Summary
The aim of the present paper is to investigate whether the so called leaking modes in the propagation of seismic waves exist or not. Physically, the idea of leaking modes whose amplitudes increase as the distance from the free surface increases does not seem to be sound. We give a detailed mathematical reasoning in support of this view. To this end, we reconsider the simple problem ofLapwood [3]2). After deforming the path of integration to the second sheet and evaluating each term which appears we see that terms which are seemingly responsible for leaking modes, cancel out. Thus mathematically also it appears that there are no leaking modes.
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References
J. H. Rosenbaum,The Long time Response of a Layered Elastic Medium to Explosive Sound, J. Geophys. Research65 (1960), 1577–1614.
R. A. Phinney,Leaking Modes in the Crustal Waveguide, J. Geophys. Research66 (1961), 1445–1470.
E. R. Lapwood,The Disturbance due to a Line Source in a Semi-infinite Elastic Medium, Phil. Trans. Roy. Soc., Lond. [A]242 (1949), 63–100.
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Gupta, U. On leaking modes. PAGEOPH 80, 27–37 (1970). https://doi.org/10.1007/BF00880191
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DOI: https://doi.org/10.1007/BF00880191