Extended formulation for Rayleigh-wave computations at high frequencies in a spherical layered earth |
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Authors: | S N Bhattacharya |
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Institution: | Seismological Observatory, India Meteorological Department, Lodi Road, New Delhi 110003, India |
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Abstract: | Summary. The earlier formulation of dispersion function, amplitude response and surface ellipticity for Rayleigh waves in a spherical layered earth has been extended by the reduced-delta matrix to avoid computational instability at high frequencies. We derive a modified formulation, where the layer thickness is kept separated during matrix multiplications. The present formulations are valid for an unlimited frequency range. A numerical experiment with single precision (six decimal digits accuracy) on an IBM 360/44 computer is performed at frequencies from 0.4 to 12.5 Hz on a Shield structure down to a depth of 1090 km below which a complete sphere is assumed. The experiment shows that both reduced-delta matrix and modified formulations generate roots of the dispersion equation without any reduction of layers. However, to avoid unnecessary computation, a layer-reduction procedure has been derived from a modified formulation when the contribution of deep layers becomes insignificant on surface waves. |
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Keywords: | dispersion function Rayleigh wave spherical earth |
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