Radiation of Seismic Surface Waves from Simple Models of Fault-Planes. Part I: Rayleigh Waves

Abstract

This paper investigates the effect of the finiteness of the seismic focus on the Rayleigh-wave pattern. The equations of motion are solved for an internal harmonic concentrated force which points in an arbitrary direction. A fault-plane is then realized by moving this source along a line with finite speed and integrating the Rayleigh pole contribution across a finite rectangle with an arbitrary strike and dip. Displacements are evaluated for long ranges and expressions are obtained for strike-slip and dip-slip fault types. Attention is mainly focused on a dipole-type motion of a vertical strike-slip model for which displacement has been actually computed and the results transformed into the time domain. It is found that there exists a considerable deviation from the point-dipole pattern when the velocity of rupture is above the Rayleigh-speed and when the wave length is of the order of the fault-dimensions. It is also found that azimuthal distribution of amplitudes in that range depends strongly on the dimensions of the source and that the energy radiated in the direction of motion highly exceeds the amount radiated in the opposite direction. Formulae are also given for theoretical seismograms in dispersive media which by comparison with real seismograms may lead to an estimation of the source-dimensions and the speed of rupture.

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