Abstract
Virtual California is a topologically realistic simulation of the interacting earthquake faults in California. Inputs to the model arise from field data, and typically include realistic fault system topologies, realistic long-term slip rates, and realistic frictional parameters. Outputs from the simulations include synthetic earthquake sequences and space-time patterns together with associated surface deformation and strain patterns that are similar to those seen in nature. Here we describe details of the data assimilation procedure we use to construct the fault model and to assign frictional properties. In addition, by analyzing the statistical physics of the simulations, we can show that that the frictional failure physics, which includes a simple representation of a dynamic stress intensity factor, leads to self-organization of the statistical dynamics, and produces empirical statistical distributions (probability density functions:PDFs) that characterize the activity. One type of distribution that can be constructed from empirical measurements of simulation data are PDFs for recurrence intervals on selected faults. Inputs to simulation dynamics are based on the use of time-averaged event-frequency data, and outputs include PDFs representing measurements of dynamical variability arising from fault interactions and space-time correlations. As a first step for productively using model-based methods for earthquake forecasting, we propose that simulations be used to generate the PDFs for recurrence intervals instead of the usual practice of basing the PDFs on standard forms (Gaussian, Log-Normal, Pareto, Brownian Passage Time, and so forth). Subsequent development of simulation-based methods should include model enhancement, data assimilation and data mining methods, and analysis techniques based on statistical physics.
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References
Barnhard, T. and Hanson, S., compilers (2000–2001 accessed), Fault parameters used in USGS 1996 Seismic Hazard maps, http://eqhazmaps.usgs.gov/html/faults.html.
Council of the National Seismic System, in association with the Northern California Earthquake Data Center (2000–2001 accessed), CNSS earthquake catalog, http://quake.geo.berkeley.edu/cnss/catalog-search.html.
Deng, J. S. and Sykes, L. R. (1997), Evolution of the stress field in southern California and triggering of moderate-size earthquakes: A 200-year perspective, J. Geophys. Res., 102(B5), 9859–9886.
Dieterich, J. S. (1979), Modeling of rock friction. I. Experimental results and constitutive equations, J. Geophys. Res. 84, 2161–2168.
Evans, M., Hastings, N., and Peacock, B., Statistical Distributions (Wiley Interscience, New York, 1993).
Jaumé, S. C. and Sykes, L. R. (1996), Evolution of moderate seismicity in the San Francisco Bay region, 1850 to 1993: Seismicity changes related to the occurrence of large and great earthquakes, J. Geophys. Res. 101(B1), 765–789.
Kanamori, H. and Anderson, D. L. (1975), Theoretical basis of some empirical relations in seismology, Bull. Seismol. Soc. Am. 65, 1073–1095.
Karner, S. L. and Marone, C., Effects of loading rate and normal stress on stress drop and stick-slip recurrence interval, pp. 187–198 in (Rundle, J. B., Turcotte, D. L., and Klein, W., eds.) GeoComplexity and the physics of Earthquakes, Geophysical Monograph, 120 (American Geophysical Union, Washington, D. C., 2000).
Matthews, M. V., Ellsworth, W. L., and Reasenberg, P. A. (2002), A Brownian model for recurrent earthquakes, Bull. Seismol. Soc. Am., 92, 2233–2250.
Petersen, M. D. and Wesnousky, S. G. (1994), Fault slip rates and earthquake histories for active faults in Southern California, Bull. Seismol. Soc. Am. 84(5), 1608–1649.
Petersen, M. D., Bryant, W. A., Cramer, C. H., Cao, T., Reichle, M., Frankel, A. D., Lienkaemper, J. J., McCrory, P. A., and Schwartz, D. P. (1996), Probabilistic seismic hazard assessment for the state of California, USGS Open-File Report 96–706, U. S. Govt. Printing Office.
Rangarajan, G. and Ding, M. (2000), First passage time problem for biased continuous-time random walks, Fractals 8, 139–145.
