Natural time analysis of critical phenomena (original) (raw)
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Natural-time analysis of critical phenomena: The case of seismicity
EPL (Europhysics Letters), 2010
A quantity exists by which one can identify the approach of a dynamical system to the state of criticality, which is hard to identify otherwise. This quantity is the variance κ 1 ð≡hχ 2 i − hχ i 2 Þ of natural time χ , where hfðχ Þi ¼ ∑ p k f ðχ k Þ and p k is the normalized energy released during the kth event of which the natural time is defined as χ k ¼ k∕N and N stands for the total number of events. Then we show that κ 1 becomes equal to 0.070 at the critical state for a variety of dynamical systems. This holds for criticality models such as 2D Ising and the Bak-Tang-Wiesenfeld sandpile, which is the standard example of self-organized criticality. This condition of κ 1 ¼ 0.070 holds for experimental results of critical phenomena such as growth of rice piles, seismic electric signals, and the subsequent seismicity before the associated main shock.
Similarity of fluctuations in systems exhibiting Self-Organized Criticality
EPL (Europhysics Letters), 2011
PACS 89.75.Da -Systems obeying scaling laws PACS 95.75.Wx -Time series analysis, time variability PACS 91.30.Ab -Theory and modeling, computational seismology Abstract -The time-series of avalanches in three systems exhibiting SOC are analyzed in natural time χ. In two of them, i.e., ricepiles and magnetic flux penetration in thin films of YBa2Cu3O7−x, the data come from laboratory measurements, while the third one is a deterministic model mimicking stick-slip phenomena. We show that their scaled distributions for the variance κ1 of natural time exhibit an exponential tail as previously found for the order parameter in seismicity and in other non-equilibrium or equilibrium critical systems. Upon considering the entropy S− in natural time under time reversal, the following important difference is found: In ricepiles evolving to the critical state, S− is systematically larger than the entropy S in natural time, while in YBa2Cu3O7−x no systematic difference between S− and S is found.
Intermittent Criticality and the Gutenberg-Richter Distribution
Pure and Applied Geophysics, 2004
In recent years there has been renewed interest in observations of accelerating moment release before large earthquakes, as well as theoretical descriptions of seismicity in terms of statistical physics. Most aspects of these works are encompassed by a concept called intermittent criticality in which a region alternately approaches and retreats from a critical-point. From this perspective, the evolution of seismicity in a region is described in terms of the growth and destruction of correlation in the stress field over the course of the seismic cycle. In this paper we test the concept of intermittent criticality by investigating the temporal evolution of the Gutenberg-Richter distribution before and after two successive M ‡ 5.0 earthquakes in western Washington State. The largest event in this distribution, M max , is observed to systematically increase before each event, producing accelerating moment release, and then to subsequently decrease. Associated variations in the b-value are minimal. This is the predicted result if M max is a measure of the correlation length of the regional stress field.
Similarity of fluctuations in correlated systems: The case of seismicity
Physical Review E, 2005
We report a similarity of fluctuations in equilibrium critical phenomena and non-equilibrium systems, which is based on the concept of natural time. The world-wide seismicity as well as that of San Andreas fault system and Japan are analyzed. An order parameter is chosen and its fluctuations relative to the standard deviation of the distribution are studied. We find that the scaled distributions fall on the same curve, which interestingly exhibits, over four orders of magnitude, features similar to those in several equilibrium critical phenomena ( e.g., 2D Ising model) as well as in non-equilibrium systems (e.g., 3D turbulent flow).
Seismic quiescence as an indicator for large earthquakes in a system of self-organized criticality
Geophysical Research Letters, 2000
Seismically active fault systems may be in a state of self-organized criticality (SOC). Investigations of simple SOC models have suggested that earthquakes might be inherently unpredictable. In this paper, we analyze the question of predictability in a more complex and realistic SOC model, which consists of a spring-block system with transient creep characteristics. Additionally to the power law distribution of earthquake sizes, this model reproduces also foreshock and aftershock sequences. Aside from a short-term increase of seismicity immediately prior to large model earthquakes, these events are preceded on average by an intermediate-term period of reduced seismicity. The stronger and the longer the duration of this period, the larger on average is the subsequent mainshock. We find that the detection of seismic quiescence can improve the time-independent hazard assessment. The improvement is most significant for the largest target events.
Dynamics of the Markov Time Scale of Seismic Activity May Provide a Short-Term Alert for Earthquakes
2005
We propose a novel method for analyzing precursory seismic data before an earthquake that treats them as a Markov process and distinguishes the background noise from real fluctuations due to an earthquake. A short time (on the order of several hours) before an earthquake the Markov time scale tM increases sharply, hence providing an alarm for an impending earthquake. To distinguish a false alarm from a reliable one, we compute a second quantity, T1, based on the concept of extended self-similarity of the data. T1 also changes strongly before an earthquake occurs. An alarm is accepted if both tM and T1 indicate it simultaneously. Calibrating the method with the data for one region provides a tool for predicting an impending earthquake within that region. Our analysis of the data for a large number of earthquakes indicate an essentially zero rate of failure for the method.
Nonlinear Dynamics in Geosciences, 2007
In this study, using the modern theory of far from equilibrium nonlinear stochastic dynamicsand nonlinear data analysis of seismic events in the Hellenic region, two significant aims have been accomplished: initially, the verification of the possibility for unification of twocompetitive and antagonistic, until now, theoretical points of view of critical complexity, such as Self Organized Criticality and Low Dimensional Chaos and subsequently, the provisionof further information, about the existence of a global and low dimensional earthquake strange attractor in the Hellenic region, as it has been supported in a previous study (Pavlos etal., 1994). Furthermore, evidence for the existence of an input-output dynamical processunderlying the earthquake dynamics, is found.
Natural Time Analysis of Seismicity
Natural Time Analysis: The New View of Time, 2011
PACS 91.30.Ab -Theory and modeling, computational seismology PACS 89.75.Da -Systems obeying scaling laws PACS 95.75.Wx -Time series analysis, time variability