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Fukuda K, Hatano T, Mochizuki K. Model for tectonic tremors: Enduring events, moment rate spectrum, and moment-duration scaling. Phys Rev E 2022; 105:014124. [PMID: 35193288 DOI: 10.1103/physreve.105.014124] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2021] [Accepted: 11/30/2021] [Indexed: 06/14/2023]
Abstract
Numerous attempts have been made to obtain earthquake statistics from a theoretical-physics perspective, but these studies mostly involve regular earthquakes. In recent years, a new category of earthquakes, referred to as slow earthquakes, has been discovered. Slow earthquakes emit only weak or no seismic signals and have different statistics than regular earthquakes. Here we propose a physical model for the tremor, which is a type of slow earthquake, introducing two competing timescales in a cellular automaton model. The proposed model reproduces some observation results for tremors, such as enduring events, moment-duration scaling, size distribution, and the power spectrum of the moment rate function.
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Affiliation(s)
- Kota Fukuda
- Earthquake Research Institute, University of Tokyo, 1-1-1 Yayoi, Bunkyo, Tokyo 113-0032, Japan
| | - Takahiro Hatano
- Department of Earth and Space Science, Osaka University, 1-1 Machikaneyama, Toyonaka, Osaka 560-0043, Japan
| | - Kimihiro Mochizuki
- Earthquake Research Institute, University of Tokyo, 1-1-1 Yayoi, Bunkyo, Tokyo 113-0032, Japan
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Nowcasting Avalanches as Earthquakes and the Predictability of Strong Avalanches in the Olami-Feder-Christensen Model. ENTROPY 2020; 22:e22111228. [PMID: 33286996 PMCID: PMC7712535 DOI: 10.3390/e22111228] [Citation(s) in RCA: 20] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 09/08/2020] [Revised: 10/20/2020] [Accepted: 10/26/2020] [Indexed: 11/17/2022]
Abstract
Nowcasting earthquakes, suggested recently as a method to estimate the state of a fault and hence the seismic risk, is based on the concept of natural time. Here, we generalize nowcasting to a prediction method the merits of which are evaluated by means of the receiver operating characteristics. This new prediction method is applied to a simple (toy) model for the waiting (natural) time of the stronger earthquakes, real seismicity, and the Olami-Feder-Christensen earthquake model with interesting results revealing acceptable to excellent or even outstanding performance.
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Zhang X, Shcherbakov R. Power-law rheology controls aftershock triggering and decay. Sci Rep 2016; 6:36668. [PMID: 27819355 PMCID: PMC5098201 DOI: 10.1038/srep36668] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/22/2016] [Accepted: 10/18/2016] [Indexed: 11/17/2022] Open
Abstract
The occurrence of aftershocks is a signature of physical systems exhibiting relaxation phenomena. They are observed in various natural or experimental systems and usually obey several non-trivial empirical laws. Here we consider a cellular automaton realization of a nonlinear viscoelastic slider-block model in order to infer the physical mechanisms of triggering responsible for the occurrence of aftershocks. We show that nonlinear viscoelasticity plays a critical role in the occurrence of aftershocks. The model reproduces several empirical laws describing the statistics of aftershocks. In case of earthquakes, the proposed model suggests that the power-law rheology of the fault gauge, underlying lower crust, and upper mantle controls the decay rate of aftershocks. This is verified by analysing several prominent aftershock sequences for which the rheological properties of the underlying crust and upper mantle were established.
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Affiliation(s)
- Xiaoming Zhang
- Department of Earth Sciences, University of Western Ontario, London, Ontario, N6A 5B7, Canada
| | - Robert Shcherbakov
- Department of Earth Sciences, University of Western Ontario, London, Ontario, N6A 5B7, Canada.,Department of Physics and Astronomy, University of Western Ontario, London, Ontario, N6A 3K7, Canada
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Shcherbakov R, Davidsen J, Tiampo KF. Record-breaking avalanches in driven threshold systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:052811. [PMID: 23767588 DOI: 10.1103/physreve.87.052811] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/09/2012] [Revised: 02/03/2013] [Indexed: 06/02/2023]
Abstract
Record-breaking avalanches generated by the dynamics of several driven nonlinear threshold models are studied. Such systems are characterized by intermittent behavior, where a slow buildup of energy is punctuated by an abrupt release of energy through avalanche events, which usually follow scale-invariant statistics. From the simulations of these systems it is possible to extract sequences of record-breaking avalanches, where each subsequent record-breaking event is larger in magnitude than all previous events. In the present work, several cellular automata are analyzed, among them the sandpile model, the Manna model, the Olami-Feder-Christensen (OFC) model, and the forest-fire model to investigate the record-breaking statistics of model avalanches that exhibit temporal and spatial correlations. Several statistical measures of record-breaking events are derived analytically and confirmed through numerical simulations. The statistics of record-breaking avalanches for the four models are compared to those of record-breaking events extracted from the sequences of independent and identically distributed (i.i.d.) random variables. It is found that the statistics of record-breaking avalanches for the above cellular automata exhibit behavior different from that observed for i.i.d. random variables, which in turn can be used to characterize complex spatiotemporal dynamics. The most pronounced deviations are observed in the case of the OFC model with a strong dependence on the conservation parameter of the model. This indicates that avalanches in the OFC model are not independent and exhibit spatiotemporal correlations.
