Stress transfer in earthquakes, hazard estimation and ensemble forecasting: Inferences from numerical simulations

Observations indicate that earthquake faults occur in topologically complex, multi-scale networks driven by plate tectonic forces. We present realistic numerical simulations, involving data-mining, pattern recognition, theoretical analyses and ensemble forecasting techniques, to understand how the observable space–time earthquake patterns are related to the fundamentally inaccessible and unobservable dynamics. Numerical simulations can also help us to understand how the different scales involved in earthquake physics interact and influence the resulting dynamics. Our simulations indicate that elastic interactions (stress transfer) combined with the nonlinearity in the frictional failure threshold law lead to the self-organization of the statistical dynamics, producing 1) statistical distributions for magnitudes and frequencies of earthquakes that have characteristics similar to those possessed by the Gutenberg–Richter magnitude–frequency distributions observed in nature; and 2) clear examples of stress transfer among fault activity described by stress shadows, in which an earthquake on one group of faults reduces the Coulomb failure stress on other faults, thereby delaying activity on those faults. In this paper, we describe the current state of modeling and simulation efforts for Virtual California, a model for all the major active strike slip faults in California. Noting that the Working Group on California Earthquake Probabilities (WGCEP) uses statistical distributions to produce earthquake forecast probabilities, we demonstrate that Virtual California provides a powerful tool for testing the applicability and reliability of the WGCEP statistical methods. Furthermore, we show how the simulations can be used to develop statistical earthquake forecasting techniques that are