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Bulletin of the Seismological Society of America; February 1972; v. 62; no. 1; p. 369-384
© 1972 Seismological Society of America
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A real frequency, complex wave-number analysis of leaking modes

THOMAS H. WATSON*

DEPARTMENT OF EARTH AND PLANETARY SCIENCES UNIVERSITY OF PITTSBURGH, PITTSBURGH, PENNSYLVANIA, 15213

Abstract

Leaking-mode dispersion and attenuation is computed for two single-layer models. Roots of the dispersion relation are obtained in the complex wave-number plane, using real frequency as the independent variable. At low frequencies the root loci on the (+, +) sheet determine the fundamental propagating mode plus a series of attenuated standing-wave modes in the vicinity of the source. As frequency increases, the complex roots on all four sheets migrate through the wave-number plane, producing (successively) organ-pipe modes, PL modes, and normal modes. For higher frequencies, the modes exhibit a tendency to couple with pure P- (and S-) type motion in the wave guide. These effects are related to similar phenomena which occur for the case of the free elastic plate.

Results are also calculated for a six-layer continental model. Here the pseudo-modes on the (+, –) sheet noted by Cochran et al. (using real wave-number analysis) are found to be decoupled P- and S-related modes whose phase-velocity curves freely intersect one another when frequency is assumed real.

Footnotes

* Now at Gulf Research and Development Company, Pittsburgh, Pa.




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