## Stochastic model of heterogeneity in earthquake slip spatial distributions

Daniel Lavallee, Pengcheng Liu, & Ralph J. Archuleta

Published May 2006, SCEC Contribution #871

Finite-fault source inversions reveal the spatial complexity of earthquake slip or pre-stress distribution over the fault surface. The basic assumption of this study is that a stochastic model can reproduce the variability in amplitude and the long-range correlation of the spatial slip distribution. In this paper, we compute the stochastic model for the source models of four earthquakes: the 1979 Imperial Valley, the 1989 Loma Prieta, the 1994 Northridge and 1995 Hyogo-ken Nanbu (Kobe). For each earthquake (except Imperial Valley), we consider both the dip and strike slip distributions. In each case, we use a 1-D stochastic model. For the four earthquakes, we show that the average power spectra of the raw, that is, non-interpolated, data follow a power-law behaviour with scaling exponents that range from 0.78 to 1.71. For the four earthquakes, we have found that a non-Gaussian probability law, that is, the Lévy law, is better suited to reproduce the main features of the spatial variability embedded in the slip amplitude distribution, including the presence and frequency of large fluctuations. Since asperities are usually defined as regions with large slip values on the fault, the stochastic model will allow predicting and modelling the spatial distribution of the asperities over the fault surface. The values of the Lévy parameters differ from one earthquake to the other. Assuming an isotropic spatial distribution of heterogeneity for the dip and the strike slip of he Northridge earthquake, we also compute a 2-D stochastic model. The main conclusions reached in the 1-D analysis remain appropriate for the 2-D model. The results obtained for the four earthquakes suggest that some features of the slip spatial complexity are universal and can be modelled accordingly. If this is proven correct, this will imply that the spatial variability and the long-range correlation of the slip or pre-stress spatial distribution can be described with the help of five parameters: a scaling exponent controlling the spatial correlation and the four parameters of the Lévy distribution constraining the spatial variability.

Citation
Lavallee, D., Liu, P., & Archuleta, R. J. (2006). Stochastic model of heterogeneity in earthquake slip spatial distributions. Geophysical Journal International, 165(2), 622-640. doi: 10.1111/j.1365-246X.2006.02943.x.