scholarly journals Self-organization of spatio-temporal earthquake clusters

2000 ◽  
Vol 7 (1/2) ◽  
pp. 21-29 ◽  
Author(s):  
S. Hainzl ◽  
G. Zöller ◽  
J. Kurths
Keyword(s):  
Power Law ◽  
Transient Creep ◽  
Waiting Time Distribution ◽  
Power Law Distribution ◽  
Aftershock Activity ◽  
Omori Law ◽  
Aftershock Sequences ◽  
Spatio Temporal ◽  
Large Earthquakes ◽  
Earthquake Clusters

Abstract. Cellular automaton versions of the Burridge-Knopoff model have been shown to reproduce the power law distribution of event sizes; that is, the Gutenberg-Richter law. However, they have failed to reproduce the occurrence of foreshock and aftershock sequences correlated with large earthquakes. We show that in the case of partial stress recovery due to transient creep occurring subsequently to earthquakes in the crust, such spring-block systems self-organize into a statistically stationary state characterized by a power law distribution of fracture sizes as well as by foreshocks and aftershocks accompanying large events. In particular, the increase of foreshock and the decrease of aftershock activity can be described by, aside from a prefactor, the same Omori law. The exponent of the Omori law depends on the relaxation time and on the spatial scale of transient creep. Further investigations concerning the number of aftershocks, the temporal variation of aftershock magnitudes, and the waiting time distribution support the conclusion that this model, even "more realistic" physics in missed, captures in some ways the origin of the size distribution as well as spatio-temporal clustering of earthquakes.

SELF-ORGANIZED CRITICALITY MODEL FOR EARTHQUAKES: QUIESCENCE, FORESHOCKS AND AFTERSHOCKS

1999 ◽  
Vol 09 (12) ◽  
pp. 2249-2255 ◽  
Author(s):  
S. HAINZL ◽  
G. ZÖLLER ◽  
J. KURTHS
Keyword(s):  
Power Law ◽  
B Value ◽  
Power Law Distribution ◽  
Aftershock Activity ◽  
Omori Law ◽  
Self Organized ◽  
Spatiotemporal Clustering ◽  
Self Organized Criticality ◽  
Clustering Of Events ◽  
Foreshock Activity

We introduce a crust relaxation process in a continuous cellular automaton version of the Burridge–Knopoff model. Analogously to the original model, our model displays a robust power law distribution of event sizes (Gutenberg–Richter law). The principal new result obtained with our model is the spatiotemporal clustering of events exhibiting several characteristics of earthquakes in nature. Large events are accompanied by a precursory quiescence and by localized fore- and aftershocks. The increase of foreshock activity as well as the decrease of aftershock activity follows a power law (Omori law) with similar exponents p and q. All empirically observed power law exponents, the Richter B-value, p and q and their variability can be reproduced simultaneously by our model, which depends mainly on the level of conservation and the relaxation time.

Background Seismicity before and after the 1976 Ms 7.8 Tangshan Earthquake: Is Its Aftershock Sequence Still Continuing?

2020 ◽  
Author(s):  
Yue Liu ◽  
Jiancang Zhuang ◽  
Changsheng Jiang
Keyword(s):  
Aftershock Sequence ◽  
Tangshan Earthquake ◽  
Aftershock Activity ◽  
Background Rate ◽  
Epidemic Type Aftershock Sequence ◽  
Aftershock Sequences ◽  
Background Seismicity ◽  
Before And After ◽  
Large Earthquakes ◽  
Current Stage

Abstract The aftershock zone of the 1976 Ms 7.8 Tangshan, China, earthquake remains seismically active, experiencing moderate events such as the 5 December 2019 Ms 4.5 Fengnan event. It is still debated whether aftershock sequences following large earthquakes in low-seismicity continental regions can persist for several centuries. To understand the current stage of the Tangshan aftershock sequence, we analyze the sequence record and separate background seismicity from the triggering effect using a finite-source epidemic-type aftershock sequence model. Our results show that the background rate notably decreases after the mainshock. The estimated probability that the most recent 5 December 2019 Ms 4.5 Fengnan District, Tangshan, earthquake is a background event is 50.6%. This indicates that the contemporary seismicity in the Tangshan aftershock zone can be characterized as a transition from aftershock activity to background seismicity. Although the aftershock sequence is still active in the Tangshan region, it is overridden by background seismicity.

scholarly journals Global statistics of aftershocks following large earthquakes: independence of times and magnitudes

2019 ◽  
pp. 67-76 ◽  
Author(s):  
S. V. Baranov ◽  
P. N. Shebalin
Keyword(s):  
Branching Processes ◽  
Large Data ◽  
Aftershock Sequence ◽  
Power Law Distribution ◽  
Aftershock Activity ◽  
Data Set ◽  
Omori Law ◽  
Main Shocks ◽  
The Times ◽  
Global Statistics

