A theoretical omega-square model considering the spatial variation in slipand rupture velocity

A theoretical model for constructing the omega-squared model is proposed by modifying the k-squared model of Bernard et al. (1996). The k-squared mode l provides a theoretical basis for the empirical omega-squared model under the assumptions that (1) the spatial wavenumber spectrum of the slip distri bution falls off as the inverse of the wavenumber squared (k-squared), (2) the Fourier amplitudes of the slip velocity are independent of omega at hig h frequencies, and (3) the rupture velocity is constant. In this study, a m ore realistic model is proposed by modifying the last two assumptions. Firs t, a Kostrov-type slip velocity model is proposed by superposing equilatera l triangles, in which a source-controlled fmax is imposed by the minimum du ration among the triangles. The Fourier amplitude of our slip velocity mode l falls off as the inverse of omega at high frequencies less than fmax. Nex t, in order to model variable rupture velocities, the incoherent rupture ti me (Delta t(r)), namely, the difference between the actual rupture time and the coherent (average) rupture time, is introduced. After checking various models for Delta t(r) distributions, the k-squared model for Delta t(r), s imilar to that for the slip distributions of the k-squared model, is found to be the most plausible. Finally, it is confirmed that the proposed source model (we call it as the omega-inverse-squared model), which consists of t he combination of the slip velocity proposed here and the k-squared distrib utions for both slip and Delta t(r), not only is consistent with the empiri cal omega-squared model, but also provides the theoretical basis for constr ucting realistic source models at broadband frequencies.