Comparing spatio-temporal networks of intermittent avalanche events: Experiment, model, and empirical data (original) (raw)
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Physica A: Statistical Mechanics and its Applications, 2004
Avalanche dynamics is an indispensable feature of complex systems. Here we study the self-organized critical dynamics of avalanches on scale-free networks with degree exponent γ through the Bak-Tang-Wiesenfeld (BTW) sandpile model. The threshold height of a node i is set as k 1−η i with 0 ≤ η < 1, where k i is the degree of node i. Using the branching process approach, we obtain the avalanche size and the duration distribution of sand toppling, which follow power-laws with exponents τ and δ, respectively. They are given as τ = (γ−2η)/(γ− 1 − η) and δ = (γ − 1 − η)/(γ − 2) for γ < 3 − η, 3/2 and 2 for γ > 3 − η, respectively. The power-law distributions are modified by a logarithmic correction at γ = 3 − η.
Incorporating space, time, and magnitude measures in a network characterization of earthquake events
Acta Geophysica, 2017
We investigate the structural properties of a spatio-temporal network of earthquake events that incorporates magnitude information between the connected events. The network creates temporally directed links from an origin event towards a later event if it breaks the record closest distance from the origin among all the events in the catalog so far. Additionally, the links are conditionally classified based on the magnitude difference between connected events: ''up'' (''down'') connections point from a weaker (stronger) to a stronger (weaker) event. Using earthquake records from the Philippines from 1973 to 2012 and southern California from 1982 to 2012, we observe that the out-degree distributions show slight deviations from the corresponding Poisson distribution of the same mean. The space and time separations of connected earthquakes both show power-law regimes, suggesting spatio-temporal (self-)organization. More importantly, the conditional distributions of ''up'' and ''down'' connections in space, time, and network structure point to a higher likelihood of a stronger event triggering a nearby weaker event for the first few connections, as in the case of aftershocks. The results are captured by a sandpile-based model where a small but finite probability of preferentially targeting the most susceptible grid site is introduced. Our analysis, coupled with the discrete model analog, provides a quantitative picture of the spatiotemporal and magnitude organization of seismicity beyond just the successive events. The technique may be extended to further characterize similar long-period earthquake records to yield a more complete picture of the underlying processes involved in seismicity.
Complex networks of earthquakes and aftershocks
Nonlinear Processes in Geophysics, 2005
We invoke a metric to quantify the correlation between any two earthquakes. This provides a simple and straightforward alternative to using space-time windows to detect aftershock sequences and obviates the need to distinguish main shocks from aftershocks. Directed networks of earthquakes are constructed by placing a link, directed from the past to the future, between pairs of events that are strongly correlated. Each link has a weight giving the relative strength of correlation such that the sum over the incoming links to any node equals unity for aftershocks, or zero if the event had no correlated predecessors. A correlation threshold is set to drastically reduce the size of the data set without losing significant information. Events can be aftershocks of many previous events, and also generate many aftershocks. The probability distribution for the number of incoming and outgoing links are both scale free, and the networks are highly clustered. The Omori law holds for aftershock rates up to a decorrelation time that scales with the magnitude, m, of the initiating shock as t cutoff ∼ 10 βm with β ≃ 3/4. Another scaling law relates distances between earthquakes and their aftershocks to the magnitude of the initiating shock. Our results are inconsistent with the hypothesis of finite aftershock zones. We also find evidence that seismicity is dominantly triggered by small earthquakes. Our approach, using concepts from the modern theory of complex networks, together with a metric to estimate correlations, opens up new avenues of research, as well as new tools to understand seismicity.
Journal of Physics: Conference Series, 2019
Slowly driven sandpile models has found applications in modelling earthquakes due to the observed power law statistics in its magnitude distributions, like the behaviour of earthquakes. Adding a probability to target the most susceptible site in the grid, the sandpile model recovers even the spatio-temporal statistics of earthquake events. In this work, we compare the sandpile model with targeted triggering to the Olami-Feder-Christensen (OFC) model: a standard earthquake model that also exhibits self-organized criticality. The sandpile model captures the magnitude distributions of earthquake events at a value of targeted triggering probability p = [0.004,0.007]. The triggering probability value p = 1.0, showing that the most susceptible site is always triggered, follows the magnitude distribution of the OFC model. A comparison was done by constructing a record-breaking recurrence network for the events. Spatial and magnitude criteria set the temporally directed links between events...
