The Moment Duration Scaling Relation for Slow Rupture Arises From Transient Rupture Speeds

Abstract

The relation between seismic moment and earthquake duration for slow rupture follows a different power law exponent than subshear rupture. The origin of this difference in exponents remains unclear. Here, we introduce a minimal one‐dimensional Burridge‐Knopoff model which contains slow, subshear, and supershear rupture and demonstrate that different power law exponents occur because the rupture speed of slow events contains long‐lived transients. Our findings suggest that there exists a continuum of slip modes between the slow and fast slip end‐members but that the natural selection of stress on faults can cause less frequent events in the intermediate range. We find that slow events on one‐ dimensional faults follow M 0;slow;1D∝T 0:63 with transition to M 0;slow;1D∝T 3 2 for longer systems or larger prestress, while the subshear events followM 0;sub ‐shear;1D∝T 2 . The model also predicts a supershear scaling relation M 0;super ‐shear;1D∝T 3 . Under the assumption of radial symmetry, the generalization to two‐ dimensional fault planes compares well with observations. Plain Language Summary Observations have shown that the duration of earthquakes is related to the seismic moment through a power law. The power law exponent is different for regular earthquakes and slow aseismic rupture, and the origin of this difference is currently debated in the literature. In this letter, we introduce a minimal mechanical friction model that contains both slow and regular earthquakes and demonstrate that the different power laws emerge naturally within the model because the propagation speed of slow earthquakes decays as a power law in time, whereas the propagation speed of regular earthquakes remains fairly constant.