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 (Formula presented.) with transition to (Formula presented.) for longer systems or larger prestress, while the subshear events follow (Formula presented.). The model also predicts a supershear scaling relation (Formula presented.). Under the assumption of radial symmetry, the generalization to two-dimensional fault planes compares well with observations.