Earthquakes come in a range of sizes spanning at least 10 orders of magnitude, and they exhibit clustering in both space and time. Power law distributions of number versus energy and energy versus time before and after large events suggest that a complex systems approach to earthquake mechanics may yield new insights into the spatio-temporal distribution of slip for individual earthquakes, and into the spatio-temporal patterns of regional seismicity.

Our program in Earthquake Physics attempts to bridge the gap between the well-developed continuum mechanics approach to fault instability, and the newer and less-developed mechanics of multi-scale fracture zones in a critical state. This is done by studying the behavior of 3D elastic solids containing systems of discrete heterogeneities that are characterized by different levels of disorder. We model spatio-temporal patterns of seismicity and faults, precursors, with a focus on statistics of seismicity, precursors, evolution of fault systems, and the development of a physical basis for estimating seismic risk. The goal is to relate local and regional seismic responses to geometric features of faults and interacting systems of faults, and to the rheology of the brittle seismogenic region and its ductile surroundings. Our studies explore earthquake scenarios for various plausible structural and rheological fault properties, establish the physical basis for extrapolating low-magnitude seismicity into rates of occurrence of moderate and large-size events, and examine the possibility of earthquake forecasting based on seismicity patterns.