HR: 0800h
AN: NG11A-0172    [Abstracts]
TI: Complexity Of Earthquakes: Learning From Simple Models And Exploring Statistical Surrogate Techniques
AU: * Elbanna, A E
EM: aettaf@caltech.edu
AF: California Institute of Technology, 1200 E. California Blvd MC 104-44, Pasadena, CA 91125,
AU: Heaton, T
EM: heaton_t@caltech.edu
AF: California Institute of Technology, 1200 E. California Blvd MC 104-44, Pasadena, CA 91125,
AB: It has long been recognized that earthquakes exhibit similarity at many length scales which suggests fractal characteristics of earthquake ruptures. One of the well known manifestations of earthquake complexity is the fractal nature of the Gutenberg-Richter law. Moreover, there is growing evidence that earthquakes ruptures are very complex processes; as the resolution of source inversions has increased, so has the temporal and spatial complexity of the rupture. What are the key physical parameters that control this complexity? Many methods have been tailored in an attempt to uncover the details of the complex rupture processes but due to different numerical and computational limitations scientists could not go beyond a few orders of magnitude on both of the spatial and temporal scales. Statistical methods provide an alternative way to overcome the difficulties associated with numerical models of spontaneous dynamic ruptures. Here, we present an outline for an innovative approach that aims at reproducing the different earthquake complex scaling laws using methods of statistical mechanics with the ultimate goal of finding the scaling behavior of the strength of the Earth's crust. The emphasis of this presentation is on exploring the conditions that might lead to complexity in earthquakes using simple mechanical models similar to the Burridge-Knopoff spring-block-slider models and how to describe the evolution of the system in this case. Although there are limitations in the usage of spring-block- sliders to interpret real earthquakes, these models have the advantage that they are computationally efficient and produce some earthquake statistics. This allows us to explore the nature of complexity that is produced by different types of models of dynamic friction. We show that chaotic behavior occurs for friction models with velocity or slip hyperbolic weakening rather than traditional slip weakening models. We would also show that the evolution of the spring block slider system could be predicted using a new statistical method based on Markov Modeling. The method hinges on the observation that slip pulses - which represent the prevailing rupture mode in our models- are so localized in space in a manner suggestive that the slip at any point is correlated to the pre- existing stress only over a small interaction zone surrounding that point. Using the Markovian technique we could track the variation of this interaction zone width statistically.The slip time and consequently the slip at any point is approximated as a weighted average for the pre-existing stress over the interaction zone of that point. We believe that this method could be a surrogate for solving the full equilibrium equations and could produce rough earthquake statistics.
DE: 4420 Chaos (7805)
DE: 4430 Complex systems
DE: 4440 Fractals and multifractals
DE: 4460 Pattern formation
SC: Nonlinear Geophysics [NG]
MN: 2007 Fall Meeting