Scale-free networks of earthquakes and aftershocks
Physical Review E, 2004
We propose a new metric to quantify the correlation between any two earthquakes. The metric consists of a product involving the time interval and spatial distance between two events, as well as the magnitude of the first one. According to this metric, events typically are strongly correlated to only one or a few preceding ones. Thus a classification of events as foreshocks, main shocks or aftershocks emerges automatically without imposing predefined space-time windows. To construct a network, each earthquake receives an incoming link from its most correlated predecessor. The number of aftershocks for any event, identified by its outgoing links, is found to be scale free with exponent γ = 2.0(1). The original Omori law with p = 1 emerges as a robust feature of seismicity, holding up to years even for aftershock sequences initiated by intermediate magnitude events. The measured fat-tailed distribution of distances between earthquakes and their aftershocks suggests that aftershock collection with fixed space windows is not appropriate.
Avalanche Prediction in a Self-Organized Pile of Beads
Physical Review Letters, 2009
It is a common belief that power-law distributed avalanches are inherently unpredictable. This idea affects phenomena as diverse as evolution, earthquakes, superconducting vortices, stock markets, etc; from atomic to social scales. It mainly comes from the concept of "Self-organized criticality" (SOC), where criticality is interpreted in the way that at any moment, any small avalanche can eventually cascade into a large event. Nevertheless, this work demonstrates experimentally the possibility of avalanche prediction in the classical paradigm of SOC: a sandpile. By knowing the position of every grain in a two-dimensional pile, avalanches of moving grains follow a distinct powerlaw distribution. Large avalanches, although uncorrelated, are preceded by continuous, detectable variations in the internal structure of the pile that are monitored in order to achieve prediction.
Avalanches in Out of Equilibrium Systems: Statistical Analysis of Experiments and Simulations
2015
Instead of a linear and smooth evolution, many physical system react to external stimuli in avalanche dynamics. When an out of equilibrium system governed by disorder is externally driven the evolution of internal variables is local and non-homogeneous. This process is a collective behaviour adiabatically quick known as avalanches. Avalanche dynamics are associated to the transformation of spatial domains in different scales: from microscopic, to large catastrophic events such as earthquakes or solar flares. Avalanche dynamics is also involved in interdisiplinar topics such as the return prices of stock markets, the signalling in neuron networks or the biological evolution. Many avalanche dynamics are characterised by scale invariance, trademark of criticality. The physics in a so-called critical point are the same in all observational scales. Some avalanche dynamics share empirical laws and can define Universality Classes, reducing the complexity of systems to simpler mathematical ...
Network of earthquakes and recurrences therein
Journal of Seismology, 2010
We quantify the correlation between earthquakes and use the same to distinguish between relevant causally connected earthquakes. Our correlation metric is a variation on the one introduced by Baiesi and Paczuski (2004). A network of earthquakes is constructed, which is time ordered and with links between the more correlated ones. Data pertaining to the California region has been used in the study. Recurrences to earthquakes are identified employing correlation thresholds to demarcate the most meaningful ones in each cluster. The distribution of recurrence lengths and recurrence times are analyzed subsequently to extract information about the complex dynamics. We find that the unimodal feature of recurrence lengths helps to associate typical rupture lengths with different magnitude earthquakes. The out-degree of the network shows a hub structure rooted on the large magnitude earthquakes. In-degree distribution is seen to be dependent on the density of events in the neighborhood. Power laws are also obtained with recurrence time distribution agreeing with the Omori law.
Supplemental Material : “Classes of critical avalanche dynamics in complex networks.”
2019
Filippo Radicchi, Claudio Castellano, Alessandro Flammini, Miguel A. Muñoz, and Daniele Notarmuzi Center for Complex Networks and Systems Research, Luddy School of Informatics, Computing, and Engineering, Indiana University, Bloomington, Indiana 47408, USA∗ Istituto dei Sistemi Complessi (ISC-CNR), Via dei Taurini 19, I-00185 Roma, Italy Departamento de Electromagnetismo y F́ısica de la Materia e Instituto Carlos I de F́ısica Teórica y Computacional. Facultad de Ciencias. Universidad de Granada. E-18071, Granada, Spain
Evidence of Chaos in Slab Avalanches
2002 International Snow Science Workshop Penticton British Columbia, 2002
We present evidence that slab avalanching is a chaotic process. A 20-year set of 8062 avalanches running on more than 140 paths at Mammoth Mountain was examined The distribution of crown sizes greater than a given size is scale invariant (fractal) over the entire mountain and on individual paths. Chaotic systems often exhibit fractal statistics. We reconstruct the phase space portrait and resulting attractor for crown size on one avalanche path for the period 1982/1983 through 2001/2002. Independent measures of the attractor, including comparison against surrogate sets of stochastic data, indicate the time series is deterministic and that the attractor is chaotic.