Generic dependence of the frequency-size distribution of earthquakes on depth and its relation to the strength profile of the crust

We explore the idea that the relative size distribution of earthquakes, quantified using the so-called b-value, is negatively correlated with differential stress. Because the maximum possible differential stress increases linearly in the brittle upper crust, we expect to find a decrease of b with depth. We test this expectation for seven continental areas around the world, each of which is described by a regional earthquake catalog. We find a monotonic decrease in b-value between 5 and 15 km depth. The decrease stops near the brittle-ductile transition. We specifically focus on the high-quality catalogs of earthquakes in California to perform a sensitivity test with respect to depth uncertainty; we also estimate the probability-depth gradient for the occurrence of a target magnitude event and study the behavior of b with depth in near- and off-fault zones. We also translate the observed b-depth gradients into b-differential stress gradients. Our findings suggest that b-values are negatively correlated with differential stress and hus have the potential to act as stress meters in the Earth's crust.