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Affiliation(s)
- Robert Shcherbakov
- Department of Earth Sciences, University of Western Ontario, London, Ontario, Canada N6A 5B7.
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Kawamura H, Yamamoto T, Kotani T, Yoshino H. Asperity characteristics of the Olami-Feder-Christensen model of earthquakes. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:031119. [PMID: 20365709 DOI: 10.1103/physreve.81.031119] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/06/2009] [Revised: 01/25/2010] [Indexed: 05/29/2023]
Abstract
Properties of the Olami-Feder-Christensen (OFC) model of earthquakes are studied by numerical simulations. The previous study indicated that the model exhibited "asperity"-like phenomena, i.e., the same region ruptures many times near periodically [T. Kotani, Phys. Rev. E 77, 010102(R) (2008)]. Such periodic or characteristic features apparently coexist with power-law-like critical features, e.g., the Gutenberg-Richter law observed in the size distribution. In order to clarify the origin and the nature of the asperity-like phenomena, we investigate here the properties of the OFC model with emphasis on its stress distribution. It is found that the asperity formation is accompanied by self-organization of the highly concentrated stress state. Such stress organization naturally provides the mechanism underlying our observation that a series of asperity events repeat with a common epicenter site and with a common period solely determined by the transmission parameter of the model. Asperity events tend to cluster both in time and in space.
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Affiliation(s)
- Hikaru Kawamura
- Department of Earth and Space Science, Faculty of Science, Osaka University, Toyonaka 560-0043, Japan
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Bach M, Wissel F, Drossel B. Olami-Feder-Christensen model with quenched disorder. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:067101. [PMID: 18643401 DOI: 10.1103/physreve.77.067101] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/10/2007] [Revised: 04/25/2008] [Indexed: 05/26/2023]
Abstract
We study the Olami-Feder-Christensen model with quenched disorder in the coupling parameter alpha . In contrast to an earlier study by Mousseau [Phys. Rev. Lett. 77, 968 (1996)], we do not find a phase diagram with several phase transitions, but continuous crossovers from one type of behavior to another. The crossover behavior is determined by the ratio of three length scales, which are the system size, the penetration depth of the boundary layer, and the correlation length introduced by the disorder.
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Affiliation(s)
- Manuel Bach
- Institut für Festkörperphysik, TU Darmstadt, Hochschulstrasse 6, 64289 Darmstadt, Germany
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Peixoto TP, Davidsen J. Network of recurrent events for the Olami-Feder-Christensen model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:066107. [PMID: 18643336 DOI: 10.1103/physreve.77.066107] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/10/2008] [Indexed: 05/26/2023]
Abstract
We numerically study the dynamics of a discrete spring-block model introduced by Olami, Feder, and Christensen (OFC) to mimic earthquakes and investigate to what extent this simple model is able to reproduce the observed spatiotemporal clustering of seismicity. Following a recently proposed method to characterize such clustering by networks of recurrent events [J. Davidsen, P. Grassberger, and M. Paczuski, Geophys. Res. Lett. 33, L11304 (2006)], we find that for synthetic catalogs generated by the OFC model these networks have many nontrivial statistical properties. This includes characteristic degree distributions, very similar to what has been observed for real seismicity. There are, however, also significant differences between the OFC model and earthquake catalogs, indicating that this simple model is insufficient to account for certain aspects of the spatiotemporal clustering of seismicity.
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Affiliation(s)
- Tiago P Peixoto
- Instituto de Física, Universidade de São Paulo, Caixa Postal 66318, 05315-970, São Paulo, Brazil.
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Kotani T, Yoshino H, Kawamura H. Periodicity and criticality in the Olami-Feder-Christensen model of earthquakes. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:010102. [PMID: 18351808 DOI: 10.1103/physreve.77.010102] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/02/2007] [Revised: 12/05/2007] [Indexed: 05/26/2023]
Abstract
Characteristic versus critical features of earthquakes are studied on the basis of the Olami-Feder-Christensen model. It is found that the local recurrence-time distribution exhibits a sharp delta -function-like peak corresponding to rhythmic recurrence of events with a fixed "period" uniquely determined by the transmission parameter of the model, together with a power-law-like tail corresponding to scale-free recurrence of events. The model exhibits phenomena closely resembling the asperity known in seismology.
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Affiliation(s)
- Takeshi Kotani
- Department of Earth and Space Science, Faculty of Science, Osaka University, Toyonaka 560-0043, Japan
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