Gutenberg–Richter law for deep earthquakes revisited: A dual-mechanism hypothesis

Abstract

Deep earthquake b values appear to vary with slab thermal state and earthquake magnitude. The physical reason for the variations and the relation with deep rupture mechanisms are still unclear. Here I confirm the spatial variations of b value and the dependence on slab temperature using about 40 yr of data from the Global Centroid Moment Tensor catalog. A new bimodal pattern is observed for the 500–700 km depth range: b is close to 1 in the cold Tonga slab, while in warmer slabs (e.g., South America, Japan–Kuril, Izu–Bonin–Mariana), b is close to 0.5 for intermediate magnitudes (M_w 5.3–6.5) and increases to ∼1 for large magnitudes (M_w > 6.5). To explain these observations, I propose a dual-mechanism hypothesis in which deep earthquakes nucleate only within the metastable olivine wedge (MOW), but can rupture outside MOW by a different mechanism. The fractal dimension of earthquake size distribution changes from 2 to 1 as the thermally controlled MOW thickness decreases, and back to 2 as the mechanism outside MOW dominates.