International audienceThere has been debate on whether average slip D in long ruptures should scale with rupture length L, or with rupture width W. This scaling discussion is equivalent to asking whether average stress drop σ , which is sometimes considered an intrinsic frictional property of a fault, is approximately constant over a wide range of earthquake sizes. In this paper, we examine slip-length scaling relations using a simplified 1-D model of spatially heterogeneous slip. The spatially heterogeneous slip is characterized by a stochastic function with a Fourier spectrum that decays as k −α , where k is the wavenumber and α is a parameter that describes the spatial smoothness of slip. We adopt the simple rule that an individual earthquake rupture consists of only one spatially continuous segment of slip (i.e. earthquakes are not generally separable into multiple disconnected segments of slip). In this model, the slip-length scaling relation is intimately related to the spatial heterogeneity of the slip; linear scaling of average slip with rupture length only occurs when α is about 1.5, which is a relatively smooth spatial distribution of slip. We investigate suites of simulated ruptures with different smoothness, and we show that faults with large slip heterogeneity tend to have higher D/L ratios than those with spatially smooth slip. The model also predicts that rougher faults tend to generate larger numbers of small earthquakes, whereas smooth faults may have a uniform size distribution of earthquakes. This simple 1-D fault model suggests that some aspects of stress drop scaling are a consequence of whatever is responsible for the spatial heterogeneity of slip in earthquakes
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