Rikitake, T., Earthquake Forecasting and Warning (Center for Acad. Publ. Japan, D. Reidel, Hingham, MA, USA. 1982).
Rundle, J. B. (1988), A physical model for earthquakes, 2, Application to southern California, J. Geophys. Res. 93, 6255–6274.
Rundle, P. B., Rundle, J. B., Tiampo, K. F., Sá Martins, J. S., McGinnis, S., and Klein, W. (2001), Nonlinear network dynamics on earthquake fault systems, Phys. Rev. Lett. 87(14), Art. No. 148501 (1–4).
Rundle, J. B., Tiampo, K. F., Sá Martins. , and Klein, W. (2002), Self-organization in leaky threshold systems: The influence of near mean field dynamics and its implications for earthquakes, neurobiology and forecasting, Proc. Nat. Acad. Sci. USA, 99,Supplement 1, 2514–2521.
Rundle, J. B., Rundle, P. B., Donnellan, A., and Fox, G. C. (2004), Gutenberg-Richter statistics in topologically realistic system-level earthquake stress-evolution simulations, Earth Planets Space 56, 761–771.
Rundle, J. B., Rundle, P. B., Donnellan, A., Turcotte, D. L., Shcherbakov, R. Li, P., Malamud, B. D., Grant, L. B., Fox, G. C., McLeod, D., Yakovlev, G., Parker, J., Klein, W., and Tiampo, K. F. (2006, in press), A simulation-based approach to forecasting the next great San Francisco earthquake, Proc. Nat. Acad. Sci.
Schwartz, D. P. and Coppersmith, K. J. (1984), Fault Behavior and characteristic, earthquakes: Examples from the Wasatch and San Andreas fault zones, J. Geophys. Res., 89, 5681–5698.
Southern California Earthquake Data Center (2001 accessed), Clickable Fault Map of Southern California, http://www.data.scec.org/faults/faultmap.html.
Thatcher, W. (1975). Strain accumulation and release mechanism of 1906 San Francisco Earthquake, J. Geophys. Res. 80(35), 4862–4872.
Tullis, T. E. (1996), Rock friction and its implications for earthquake prediction examined via models of Parkfield earthquakes, Proc. Nat. Acad. Sci. USA 93, 3803–3810.
Turcotte, D. L., Fractals and Chaos in Geology and Geophysics, (Cambridge University Press, Cambridge, UK. 1997).
Wald, D. J. and Heaton, T. H. (1994), Spatial and temporal distribution of slip for the 1992 Landers, California, earthquake, Bull. Seismol. Soc. Am. 84(3).
Ward, S. N. (1996), A synthetic seismicity model for southern California: Cycles, probabilities and hazard, J. Geophys. Res., 101, 22393–22418.
Ward, S. N. (2001), San Francisco Bay Area earthquake simulations: A step toward a standard physical earthquake model, Bull. Seismol. Soc. Am. 90(2), 370–386.
Ward, S. N. and Goes, S. D. B. (1993), How regularly do earthquakes recur?-A synthetic seismicity model for the San Andreas fault, Geophys. Res. Lett. 20, 2131–2134.
Wells, D. L. and Coppersmith, K. J. (1994), New empirical relationships among magnitude, rupture length, rupture width, rupture area, and surface displacement, Bull. Seismol. Soc. Am. 84(4), 974–1002.
Working Group on California Earthquake Probabilities (1999), Earthquake Probabilities in the San Francisco Bay Region: 2000 to 2030—A Summary of Findings, USGS Open-File Report 99–517, U. S. Govt. Printing Office.
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Rundle, P., Rundle, J., Tiampo, K., Donnellan, A., Turcotte, D. (2006). Virtual California: Fault Model, Frictional Parameters, Applications. In: Yin, Xc., Mora, P., Donnellan, A., Matsu’ura, M. (eds) Computational Earthquake Physics: Simulations, Analysis and Infrastructure, Part I. Pageoph Topical Volumes. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-7992-6_7
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DOI: https://doi.org/10.1007/978-3-7643-7992-6_7
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