Ergodicity in natural earthquake fault networks

作     者：K. F. Tiampo J. B. Rundle W. Klein J. Holliday J. S. Sá Martins C. D. Ferguson 

作者机构：Department of Earth Sciences University of Western Ontario London Ontario N6A 5B7 Canada Center for Computational Science and Engineering University of California Davis California 95616 USA Dept. of Physics and Center for Computational Science Boston University Boston Massachusetts 02215 USA Instituto de Fisica Universidade Federal Fluminense Av. Litoranea s/n Boa Viagem Niteroi 24210-340 RJ Brazil Council on Foreign Relations 1779 Massachusetts Avenue Washington DC 20036 USA 

出 版 物：《Physical Review E》 (物理学评论E辑：统计、非线性和软体物理学)

年 卷 期：2007年第75卷第6期

页      面：066107-066107页

核心收录：

学科分类：07[理学] 070203[理学-原子与分子物理] 0702[理学-物理学] 

主　　题：SELF-ORGANIZED CRITICALITY SAN-ANDREAS FAULT STATISTICAL-MECHANICS THRESHOLD SYSTEMS SUPERCOOLED LIQUIDS SOUTHERN-CALIFORNIA GREAT EARTHQUAKES LANDER EARTHQUAKE SCALE-INVARIANCE STRESS TRANSFER 

摘      要：Numerical simulations have shown that certain driven nonlinear systems can be characterized by mean-field statistical properties often associated with ergodic dynamics [C. D. Ferguson, W. Klein, and J. B. Rundle, Phys. Rev. E 60, 1359 (1999); D. Egolf, Science 287, 101 (2000)]. These driven mean-field threshold systems feature long-range interactions and can be treated as equilibriumlike systems with statistically stationary dynamics over long time intervals. Recently the equilibrium property of ergodicity was identified in an earthquake fault system, a natural driven threshold system, by means of the Thirumalai-Mountain (TM) fluctuation metric developed in the study of diffusive systems [K. F. Tiampo, J. B. Rundle, W. Klein, J. S. Sá Martins, and C. D. Ferguson, Phys. Rev. Lett. 91, 238501 (2003)]. We analyze the seismicity of three naturally occurring earthquake fault networks from a variety of tectonic settings in an attempt to investigate the range of applicability of effective ergodicity, using the TM metric and other related statistics. Results suggest that, once variations in the catalog data resulting from technical and network issues are accounted for, all of these natural earthquake systems display stationary periods of metastable equilibrium and effective ergodicity that are disrupted by large events. We conclude that a constant rate of events is an important prerequisite for these periods of punctuated ergodicity and that, while the level of temporal variability in the spatial statistics is the controlling factor in the ergodic behavior of seismic networks, no single statistic is sufficient to ensure quantification of ergodicity. Ergodicity in this application not only requires that the system be stationary for these networks at the applicable spatial and temporal scales, but also implies that they are in a state of metastable equilibrium, one in which the ensemble averages can be substituted for temporal averages in studying their spatiotemporal evoluti