Spatiotemporal Predictability
Seismic and aseismic slip events are often chaotic due to stress heterogeneities. Because the system self-organizes, the prestress is limited to a chaotic attractor, which is notably a smaller set than arbitrary functions in high-dimensional space. We describe the prestress with few scalars using a model reduction technique (Proper Orthogonal Decomposition). During the interseismic period, the trajectories of the dynamical system pass through certain critical regions (corresponding to certain prestresses) inside the chaotic attractor for large events to happen. Outside those regions, earthquakes can still nucleate but arrest as partial ruptures. We determine the statistically feasible optimal interevent prestress leading to large events. Using those instability regions and only the current slip rate on the fault, we establish a spatiotemporal forecast of large events in a model of a fault governed by rate-and-state friction, which produces a realistic chaotic sequence of events.
Geometry of the fault and the frictional properties (a). The diamonds are the locations of slip rate measurements for the scenario in which we do not have full access to the slip rate on the entire fault. Maximum stress along the depth is plotted as a function of distance along strike and time (b). The maximum slip rate along the depth is plotted as a function of distance along strike and time (c). Both (b) and (c) show spatiotemporal complexity in the time series of the system. MFD of the events in a simulation for 1000 years of simulation (d).
Schematic of the approximation of the chaotic attractor in the function space. The blue region represents an approximation of the chaotic attractor of the system during the interevent period. When events happen, the trajectory of the states of the system jumps outside the blue region. The green trajectories represent small partial ruptures, while the red trajectories depict large ruptures, which occur infrequently compared to the green trajectories, as indicated by Magnitude Frequency Distribution. Orange regions correspond to instability regions inside the interevent period part of the chaotic attractor through which the trajectories of the system have to pass for a large event to happen. Orange regions are critical prestress. By finding them, we are able to predict the time and extent of large rupture.
Video of Prediction of Large events