A Barnes-Hut scheme for simulating fault slip

To account for natural spatial and temporal com- plexity, large-scale, long-duration calculations are required for simulations of seismicity in fault zones that host large earthquakes. Without advances in computational methods, the rate of progress in "earthquake simulator" models and as- sociated earthquake forecasts is limited by the rates at which computer speed and storage increase. To explore improve- ments in computational efficiency we develop the first im- plementation of the Barnes-Hut algorithm (Barnes and Hut, 1986) to calculate elastic interactions in a fault model. The Barnes-Hut method is an efficient, numerical scheme that treats local forces exactly and distant forces approximately. The approach is illustrated in example simulations of non- linear fault strength in plane strain. Rudimentary error analy- sis indicates that efficient calculations, where execution time scales with number of grid points (N ) as N logN , can be conducted routinely with errors on the order of 0.1%. We ex- pect the Barnes-Hut method to be well suited for conducting initial exploration of parameter space for fault simulations with non-linear constitutive equations, and for efficient cal- culations of stress interaction in complex fault systems.