Self-Organized Criticality in a Fibre-Bundle type model

The dynamics of a fibre-bundle type model with equal load sharing rule is numerically studied. The system, formed by N elements, is driven by a slow increase of the load upon it which is removed in a novel way through internal transfers to the elements broken during avalanches. When an avalanche ends, failed elements are regenerated with strengths taken from a probability distribution. For a large enough N and certain restrictions on the distribution of individual strengths, the system reaches a self-organized critical state where the spectrum of avalanche sizes is a power law with an exponent $\tau\simeq 1.5$.Comment: 10 pages, 6 figures. To be published in Physica

Spatial Heterogeneities in a Simple Earthquake Fault Model

Natural earthquake fault systems are composed of a variety of materials with different spatial configurations a complicated, inhomogeneous fault surface. The associated inhomogeneities with their physical properties can result in a variety of spatial and temporal behaviors. As a result, understanding the dynamics of seismic activity in an inhomogeneous environment is fundamental to the investigation of the earthquakes processes. This study presents the results from an inhomogeneous earthquake fault model based on the Olami-Feder-Christensen (OFC) and Rundle-Jackson-Brown (RJB) cellular automata models with long-range interactions that incorporates a fixed percentage of stronger sites, or ‘asperity cells’, into the lattice. These asperity cells are significantly stronger than the surrounding lattice sites but eventually rupture when the applied stress reaches their higher threshold stress. The introduction of these spatial heterogeneities results in temporal clustering in the model that mimics that seen in natural fault systems. Sequences of activity that start with a gradually accelerating number of larger events (foreshocks) prior to a mainshock that is followed by a tail of decreasing activity (aftershocks) are observed for the first time in simple models of this type. These recurrent large events occur at regular intervals, similar to characteristic earthquakes frequently observed in historic seismicity, and the time between events and their magnitude are a function of the stress dissipation parameter. The relative length of the foreshock to aftershock sequences can vary and also depends on the amount of stress dissipation in the system. The magnitude-frequency distribution of events for various amounts of inhomogeneities (asperity sites) in the lattice is investigated in order to provide a better understanding of Gutenberg-Richter (GR) scaling. The spatiotemporal clustering of events in systems with different spatial distribution of asperities and the Thirumalai and Mountain (TM) metric behaviour, an indicator of changes in activity before the main event in the sequence, also are investigated. Accelerating Moment Release (AMR) is observed before the mainshock. The Omori law behaviour for foreshocks and aftershocks is quantified for the model in this study. Finally, a fixed percentage of randomly distributed asperity sites were aggregated into bigger asperity blocks in order to investigate the effect of changing the spatial configuration of stronger sites. The results show that the larger block of asperities generally increases the capability of the fault system to generate larger events, but the total percentage of asperities is important as well. The increasing number of larger events is also associated with an increase in the total number of asperities in the lattice. This work provides further evidence that the spatial and temporal patterns observed in natural seismicity may be controlled by the underlying physical properties and are not solely the result of a simple cascade mechanism and, as a result, may not be inherently unpredictable

Spatial and temporal forecasting of large earthquakes in a spring-block model of a fault

We study a recently proposed statistical physics model of earthquake dynamics that includes stress relaxation in the plates as a fundamental ingredient. The model is known to reproduce many realistic features of seismic phenomena, such as: the Gutenberg?Richter law for the event size distribution, the Omori law for aftershocks and an overall velocity-weakening dependence of the average friction force. Here, we analyse the dynamics of the model in detail, in order to investigate to what extent the occurrence of large events in the model can be anticipated. We systematically find that large events occur in fault patches where strain accumulation has exceeded some threshold value. The spatial extent of these patches (which correlate with the magnitude of forthcoming events) can be calculated if the strain state of the system is supposed to be known. In addition, we find that some large events are preceded by well-defined precursor activity. This allows, in a fraction of cases, to complement the forecast of magnitude and spatial location, with a sensible prediction of time of occurrence. Although our work is exclusively limited to the numerical model analysed, we argue that it gives new breath to earthquake forecast techniques that combine the historical analysis of seismic activity with a search of appropriate precursor activity.Fil: Aragón, Luis Enrique. Comision Nacional de Energia Atomica. Centro Atomico Bariloche; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Area de Energía Nuclear. Instituto Balseiro; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Patagonia Norte; ArgentinaFil: Jagla, Eduardo Alberto. Comision Nacional de Energia Atomica. Centro Atomico Bariloche; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Area de Energía Nuclear. Instituto Balseiro; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Patagonia Norte; Argentin

The influence of the brittle-ductile transition zone on aftershock and foreshock occurrence

