Tormann, Thessa

We derive a unifying formulation, reliable at all scales, linking Anderson’s faulting theory with the earthquake size-distribution, whose exponent is known as the b-value. Anderson’s theory, introduced in 1905, related fault orientation to stress conditions. Independently, laboratory measurements on acoustic emissions have established that the applied differential stress controls their b-value. Our global survey revealed that observed spatial variations of bare controlled by different stress regimes, generally being lower in compressional (subduction trenches and continental collisional systems) and higher in extensional regimes (oceanic ridges). This confirmed previous observations that the b-value depends on the rake angle of focal mechanisms. Using a new plunge/dip-angles-based b-value analysis, we also identified further systematic influences of faulting geometry: steep normal faults (also typical of the oldest subduction zones) experience the highest proportion of smaller events, while low-angle thrust faults (typical of youngest subduction zones) undergo proportionally larger, more hazardous, events, differently from what would be expected by only allowing for rake-angle dependency. To date, however, no physical model has ever been proposed to explain how earthquakes size-distribution, differential stress and faulting styles relate to each other. Here, we propose and analytically derive a unifying formulation for describing how fault orientation and differential stresses determine b-value. Our formulation confirms that b-values decay linearly with increasing differential stress, but it also predicts a different dip-dependent modulation according to the tectonic environment, opening up new ways of assessing a region’s seismic hazard.

We analyse two high-quality Southern Californian earthquake catalogues, one with focal mechanisms, to statistically model and test for dependencies of the earthquake-size distribution, the b-values, on both faulting style and depth. In our null hypothesis, b is assumed constant. We then develop and calibrate one model based only on faulting style, another based only on depth dependence and two models that assume a simultaneous dependence on both parameters. We develop a new maximum-likelihood estimator corrected for the degrees of freedom to assess models’ performances. Our results show that all models significantly reject the null hypothesis. The best performing is the one that simultaneously takes account of depth and faulting style. Our results suggest that differential-stress variations in the Earth’s crust systematically influence b-values and that this variability should be considered for contemporary seismic hazard studies.

A systematic decay of the aftershock rate over time is one of the most fundamental empirical laws in Earth science. However, the equally fundamental effect of a mainshock on the size distribution of subsequent earthquakes has still not been quantified today and is therefore not used in earthquake hazard assessment. We apply a stacking approach to well-recorded earthquake sequences to extract this effect. Immediately after a mainshock, the mean size distribution of events, or b-value, increases by 20-30%, considerably decreasing the chance of subsequent larger events. This increase is strongest in the immediate vicinity of the mainshock, decreasing rapidly with distance but only gradually over time. We present a model that explains these observations as a consequence of the stress changes in the surrounding area caused by the mainshocks slip. Our results have substantial implications for how seismic risk during earthquake sequences is assessed.

Can We Map Asperities Using b-Values?