NPG Nonlinear Processes in Geophysics NPG Nonlin. Processes Geophys. 1607-7946 Copernicus Publications Göttingen, Germany 10.5194/npg-18-133-2011 A Barnes-Hut scheme for simulating fault slip Beeler N. M. 1 Tullis T. E. 2 US Geological Survey, Cascades Observatory, Vancouver, Washington, 98683, USA Brown University, Providence, Rhode Island, 02712, USA 04 03 2011 18 2 133 146 Copyright: © 2011 N. M. Beeler 2011 This work is licensed under the Creative Commons Attribution 3.0 Unported License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/3.0/ This article is available from https://npg.copernicus.org/articles/18/133/2011/npg-18-133-2011.html The full text article is available as a PDF file from https://npg.copernicus.org/articles/18/133/2011/npg-18-133-2011.pdf

To account for natural spatial and temporal complexity, 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 associated earthquake forecasts is limited by the rates at which computer speed and storage increase. To explore improvements in computational efficiency we develop the first implementation 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 analysis indicates that efficient calculations, where execution time scales with number of grid points (<i>N</i>) as <i>N</i> log <i>N</i>, can be conducted routinely with errors on the order of 0.1%. We expect 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 calculations of stress interaction in complex fault systems.

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