The similarity between ruptures in scaled laboratory seismotectonic models and slow earthquakes

Modeling the seismic cycle requires multiple assumptions and parameters. Providing a quantitative assessment of the model behavior is pivotal for determining the degree of similarity between different scales and modeling strategies and for exploring dependencies with respect to selected parameters. Here we compare stick-slip ruptures nucleating spontaneously in scaled seismotectonic models (i.e., laboratory experiments capturing the first-order physics of the seismic cycle of subduction megathrusts) with slow earthquakes in nature. We rely on two non-dimensional parameters, namely the Ruina number (Ru) and system dimension (D) to quantify model behavior. Ru is proportional to the ratio of the asperity size to the critical nucleation size. Within the rate- and state friction framework, for velocity weakening asperities Ru controls the behavior of the system, which can be either periodic or not, and it can exhibit both slow and fast ruptures. D measures how complicated the system evolution is. D reveals how many variables are required to describe the seismic cycle because it tells us the minimum dimension needed to embed the observed dynamics. 

By coupling the Simulated Annealing algorithm and quasi-dynamic numerical simulations, we retrieve rate and state friction parameters characterizing single asperity models with different lateral extent of the velocity weakening patch. Similarly to slow earthquakes, we found optimal rate and state parameters indicative of low (< 4) Ru. We also found a direct proportionality between Ru and the lateral extent of the asperity. 

Next, we implement tools from non-linear time-series analysis and Extreme Value Theory to compute D from models of different sizes, materials, deformation rates and frictional configurations (single or twin asperities along strike). Our analysis supports the existence of a low dimensional attractor (D<5) describing the dynamics of scaled seismotectonic models. In particular, our models display D=3.0-4.2, which is remarkably similar to D=3.2 of slow earthquakes identified along the Cascadia subduction zone. Under the explored conditions, D appears more affected by the material behavior of the analog upper plate (i.e., gelatin vs. foam rubber) than by the lateral frictional segmentation of the megathrust.

Despite the different spatio-temporal scales, our results support a scenario where scaled seismotectonic models and slow earthquakes share similar dynamics.