1 Gutenberg-Richter Statistics in Topologically Realistic System-Level Earthquake Stress-Evolution Simulations John B. Rundle1, Paul B. Rundle2 , Andrea Donnellan3 and Geoffrey Fox4 1Center for Computational Science and Engineering, University of California, Davis, Davis, CA 95616; and Distinguished Visiting Scientist, Earth & Space Sciences Division Jet Propulsion Laboratory, Pasadena, CA 91125 ([email protected]; http://naniloa.ucdavis.edu/~rundle/) 2Department of Physics, Harvey Mudd College, Claremont, CA 3Earth & Space Sciences Division, Jet Propulsion Laboratory, Pasadena, CA 4Department of Computer Science, Indiana University, Bloomington, IN Abstract. We discuss the problem of earthquake forecasting in the context of new models for the dynamics based on statistical physics. Here we focus on new, topologically realistic system-level approaches to the modeling of earthquake faults. We show that the frictional failure physics of earthquakes in these complex, topologically realistic models leads to self-organization of the statistical dynamics, and produces statistical distributions characterizing the activity, notably the Gutenberg-Richter magnitude frequency distribution, that are similar to those observed in nature. In particular, we show that a parameterization of friction that includes a simple representation of a dynamic stress intensity factor is needed to organize the dynamics. We also show that the slip distributions for synthetic events obtained in the model are also similar to those observed in nature2 1. Introduction Earthquakes have great scientific, societal, and economic significance. During the first three months of 2001, the January 13, 2001 magnitude 7.6 El Salvador earthquake, the January 26, magnitude 7.9 Gujarat, India earthquake, and the February 28, 2001 magnitude 6.8 Seattle, Washington, USA event killed thousands of persons and caused billions of dollars in property losses. The January 16, 1995 Kobe, Japan earthquake was only a magnitude 6.9 event and yet produced an estimated $200 billion loss. Despite an active earthquake forecasting/prediction program in Japan, this event was a complete surprise. Similar scenarios are possible in Los Angeles, San Francisco, Seattle, and other urban centers around the Pacific plate boundary. The magnitude of the potential loss of life and property in earthquakes is so great that reliable earthquake forecasting has been a long-sought goal. Examples of recent large earthquakes affecting life and property include the January 13, 2001 magnitude 7.6 El Salvador earthquake, the January 26, magnitude 7.9 Gujarat, India earthquake, and the February 28, 2001 magnitude 6.8 Seattle, Washington, USA event. Many millions of dollars and many thousands of work years have been spent on observational programs searching for reliable precursory phenomena. Possible precursory phenomena include changes in seismicity, changes in seismic velocities, tilt and strain precursors, electromagnetic signals, hydrologic phenomena, and chemical emissions (Turcotte, 1991; Scholz, 1990). A few successes have been reported, but to date, no precursors to large earthquakes have been detected that would provide reliable forecasts (Nature, 1999). In terms of data acquisition several major approaches are currently being emphasized. These include: 1. Paleoseismic observations of historic earthquakes whose occurrence and locations are preserved in offset surface sediments; 2. Patterns of seismicity (origin time, location, magnitude of earthquakes); 3. Surface deformation measured via Global Positioning System (GPS) networks such as the Southern California Integrated GPS Network (SCIGN), and the Bay Area Regional Deformation (BARD) network (SCEC; Nature, 1999). 4. Synthetic Aperture Radar Interferometry (InSAR) observations of surface displacement. Observations of these data types are also planned as part of the Earthscope NSF/GEO/EAR/MRE initiative. In fact, the Plate Boundary Observatory (PBO) plans to place more than a thousand GPS, strainmeter, and deformation sensors along the active plate boundary of the western coast of the United States, Mexico and Canada, at an eventual cost in excess of $100 million (Nature, 1999). It is clearly a very high priority to utilize this wealth of new data to better understand the fundamentals of earthquake occurrence. This understanding can improve several aspects of the earthquake hazard. For example:3 1. Risk assessment. Determining the probability of the occurrence of an earthquake of a specified magnitude in a specified area within a specified time window. 2. Earthquake forecasting (prediction). Finding patterns of behavior that can provide statistically acceptable forecasts of future major earthquakes. 2. Earthquakes Numerical Simulations. Earthquakes are a complex nonlinear dynamical system, so that techniques appropriate for the study of linear systems have not been of much use. There are two serious drawbacks to a purely observational approach to the problem of earthquake forecasting: 1) Inaccessible and unobservable stress-strain dynamics, and 2) Multiscale dynamics that cover a vast range of space and time scales. Because of these fundamental problems, the use of numerical simulations, together with theory and analysis, is mandatory if we are to discover answers to the questions above. Correspondingly, all types of earthquake-related data, including seismic, geodetic, paleoseismic, and laboratory rock mechanics experiments must be employed. The data are used both to determine physical properties of the models we simulate, a process of data assimilation, as well as to critically test the results of our simulation-derived hypotheses, so that future hypotheses can be developed. Several authors have pursued numerical simulations of this type (Rundle, 1988; Ward, 2000; Hashimoto, 2001; Rundle et al., 2001). Unobservable Dynamics. Geologic observations indicate that earthquake faults occur in topologically complex, multi-scale networks that are driven to failure by external forces arising from plate tectonic motions (Rundle et al., 2000a; Rundle et al., 2001; Ward, 2000). The basic problem in this class of systems is that the true stress-strain dynamics is inaccessible to direct observations, or unobservable. For example, the best current compendium of stress magnitudes and directions in the earth’s crust is the World Stress Map (Zoback, 1992),