| Abstract: | Theoretical study has been made investigating the seismic source spectrum generated from a coherent and incoherent rupture. An earthquake is modeled by a finite propagating rupture on a fault plane where fault heterogeneities, fault patches, are randomly distributed. The dislocation velocity of such a fracture is assumed to be approximated by a stochastic process of random impacts of particles obeying Brownian motion. The parameters of the present stochastic source are seismic moment, fault dimension, fault patch intensity, and patch fracture time. The model predicts two corner frequencies; one originates from the fault finiteness and the other from the fracturing of fault patches. The seismic source spectrum from the model consequently shows distinct frequency dependence of ω0 − ω−2 − ω−γ − ω−2 with increasing angular frequency ω, where γ is about 1.0. The seismic moment is controlled by an average dislocation on the fault and by the fault dimension. The short-period spectrum, which is much more abundant than that of the ordinary deterministic models, is controlled by the product of the fault patch intensity and the square root of their total number. The ω−2 high frequency asymptote of the theoretical spectrum is in conformity with the white acceleration spectrum usually found in the literature, and it guarantees the finite total energy of the rupture process. |
