MODELING OF EARTHQUAKE RUPTURING AS A STOCHASTIC-PROCESS AND ESTIMATION OF ITS DISTRIBUTION FUNCTION FROM EARTHQUAKE OBSERVATIONS

The effect on earthquake rupturing of heterogeneities in tectonic stre ss and in material strength along a large fault zone is incorporated i n the potential dynamic stress drop, defined as the difference between the tectonic shear stress and the dynamic frictional strength accordi ng to a slip-weakening model. The distribution of the potential dynami c stress drop Delta tau(d)(x) along the strike of the fault plane is m odelled as a 1-D stochastic process. Using a simple dynamic fracture c riterion, a relation is established between earthquake rupturing and p otential dynamic stress drop, by which any earthquake rupture process can be regarded as a segment of a realization of the process Delta tau (d)(x) where Delta tau(d)(x) > 0. Since dynamic slip varies approximat ely linearly with dynamic stress drop, it has the same distribution fu nction as Delta tau(d)(x), provided that Delta tau(d)(x) is a Gaussian process. Three independent earthquake observations, i.e. the average stress drop, the Gutenberg-Richter relation and the surface slip along earthquake faults, are used to estimate the distribution function of Delta tau(d)(x). An analytical solution is derived for the distributio n function of Delta tau(d)(x), which shows that, among all known distr ibution models, only the fractional Brownian motion with index H-->0 ( fractal dimension D = 2 in the 1-D case) can give rise to the observed approximately constant stress drop independent of earthquake size. Th e probability distribution of the size of zerosets of the fractional B rownian motion shows a power-law relation with frequency, which resemb les the frequency-seismic-moment relation. Using an average b value of 1.0 for small earthquakes, an index H-->0 of the fractional Brownian motion is obtained. The model predicts that the b value for large eart hquakes is smaller than that for small earthquakes along the same faul t zone, which is in agreement with observations. The surface slip data of two strike-slip-dominated earthquake faults with rupture lengths l arger than 100 km are inverted using power spectral analysis. Both dat a sets display a power-law relation between the sample power spectrum and the spatial frequency, which implies a fractional Brownian distrib ution. The estimated index H is close to zero for both earthquake faul ts. Stress drops, b values, and surface slips all independently sugges t that the earthquake rupturing process can be modelled stochastically as a fractional Brownian motion with index H-->0.