The moment duration scaling relation for slow rupture arises from transient rupture speeds

Kjetil Thøgersen , Henrik Andersen Sveinsson, Julien Scheibert, Francois Renard, Anders Malthe-Sørenssen

The relation between seismic moment and earthquake duration for slow rupture follows a different power law exponent than sub-shear rupture. The origin of this difference in exponents remains unclear.
Here, we introduce a minimal one-dimensional Burridge-Knopoff model which contains slow, sub-shear and super-shear 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-dimenional faults follow $\bar{M}_{0,\text{slow,1D}}\propto\bar{T}^{0.63}$ with transition to $\bar{M}_{0,\text{slow,1D}}\propto\bar{T}^\frac{3}{2}$ for longer systems or larger prestress, while the sub-shear events follow $\bar{M}_{0,\text{sub-shear},1D}\propto\bar{T}^2$. The model also predicts a super-shear scaling relation $\bar{M}_{0,\text{super-shear,1D}}\propto\bar{T}^3$. Under the assumption of radial symmetry, the generalization to two-dimensional fault planes compares well with observations.