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Energy radiation from a spherically symmetric homogeneous source

DEPARTMENT OF CIVIL ENGINEERING THE TECHNOLOGICAL INSTITUTE NORTHWESTERN UNIVERSITY, EVANSTON, ILLINOIS 60201

Abstract

General expressions for energy radiated from seismic sources in linear elastic bodies are illustrated and clarified by examining the energy radiated from a spherically symmetric source. Calculations with the spherical source demonstrate that the point source approximation for the radiated energy is not asymptotic in the sense that it does not approach the actual radiated energy for small source dimension. Comparison between the energies radiated from the spherical source for a ramp time function and for a modulated ramp demonstrate that the modulation is not effective in increasing the total radiated energy even though it does cause a peak in the spectrum of the far-field particle velocity at the characteristic frequency of the modulation. For a/cT > 2, where a is the radius of the spherical source, c is the wave speed, and T is the rise time, the strain energy change overestimates the radiated energy by less than a factor of two.

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