Abstract
SUMMARY The resonant eigenfrequencies of three-dimensional models of sedimentary basins are calculated through the use of high-frequency asymptotics. The results are valid for the areas near the geometrical centre of the basin, where the thickness of sediments is greatest. By analogy with the theory of electromagnetic resonators it is shown that the modes of oscillation of trapped seismic waves can be easily computed from simple formulas that relate the geometry of the basin to the type of resonant mode and to the eigenfrequencies. All results are approximations based on WKB solutions to the wave equation whose phase function satisfy resonant or ‘quantum’ conditions inside the basin. Comparison with published numerical data indicates that the analytical approach here described .may be of more general application than the empirical formulations that have been proposed previously for two-dimensional basins.
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