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 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.

Repeating Low Frequency Icequakes in the Mont‐Blanc Massif Triggered by Snowfalls

“…Both faults and subglacial slip exhibit a wide spectrum of behavior, from stable slow slip to dynamic rupture, with transient slip events ranging over a wide range of spatial and temporal scales (Peng & Gomberg, 2010). Tectonic faults and subduction zones produce both fast earthquakes, with rupture duration of the order of seconds, and slow slip events, with duration of days or months, and probably a continuum of slip modes in between (Thøgersen et al., 2019). LFIs in the Mont‐Blanc area share several properties with low‐frequency earthquakes (LFEs).…”

Integrated rupture mechanics for slow slip events and earthquakes

“…The comparison of moment-duration scaling relations between SSEs and earthquakes has been considered in discussions of their physical mechanisms 14,[45][46][47][48][49][50][51][52] . However, the moment-duration relation of SSEs observed in a particular environment features a cubic scaling 14 that is radically different from the linear scaling observed in global compilations from different fault environments 45 .…”

“…Though laboratory experiments 22,34,43,44 have suggested a continuum of rupture speeds, these experiments lack a finite rupture width, an essential ingredient of large slow and fast ruptures on natural faults, and the general rupture mechanics controlled by such finite rupture width is not completely understood. Empirical moment-duration scaling relations 14,[45][46][47][48][49][50][51][52] have been used to compare the physical mechanisms of SSEs and earthquakes, yet it is still debated whether the scaling of SSEs is linear 45,46 or cubic 14,47,48 and a fundamental model that integrates SSEs and earthquakes is still lacking.…”

Repeating low frequency icequakes in the Mont-Blanc massif triggered by snowfalls

“…Both faults and subglacial slip exhibit a wide spectrum of behavior, from stable slow slip to dynamic rupture, with transient slip events ranging over a wide range of spatial and temporal scales (Peng and Gomberg, 2010). Tectonic faults and subduction zones produce both fast earthquakes, with duration of the order of seconds, and slow slip events, with duration of days or months, and probably a continuum of slip modes in between (Thøgersen et al, 2019). LFIs in the Mont-Blanc area share several properties with lowfrequency earthquakes (LFEs).…”