Aftershock occurrence is characterized by scaling behaviors with quite universal exponents. At the same time, deviations from universality have been proposed as a tool to discriminate aftershocks from foreshocks. Here we show that the change in rheological behavior of the crust, from velocity weakening to velocity strengthening, represents a viable mechanism to explain statistical features of both aftershocks and foreshocks. More precisely, we present a model of the seismic fault described as a velocity weakening elastic layer coupled to a velocity strengthening visco-elastic layer. We show that the statistical properties of aftershocks in instrumental catalogs are recovered at a quantitative level, quite independently of the value of model parameters. We also find that large earthquakes are often anticipated by a preparatory phase characterized by the occurrence of foreshocks. Their magnitude distribution is significantly flatter than the aftershock one, in agreement with recent results for forecasting tools based on foreshocks

Evolution in complex systems

What features characterise complex system dynamics? Power laws and scale invariance of fluctuations are often taken as the hallmarks of complexity, drawing on analogies with equilibrium critical phenomena[1-3]. Here we argue that slow, directed dynamics, during which the system's properties change significantly, is fundamental. The underlying dynamics is related to a slow, decelerating but spasmodic release of an intrinsic strain or tension. Time series of a number of appropriate observables can be analysed to confirm this effect. The strain arises from local frustration. As the strain is released through "quakes", some system variable undergoes record statistics with accompanying log-Poisson statistics for the quake event times[4]. We demonstrate these phenomena via two very different systems: a model of magnetic relaxation in type II superconductors and the Tangled Nature model of evolutionary ecology, and show how quantitative indications of ageing can be found.Comment: 8 pages, 5 figures all in one fil

A stochastic rupture earthquake code based on the fiber bundle model (TREMOL v0.1): application to Mexican subduction earthquakes

In general terms, earthquakes are the result of brittle failure within the heterogeneous crust of the Earth. However, the rupture process of a heterogeneous material is a complex physical problem that is difficult to model deterministically due to numerous parameters and physical conditions, which are largely unknown. Considering the variability within the parameterization, it is necessary to analyze earthquakes by means of different approaches. Computational physics may offer alternative ways to study brittle rock failure by generating synthetic seismic data based on physical and statistical models and through the use of only few free parameters. The fiber bundle model (FBM) is a stochastic discrete model of material failure, which is able to describe complex rupture processes in heterogeneous materials. In this article, we present a computer code called the stochasTic Rupture Earthquake MOdeL, TREMOL. This code is based on the principle of the FBM to investigate the rupture process of asperities on the earthquake rupture surface. In order to validate TREMOL, we carried out a parametric study to identify the best parameter configuration while minimizing computational efforts. As test cases, we applied the final configuration to 10 Mexican subduction zone earthquakes in order to compare the synthetic results by TREMOL with seismological observations. According to our results, TREMOL is able to model the rupture of an asperity that is essentially defined by two basic dimensions: (1) the size of the fault plane and (2) the size of the maximum asperity within the fault plane. Based on these data and few additional parameters, TREMOL is able to generate numerous earthquakes as well as a maximum magnitude for different scenarios within a reasonable error range. The simulated earthquake magnitudes are of the same order as the real earthquakes. Thus, TREMOL can be used to analyze the behavior of a single asperity or a group of asperities since TREMOL considers the maximum magnitude occurring on a fault plane as a function of the size of the asperity. TREMOL is a simple and flexible model that allows its users to investigate the role of the initial stress configuration and the dimensions and material properties of seismic asperities. Although various assumptions and simplifications are included in the model, we show that TREMOL can be a powerful tool to deliver promising new insights into earthquake rupture processes.The authors are grateful to two anonymous reviewers and the editor for their relevant and constructive comments that have greatly contributed to improving the paper. M. Monterrubio-Velasco and J. de la Puente thank the European Union’s Horizon 2020 Programme under the ChEESE Project (https://cheese-coe.eu/, last access: 1 May 2019), grant agreement no. 823844, for partially funding this work. M. Monterrubio- Velasco and A. Aguilar-Meléndez thank CONACYT for support of this research project. Quetzalcoatl Rodríguez-Pérez was supported by the Mexican National Council for Science and Technology (CONACYT) (Catedras program, project 1126). This project has received funding from the European Union’s Horizon 2020 research and innovation program under Marie Skłodowska-Curie grant agreement no. 777778, MATHROCKS, and from the Spanish Ministry project TIN2016-80957-P. Initial funding for the project through grant UNAM-PAPIIT IN108115 is also gratefully acknowledged.Peer ReviewedPostprint (published version