The effect of rupture velocity upon seismic first motions

Abstract

Abstract The effect of rupture velocity upon the first motion radiated by seismic sources is to multiply the radiation pattern by a scalar factor. This modulating function is F1 = ζ/(1 − (ζ/c) cosψ) for unilateral dislocations and F2 = 2ζ/(1 − (ζ/c)2 cos2ψ) for bilateral dislocations; here ζ and c are the velocities of rupture and wave propagation respectively and ψ is the angle between the direction of rupture propagation and the radius vector to the observer. It is presumed that ζ > c. This result constitutes a correction to the first motion theories of Knopoff and Gilbert. The relation of the first motion to the complete response is shown by a sample calculation. It is concluded that the amplitude of the first half cycle of trace displacement on a seismogram is probably a valid measure of the first motion at least for major shallow-focus earthquakes.