This paper considers the global statistics of times of largest aftershocks relative to the times of the corresponding main shocks. A large data set was used to show that the time-dependent distribution of largest aftershocks obeys a power law distribution. This is analogous to the Omori law for the sequence of all after- shocks. It is also shown that the times of the second, etc., largest aftershocks obey the same distribution. Thereby, we have confirmed the hypothesis that the times and magnitudes in an aftershock sequence are independent and make a good case for the Reasenberg-Jones representation of the aftershock process as a superposition of the Omori-Utsu law and the Gutenberg–Richter relation. Events that are smaller than the largest in an aftershock sequence show no delay relative to the largest event; this rejects the idea of the after- shock process as a direct failure cascade involving gradual transitions from larger to lesser scales, which imposes certain restrictions on the widely popular stochastic models of aftershock generation as branching processes. The above result is important in practice for prediction of aftershock activity and for assessing the hazard of large aftershocks.

scholarly journals On the temporal spreading of the SARS-CoV-2

2020 ◽  
Author(s):  
Francesca Bertacchini ◽  
Eleonora Bilotta ◽  
Pietro S. Pantano
Keyword(s):  
Mathematical Modelling ◽  
Power Law ◽  
Hot Spots ◽  
Control Measures ◽  
Power Law Distribution ◽  
Physical Systems ◽  
Temporal Characteristics ◽  
Contemporary World ◽  
Spatio Temporal ◽  
And Control

The behaviour of SARS-CoV-2 virus is certainly one of the most challenging in contemporary world. Although the mathematical modelling of the virus has made relevant contributions, the unpredictable behaviour of the virus is still not fully understood. To identify some aspects of the virus elusive behaviour, we focused on the temporal characteristics of its course. We have analysed the latency trends the virus has realized worldwide, the outbreak of the hot spots, and the decreasing trends of the pandemic. We found that the spatio-temporal pandemic dynamics shows a power law distribution. As with physical systems, these changes in the pandemic's course, which we have called transitional stages of contagion, highlight shared characteristics in many countries. The main results of this work is that the pandemic progression rhythms have been clearly identified for each country, providing the processes and the stages at which the virus develops, thus giving important information on the activation of containment and control measures.

scholarly journals Global statistics of aftershocks following large earthquakes: independence of times and magnitudes

2019 ◽  
pp. 67-76
Author(s):  
S. V. Baranov ◽  
P. N. Shebalin
Keyword(s):  
Branching Processes ◽  
Large Data ◽  
Aftershock Sequence ◽  
Power Law Distribution ◽  
Aftershock Activity ◽  
Data Set ◽  
Omori Law ◽  
Main Shocks ◽  
The Times ◽  
Global Statistics

This paper considers the global statistics of times of largest aftershocks relative to the times of the corresponding main shocks. A large data set was used to show that the time-dependent distribution of largest aftershocks obeys a power law distribution. This is analogous to the Omori law for the sequence of all after- shocks. It is also shown that the times of the second, etc., largest aftershocks obey the same distribution. Thereby, we have confirmed the hypothesis that the times and magnitudes in an aftershock sequence are independent and make a good case for the Reasenberg-Jones representation of the aftershock process as a superposition of the Omori-Utsu law and the Gutenberg–Richter relation. Events that are smaller than the largest in an aftershock sequence show no delay relative to the largest event; this rejects the idea of the after- shock process as a direct failure cascade involving gradual transitions from larger to lesser scales, which imposes certain restrictions on the widely popular stochastic models of aftershock generation as branching processes. The above result is important in practice for prediction of aftershock activity and for assessing the hazard of large aftershocks.

Evaluation of seismogenesis behavior in Himalayan belt using data mining tools for forecasting

2013 ◽  
Vol 5 (2) ◽  
Author(s):  
Pushan Dutta ◽  
O. Mishra ◽  
Mrinal Naskar
Keyword(s):  
Neural Network ◽  
Power Law ◽  
Statistical Tests ◽  
Probabilistic Forecasting ◽  
Power Law Distribution ◽  
Feed Forward Neural Network ◽  
Seismic Regime ◽  
Independent Events ◽  
Aftershock Sequences ◽  
Himalayan Belt

