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.