## Implications of Strong-Rate-Weakening Friction for the Length-Scale Dependence of the Strength of the Crust; Why Earthquakes Are so Gentle

#### Thomas Heaton, Cal Tech, Director of the Earthquake Engineering Research Lab

Friday, February 22, 2013 at 10:30 AM

- Location:
- Building 3, Room 3240 (main USGS conference room)
- Host:
- Dave Hill

The thinness of fault slipping zones and the paucity of observed melts implies very low dynamic friction compared to the overburden pressure (less than 0.05 for a meter of slip at 10 km). However, if static friction was comparably low, then the crust could not support observed topographic relief. Strong-rate-weakening friction seems to be a plausible explanation for these seemingly conflicting

observations. Strong-rate-weakening friction leads to slip-pulses with extremely complex failure dynamics; strong positive feedback between the slip and the friction produces multi-scale chaos. Unfortunately, 3-d continuum problems with strong-rate-weakening friction are numerically intractable. Therefore we (Ahmed Elbanna and I) investigated the much simpler problem of 1-d spring block sliders with strong-rate-weakening-friction. We show that the system produces powerlaw complexity. That is, the pre-stress evolves into a state that is heterogeneous

at all scales. Since the pre-stress and the events are spatially heterogeneous, we must generalize our definition of “strength.” We define stress based strength to

be the spatial average of the pre-stress in a failure region, and we define workbased strength to be the average work per unit of deformation. We show that these strengths are not the same. Furthermore, we show that the larger the

event (or system), the smaller the strength. We show that the strength decreases as a power with the size; the exponent of this relation is related to the dynamic

heterogeneity of the system. Since the model is homogeneous, all complexity is dynamic. Earthquakes are so gentle because the Earth is so big. Finally we show a surprising new energy transport equation that reproduces the chaotic behavior of the full numerical simulation. The equation is multi-scale and many orders of magnitude faster than the full numerical system.