AbstractIn the proposed study, non-linear behavioral patterns in the seismic regime for earthquakes in the Himalayan basin have been studied using a complete, verified EQ catalogue comprised of all major events and their aftershock sequences in the Himalayan basin for the past 110 years [1900–2010]. The dataset has been analyzed to give better decision making criteria for impending earthquakes. A series of statistical tests based on multi-dimensional rigorous statistical studies, inter-event distance analyses, and statistical time analyses have been used to obtain correlation dimensions. The time intervals of earthquakes within a seismic regime have been used to train the neural network to analyze the nature of earthquake patterns in the different clusters. The results obtained from descriptive statistics show high correlation with previously conducted gravity studies and radon anomaly variation. A study of the time of recurrence of the numerical properties of the regime for 60 years from 1950 to 2010 for the Himalayan belt for analysis of significant EQ failure events has been done to find the best fit for an empirical data probability distribution. The distribution of waiting time of swarm events occurring in the Himalayan basin follows a power-law model, while independent events do not fit the power-law distribution. This suggests that probability of the occurrence of swarm events [M ⩽ 6.0] with frequent shaking may be more frequent than that of the occurrence of independent events of magnitude [M >6.0] in the Himalayan belt. We propose a three-layer feed forward neural network model to identify factors, with the actual occurrence of the maximum earthquake level M as input and target vectors in Himalayan basin area. We infer through a series of statistical results and evaluations that probabilistic forecasting of earthquakes can be achieved by finding the meta-stable cluster zones of the Himalayan clusters for the spatio-temporal distribution of earthquakes in the area.

scholarly journals Synchronization and desynchronization in the Olami-Feder-Christensen earthquake model and potential implications for real seismicity

2011 ◽  
Vol 18 (5) ◽  
pp. 635-642 ◽  
Author(s):  
S. Hergarten ◽  
R. Krenn
Keyword(s):  
Power Law ◽  
Statistical Properties ◽  
Scaling Exponent ◽  
Power Law Distribution ◽  
Scaling Properties ◽  
Temporal Clustering ◽  
Self Organized ◽  
Earthquake Model ◽  
Self Organized Criticality ◽  
Large Earthquakes

Abstract. The Olami-Feder-Christensen model is probably the most studied model in the context of self-organized criticality and reproduces several statistical properties of real earthquakes. We investigate and explain synchronization and desynchronization of earthquakes in this model in the nonconservative regime and its relevance for the power-law distribution of the event sizes (Gutenberg-Richter law) and for temporal clustering of earthquakes. The power-law distribution emerges from synchronization, and its scaling exponent can be derived as τ = 1.775 from the scaling properties of the rupture areas' perimeter. In contrast, the occurrence of foreshocks and aftershocks according to Omori's law is closely related to desynchronization. This mechanism of foreshock and aftershock generation differs strongly from the widespread idea of spontaneous triggering and gives an idea why some even large earthquakes are not preceded by any foreshocks in nature.

scholarly journals The structure of co-publications multilayer network

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Ghislain Romaric Meleu ◽  
Paulin Yonta Melatagia
Keyword(s):  
Power Law ◽  
Degree Distribution ◽  
Preferential Attachment ◽  
Small World ◽  
Generation Model ◽  
Small World Network ◽  
Power Law Distribution ◽  
Multilayer Networks ◽  
Multilayer Network ◽  
Scientific Papers

AbstractUsing the headers of scientific papers, we have built multilayer networks of entities involved in research namely: authors, laboratories, and institutions. We have analyzed some properties of such networks built from data extracted from the HAL archives and found that the network at each layer is a small-world network with power law distribution. In order to simulate such co-publication network, we propose a multilayer network generation model based on the formation of cliques at each layer and the affiliation of each new node to the higher layers. The clique is built from new and existing nodes selected using preferential attachment. We also show that, the degree distribution of generated layers follows a power law. From the simulations of our model, we show that the generated multilayer networks reproduce the studied properties of co-publication networks.

scholarly journals Power-law behavior of transcription factor dynamics at the single-molecule level implies a continuum affinity model

2021 ◽  
Author(s):  
David A Garcia ◽  
Gregory Fettweis ◽  
Diego M Presman ◽  
Ville Paakinaho ◽  
Christopher Jarzynski ◽  
...  
Keyword(s):  
Transcription Factor ◽  
Single Molecule ◽  
Power Law ◽  
Dwell Time ◽  
Specific Binding ◽  
Power Law Distribution ◽  
Single Molecule Level ◽  
Binding Behavior ◽  
Chromatin Template ◽  
Nuclear Domains

Abstract Single-molecule tracking (SMT) allows the study of transcription factor (TF) dynamics in the nucleus, giving important information regarding the diffusion and binding behavior of these proteins in the nuclear environment. Dwell time distributions obtained by SMT for most TFs appear to follow bi-exponential behavior. This has been ascribed to two discrete populations of TFs—one non-specifically bound to chromatin and another specifically bound to target sites, as implied by decades of biochemical studies. However, emerging studies suggest alternate models for dwell-time distributions, indicating the existence of more than two populations of TFs (multi-exponential distribution), or even the absence of discrete states altogether (power-law distribution). Here, we present an analytical pipeline to evaluate which model best explains SMT data. We find that a broad spectrum of TFs (including glucocorticoid receptor, oestrogen receptor, FOXA1, CTCF) follow a power-law distribution of dwell-times, blurring the temporal line between non-specific and specific binding, suggesting that productive binding may involve longer binding events than previously believed. From these observations, we propose a continuum of affinities model to explain TF dynamics, that is consistent with complex interactions of TFs with multiple nuclear domains as well as binding and searching on the chromatin template.

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