Factors controlling high-frequency radiation from extended ruptures

Small-scale slip heterogeneity or variations in rupture velocity on the fault plane are often invoked to explain the high-frequency radiation from earthquakes. This view has no theoretical basis, which follows, for example, from the representation integral of elasticity, an exact solution for the radiated wave field. The Fourier transform, applied to the integral, shows that the seismic spectrum is fully controlled by that of the source time function, while the distribution of final slip and rupture acceleration/deceleration only contribute to directivity. This inference is corroborated by the precise numerical computation of the full radiated field from the representation integral. We compare calculated radiation from four finite-fault models: (1) uniform slip function with low slip velocity, (2) slip function spatially modulated by a sinusoidal function, (3) slip function spatially modulated by a sinusoidal function with random roughness added, and (4) uniform slip function with high slip velocity. The addition of “asperities,” both regular and irregular, does not cause any systematic increase in the spectral level of high-frequency radiation, except for the creation of maxima due to constructive interference. On the other hand, an increase in the maximum rate of slip on the fault leads to highly amplified high frequencies, in accordance with the prediction on the basis of a simple point-source treatment of the fault. Hence, computations show that the temporal rate of slip, not the spatial heterogeneity on faults, is the predominant factor forming the high-frequency radiation and thus controlling the velocity and acceleration of the resulting ground motions.