On the scale dependence of earthquake stress drop

Abstract

We discuss the debated issue of scale dependence in earthquake source mechanics with the goal of providing supporting evidence to foster the adoption of a coherent interpretative framework. We examine the heterogeneous distribution of source and constitutive parameters during individual ruptures and their scaling with earthquake size. We discuss evidence that slip, slip- weakening distance and breakdown work scale with seismic moment and are interpreted as scale dependent parameters. We integrate our estimates of earthquake stress drop, computed through a pseudo-dynamic ap- proach, with many others available in the literature for both point sources and finite fault models. We obtain a picture of the earthquake stress drop scaling with seis- mic moment over an exceptional broad range of earth- quake sizes (−8 < MW < 9). Our results confirm that stress drop values are scattered over three order of mag- nitude and emphasize the lack of corroborating evidence that stress drop scales with seismic moment. We discuss these results in terms of scale invariance of stress drop with source dimension to analyse the interpretation of this outcome in terms of self-similarity. Geophysicists are presently unable to provide physical explanations of dy- namic self-similarity relying on deterministic descriptions of micro-scale processes. We conclude that the interpre- tation of the self-similar behaviour of stress drop scaling is strongly model dependent. We emphasize that it relies on a geometric description of source heterogeneity through the statistical properties of initial stress or fault- surface topography, in which only the latter is constrained by observations.