Radiation from a realistic model of faulting

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Abstract
The Knopoff-deHoop representation theorem has been used to calculate the form of the body waves radiated from an elliptical fault. Rupture is assumed to initiate at one focus of the ellipse and then spread out radially on the fault plane. Two cases are considered: 1) constant slip everywhere on the fault surface and 2) a variable slip which approaches zero at the fault edge. The radiation is calculated for distances from the fault which are large compared to the fault dimensions. The body waves are described by the product of two factors, one of which is the familiar equivalent-force system radiation pattern. The other factor includes the time dependence of the signal; it does not depend upon the direction of slip. The body waves exhibit two stopping phases. The theory is used to estimate the fault dimensions associated with six deep-focus earthquakes studied by Kasahara. The estimated fault dimensions are about twice the dimensions of the focal sphere as found by Kasahara. Finally, the difference between the phase spectrums of shallow and deep-focus earthquake radiation observed by Kishimoto is shown to be related to a difference in shape of the two fault surfaces; shallow-focus earthquakes appear to be associated with elongated fault surfaces, whereas deep-focus earthquakes are associated with more circular fault surfaces.

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