Mesh dependence and slip complexity in earthquake fault models

We study the origins of mesh dependence in earthquake dynamics and show that mesh sensitivity in numerical models of earthquake rupture can unearth new, exciting physical phenomena, and provide hidden clues to discovering the physics underlying earthquake complexity. We show (in agreement with previous numerical studies of dynamic rupture at faults) that coarse meshes or discrete models produce more interesting physics because these numerical simulations produce richer spatio-temporal complexity at faults over multiple earthquake cycles. These discrete models are desirable as they reproduce the observed Gutenberg-Richter power-law frequency magnitude distribution of earthquakes more accurately. However, this complexity is lost as the mesh size is refined, which is undersirable from a physical point of view. We investigate this mesh sensitivity by analysing the higher-order perturbative terms introduced into numerical models with coarse meshes. The introduction of these higher-order, nonlinear terms into standard continuum models generally used to describe earthquake dynamics may provide a key to reproducing earthquake complexity while partially removing the associated mesh dependence without the need to modify the underlying mesh. This is a first step towards deriving a physical law capable of reproducing the scale-invariant behaviour in earthquake sizes and reconciling continuum and discrete models of earthquake rupture. Copyright © 2009 John Wiley & Sons, Ltd