Radiation from supersonic faulting

Abstract

The far-field radiation from a simple fault model is given by the radiation pattern associated with the appropriate strain nucleus (e.g., double couple) multiplied by a fault propagation factor. For a unilateral fault model the propagation factor is $F(c;t)=ζbd[H(τ)−H(τ−(L/ζ)(1−(ζ/c)cosψ))]/(1−(ζ/c)cosψ)$ where ξ is the velocity of fault propagation, b is the fault slip, d is the fault width, τ = t − r₀/c, r₀ is the distance of the observer from the initial point of faulting, c is the velocity of the seismic wave, H(τ) is the unit-step function, L is the length of the fault, and ψ the angle between r₀ and the direction of fault propagation. This representation is valid for both subsonic and supersonic fault propagation. The latter case is important because Weertman (1969) has recently shown that spontaneous faulting may propagate at supersonic velocities. Because the propagation factor is always positive, the nodal planes for the radiation are the same as for the appropriate strain nucleus. Finally, it is shown by the application of this equation that the radiation from a screw dislocation segment is represented by the double-couple nucleus, not the compensated linear-vector dipole nucleus as recently suggested by Knopoff and Randall (1970).