# Marian Anghel

Center for Nonlinear Studies
Los Alamos National Laboratory

We perform numerical simulations of a discrete 2D cellular fault zone embedded in a 3D elastic solid. The model contains a vertical planar fault with a uniform grid of cells where slip is governed by a static/kinetic friction law surrounded by regions where a uniform slip rate is prescribed to represent the tectonic loading. Quasi-static stress transfer and tectonic loading along the fault are calculated using 3D elastic dislocation theory. Inertial effects are accounted for approximately by a dynamic overshoot coefficient defined as D = [tau_s - tau_a] / [tau_s - tau_d], where tau_s, tau_d, and tau_a are respectively static strength, dynamic strength, and arrest stress. The model incorporates strong heterogeneities by assigning different levels of dynamic (and hence also arrest) stress to different fault regions. The static strength and the dynamic overshoot coefficient are uniform along the fault. The key question we address is how are geometrical, mechanical, and rheological properties of fault systems and their surrounding medium are related to different types of patterns in space-time-energy domains.

The simulations indicate that faults with no dynamic weakening, D \rightarrow \infty, produce the typical Gutenberg-Richter scaling behavior with a dissipation dependent cutoff size (controlled by the fault aspect ratio L/W) and a mean-field scaling exponent. When the dynamic weakening is non-zero, the simple scaling regime that characterizes in the previous case all the events is destroyed. For small weakening effects it is still possible to separate the events into different classes: a mean-field class with a mean-field scaling exponent; a second class of scaling events that has a scaling exponent that depends on the amount of dynamic weakening; and a characteristic event'' class.

Increasing the dynamic effects, D \rightarrow 1, leads to the disappearance of the mean-field events class - this indicates a breakdown of scaling- and the appearance of many characteristic'' events. Dynamic weakening also reduces the number of effective degrees of freedom and projects the fault dynamics into a low dimensional atractor. We present some preliminary results from the application of the principal orthogonal decomposition (POD) analysis to the fault dynamics. The POD yields a finite-dimensional subspace of the full phase space which contains the dominant dynamics and we analyze how heterogeneity and dynamical effects control the dimensionality of this subspace.