Spatial Heterogeneity of Fault Slip and the Radiated Spectra of Ground Motions

Kinematic models of simulating earthquake radiation in seismic hazard analysis typically require prescribing the distribution of final slip over the hypothetical fault planes. The spatial spectra of heterogeneous slip affect the frequency spectra of the seismic body waves. The representation integral of elasticity provides a convenient analytical tool by which the relationships between the slip spectra in the wavenumber domain and the wave spectra in the frequency domain can be scrutinized. In the limit of the waves from a small source in the far field, the Fourier spectrum of wave displacement is the spectrum of the slip-rate function multiplied by the spatial slip spectrum representing fault directivity. A popular model for the latter is the k-square slip distribution. Classic results prescribe that for a typical ??-square source time function, such multiplication, conversely to a common assumption that the k-square slip distribution always leads to the ??-square decay of the high-frequency seismic spectra, can result in the ?????4 power-law decay. Such steep fall-off rates are highly unusual in observations, suggesting that the k-square heterogeneous slip in certain cases may significantly underpredict the realistic high-frequency ground motions, including peak velocities and accelerations. An alternative use of heterogeneous slip distributions would be to explain the additional high-frequency diminution of the observed spectra that is usually attributed to ad hoc cutoff (???fmax??? or ???kappa???) filters. The simple asymptotic relationships between heterogeneous fault slip and body wave spectra may not hold true in the vicinity of large earthquakes, at distances of main interest to hazard calculations.