Ergodicity in natural earthquake fault networks

Abstract

Numerical simulations have shown that certain driven nonlinear systems can be characterized by mean-field statistical properties often associated with ergodic dynamics 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 equilibrium-like systems with dynamics that are statistically stationary 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)]. In this work we analyze the seismicity of three naturally-occurring earthquake faults 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 2 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. Specifically, we demonstrate that stationarity, while a necessary condition, is not sufficient to ensure ergodicity in fault systems.

Scaling of earthquake models with inhomogeneous stress dissipation

“…Because this history is typically quite complex, the spatial distribution of the various inhomogeneities occurs on many length scales. One way that the inhomogeneous nature of fault systems manifests itself is in the spatial patterns which emerge in seismicity graphs [1,2].…”

A simple metric to quantify seismicity clustering

“…This metric, originally developed to study liquid systems and glasses Thirumalai and Mountain, 1993), was applied to earthquake simulations (Ferguson et al, 1999) and to regional seismicity by Tiampo et al (2003Tiampo et al ( , 2007. The result was the identification of periods of metastable equilibrium in seismic activity.…”

“…The Thirulamai-Mountain (TM) metric was first developed to study ergodicity in fluids and glasses (Thirumalai and Mountain, 1993) using the concept of effective ergodicity, where a large but finite time interval is considered. Tiampo et al (2007) employed the TM metric to earthquake systems to search for effective ergodic periods, which are considered to be metastable equilibrium states that are disrupted by large events. The physical meaning of the TM metric for seismicity is addressed here in terms of the clustering of earthquakes in both time and space for different sets of data.…”

Epistemic uncertainties and natural hazard risk assessment. 1. A review of different natural hazard areas

“…The quality, completeness and reliability of an earthquake catalogue evolves over 20 time, affected by the distribution of human settlements and the way in which major events in the historical record have been reported, and by advances in measurement technology and, more recently, the wider geographical coverage of seismographic networks. This often results in inhomogeneous detection and monitoring capabilities of instrumental catalogues (Tiampo et al, 2007), which needs to be accounted for in evaluating earthquake occurrence rates. In addition, new information from terrestrial and ocean geodesy (McCaffrey et al, 2013;Bürgmann and Chadwell, 2014) will help constrain seismic hazard 25 estimates derived from PSHA.…”