The occupation of a box as a toy model for the seismic cycle of a fault

González, Ángel Poncela; Gómez, J.; Pacheco, A. F.

doi:10.1119/1.2013310

Cited by 13 publications

(15 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This characteristic is shared by a discrete‐time box‐filling model presented by Gonzalez et al . []. In contrast, the log‐normal distribution predicts that the conditional probability of event occurrence slowly declines with increasing time after passing through a maximum.…”

Section: Conditional Probability Computed Under Renewal Modelsmentioning

confidence: 99%

Renewal models and coseismic stress transfer in the Corinth Gulf, Greece, fault system

et al. 2013

View full text Add to dashboard Cite

[1] We model interevent times and Coulomb static stress transfer on the rupture segments along the Corinth Gulf extension zone, a region with a wealth of observations on strong-earthquake recurrence behavior. From the available information on past seismic activity, we have identified eight segments without significant overlapping that are aligned along the southern boundary of the Corinth rift. We aim to test if strong earthquakes on these segments are characterized by some kind of time-predictable behavior, rather than by complete randomness. The rationale for time-predictable behavior is based on the characteristic earthquake hypothesis, the necessary ingredients of which are a known faulting geometry and slip rate. The tectonic loading rate is characterized by slip of 6 mm/yr on the westernmost fault segment, diminishing to 4 mm/yr on the easternmost segment, based on the most reliable geodetic data. In this study, we employ statistical and physical modeling to account for stress transfer among these fault segments. The statistical modeling is based on the definition of a probability density distribution of the interevent times for each segment. Both the Brownian Passage-Time (BPT) and Weibull distributions are tested. The time-dependent hazard rate thus obtained is then modified by the inclusion of a permanent physical effect due to the Coulomb static stress change caused by failure of neighboring faults since the latest characteristic earthquake on the fault of interest. The validity of the renewal model is assessed retrospectively, using the data of the last 300 years, by comparison with a plain time-independent Poisson model, by means of statistical tools including the Relative Operating Characteristic diagram, the R-score, the probability gain and the log-likelihood ratio. We treat the uncertainties in the parameters of each examined fault source, such as linear dimensions, depth of the fault center, focal mechanism, recurrence time, coseismic slip, and aperiodicity of the statistical distribution, by a Monte Carlo technique. The Monte Carlo samples for all these parameters are drawn from a uniform distribution within their uncertainty limits. We find that the BPT and the Weibull renewal models yield comparable results, and both of them perform significantly better than the Poisson hypothesis. No clear performance enhancement is achieved by the introduction of the Coulomb static stress change into the renewal model. Citation: Console, R., G. Falcone, V. Karakostas, M. Murru, E. Papadimitriou, and D. Rhoades (2013), Renewal models and coseismic stress transfer in th8e Corinth Gulf, Greece, fault system,

show abstract

Section: Conditional Probability Computed Under Renewal Modelsmentioning

confidence: 99%

Renewal models and coseismic stress transfer in the Corinth Gulf, Greece, fault system

et al. 2013

View full text Add to dashboard Cite

show abstract

“…Depending on the context, the objects may represent stickers in a football album, vertices on a fully connected graph, or people in an epidemic. Close analogies to the coupon collector can be found in a toy model for the buildup of strain in a seismic fault [2], the random deposition of k-mers on a substrate [3], the infection of nodes on a network [4], or the parasitization of hosts [5]. More generally, the coupon collector belongs to the family of urn problems [6,7].…”

Section: Introductionmentioning

confidence: 99%

Dynamically accelerated cover times

Maziya

Cocconi

Pruessner

et al. 2020

Phys. Rev. Research

View full text Add to dashboard Cite

Among observables characterizing the random exploration of a graph or lattice, the cover time, namely, the time to visit every site, continues to attract widespread interest. Much insight about cover times is gained by mapping to the (spaceless) coupon collector problem, which amounts to ignoring spatiotemporal correlations, and an early conjecture that the limiting cover time distribution of regular random walks on large lattices converges to the Gumbel distribution in d 3 was recently proved rigorously. Furthermore, a number of mathematical and numerical studies point to the robustness of the Gumbel universality to modifications of the spatial features of the random search processes (e.g., introducing persistence and/or intermittence, or changing the graph topology). Here we investigate the robustness of the Gumbel universality to dynamical modification of the temporal features of the search, specifically by allowing the random walker to "accelerate" or "decelerate" upon visiting a previously unexplored site. We generalize the mapping mentioned above by relating the statistics of cover times to the roughness of 1/ f α Gaussian signals, leading to the conjecture that the Gumbel distribution is but one of a family of cover time distributions, ranging from Gaussian for highly accelerated cover, to exponential for highly decelerated cover. While our conjecture is confirmed by systematic Monte Carlo simulations in dimensions d > 3, our results for acceleration in d = 3 challenge the current understanding of the role of correlations in the cover time problem.

show abstract

“…The reference strategy consists simply in declaring an alarm some time after each target event, and maintaining it on until the next target event (Newman and Turcotte, 2002;Vázquez-Prada et al, 2003;González et al, 2005). As a general rule, the shorter this time, the bigger f a and the lesser f e .…”

Section: Reference Strategymentioning

confidence: 99%

“…In this approach the positions of the cells in the clone are irrelevant. Each clone is thus equivalent to the so-called box model (González et al, 2005).…”

Section: Synchronization-based Forecastingmentioning

confidence: 99%

A way to synchronize models with seismic faults for earthquake forecasting: Insights from a simple stochastic model

et al. 2006

Self Cite

View full text Add to dashboard Cite

Numerical models are starting to be used for determining the future behaviour of seismic faults and fault networks. Their final goal would be to forecast future large earthquakes. In order to use them for this task, it is necessary to synchronize each model with the current status of the actual fault or fault network it simulates (just as, for example, meteorologists synchronize their models with the atmosphere by incorporating current atmospheric data in them). However, lithospheric dynamics is largely unobservable: important parameters cannot (or can rarely) be measured in Nature. Earthquakes, though, provide indirect but measurable clues of the stress and strain status in the lithosphere, which should be helpful for the synchronization of the models.The rupture area is one of the measurable parameters of earthquakes. Here we explore how it can be used to at least synchronize fault models between themselves and forecast synthetic earthquakes. Our purpose here is to forecast synthetic earthquakes in a simple but stochastic (random) fault model. By imposing the rupture area of the synthetic earthquakes of this model on other models, the latter become partially synchronized with the first one. We use these partially synchronized models to successfully forecast most of the largest earthquakes generated by the first model. This forecasting strategy outperforms others that only take into account the earthquake series. Our results suggest that probably a good way to synchronize more detailed models with real faults is to force them to reproduce the sequence of previous earthquake ruptures on the faults. This hypothesis could be tested in the future with more detailed models and actual seismic data.

show abstract

The occupation of a box as a toy model for the seismic cycle of a fault

Cited by 13 publications

References 37 publications

Renewal models and coseismic stress transfer in the Corinth Gulf, Greece, fault system

Renewal models and coseismic stress transfer in the Corinth Gulf, Greece, fault system

Dynamically accelerated cover times

A way to synchronize models with seismic faults for earthquake forecasting: Insights from a simple stochastic model

Contact Info

Product

Resources

About