This shows explicitly the low-frequency approximation by moments of low degree, and suggests suitable ways of extrapolation. In extrapolating to higher frequencies the spectral assumption implied restricts the source model to a particular class, and several possibilities, including ω2 and Gaussian models, are here considered. The model has 20 parameters, involving moments of degree zero, one, and two. Model-dependent constraints can reduce this number to that employed in other methods. Deterministic and stochastic interpretations are given, together with the relations to source dimension and correlation length. The models considered lead to simple expressions for the displacement field and the total radiated seismic energy, and can be made to satisfy certain general properties of observed far-field spectra, including the corner-frequency shift of P waves with respect to S waves. Moments of first degree determine the phase spectrum of the model, and their determination is equivalent to the classical source location problem by travel-time analysis. Moments of second degree control the spectral bandwidth and its variation with take-off angle and wave velocity, and their determination is comparable (but not equivalent) to corner-frequency methods of determining source dimensions. A preliminary investigation suggests that in particular the class of Gaussian models satisfies a number of criteria set forth in this paper.
A practical inversion method and its restrictions are discussed and illustrated by the analysis of SRO/ASRO data from a deep-focus event. It is observed that the digital SRO response presently employed can resolve only poorly the excitation spectra of this source, and that frequency-dependent Q and anomalous short-period amplitude variations can significantly affect the estimates. The numerical results in this example should be regarded as tentative.
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