## 1. Introduction

[2] The Gutenberg-Richter law for the distribution of sizes of events, stating that earthquakes follow a power law distribution of sizes of events, is one of the most important and ubiquitous observations in seismology. If one looks in detail at it, however, interesting issues emerge. While the law describes the complete population of events, the distributions of events on the individual faults which make up the whole fault system remains an open question. One extreme posits that each fault segment breaks with some characteristic size event, and it is the distribution of sizes of faults which then leads to the distribution of sizes of events. An alternative extreme posits that each fault itself produces a power law distribution of sizes of events, and it is the dynamics of individual faults which underlie the distribution of sizes of events. Other positions link these extremes, e.g., through the evolution of fault properties over geological timescales, with faults evolving from young rough faults with power law distributions towards more mature smooth faults with more characteristic distributions [*Stirling et al.*, 1996]. To get at these issues from a theoretical point of view, we need to tackle both the issue of fault system geometry, and event dynamics, over many earthquake cycles.

[3] Here, we present a new model which both generates self-consistent complex fault geometries, and generates self-consistent elastodynamic events on those geometries. Further, because of the numerical efficiency of the model, we can generate long sequences of events, and study the statistics of the populations. With this model, we can thus begin to address the fundamental questions of the interaction of geometry and dynamics. In this letter, we present this new model, and its application to the issue of fault geometry and the distribution of sizes of events.

[4] Previous work has examined the evolution of populations of events on complex fault systems; these approaches have, however, neglected the dynamics on the rupture timescale, simplifying the interactions to be quasistatic [*Lyakhovsky et al.*, 2001]. Other models have treated elastodynamic event populations, but only with simple fault geometries [*Carlson and Langer*, 1989; *Myers et al.*, 1996]. Other models have examined individual elastodynamic events on nonplanar fault geometries, but not populations of events [*Harris et al.*, 1991; *Kame and Yamashita*, 1997; *Bouchon and Streiff*, 1997]. One modeling approach has looked at event sequences on an individual complex fault [*Mora and Place*, 1999]. With our new model, we open up a new regime of study, of elastodynamic event sequences on complex fault systems.