arXiv subjects

Javier B. Gomez

Publications and source records attributed to Javier B. Gomez.

7 recordsLinked to original sources

arXiv2007

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

We illustrate how a simple statistical model can describe the quasiperiodic occurrence of large earthquakes. The model idealizes the loading of elastic energy in a seismic fault by the stochastic filling of a box. The emptying of the box after it is full is analogous to the generation of a large earthquake in which the fault relaxes after having been loaded to its failure threshold. The duration of the filling process is analogous to the seismic cycle, the time interval between two successive large earthquakes in a particular fault. The simplicity of the model enables us to derive the statistical distribution of its seismic cycle. We use this distribution to fit the series of earthquakes with magnitude around 6 that occurred at the Parkfield segment of the San Andreas fault in California. Using this fit, we estimate the probability of the next large earthquake at Parkfield and devise a simple forecasting strategy.

physics.geo-ph↗

arXiv2006

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

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.

physics.geo-ph↗

arXiv2005

Updating seismic hazard at Parkfield

The occurrence of the September 28, 2004 Mw=6.0 mainshock at Parkfield, California, has significantly increased the mean and aperiodicity of the series of time intervals between mainshocks in this segment of the San Andreas fault. We use five different statistical distributions as renewal models to fit this new series and to estimate the time-dependent probability of the next Parkfield mainshock. Three of these distributions (lognormal, gamma and Weibull) are frequently used in reliability and time-to-failure problems. The other two come from physically-based models of earthquake recurrence (the Brownian Passage Time Model and the Minimalist Model). The differences resulting from these five renewal models are emphasized.

physics.geo-ph↗

arXiv2003

Epidemic Incidence in Correlated Complex Networks

We introduce a numerical method to solve epidemic models on the underlying topology of complex networks. The approach exploits the mean-field like rate equations describing the system and allows to work with very large system sizes, where Monte Carlo simulations are useless due to memory needs. We then study the SIR epidemiological model on assortative networks, providing numerical evidence of the absence of epidemic thresholds. Besides, the time profiles of the populations are analyzed. Finally, we stress that the present method would allow to solve arbitrary epidemic-like models provided that they can be described by mean-field rate equations.

cond-mat.stat-mech↗

arXiv2003

Forecasting characteristic earthquakes in a minimalist model

Using error diagrams, we quantify the forecasting of characteristic-earthquake occurrence in a recently introduced minimalist model. Initially we connect the earthquake alarm at a fixed time after the ocurrence of a characteristic event. The evaluation of this strategy leads to a one-dimensional numerical exploration of the loss function. This first strategy is then refined by considering a classification of the seismic cycles of the model according to the presence, or not, of some factors related to the seismicity observed in the cycle. These factors, statistically speaking, enlarge or shorten the length of the cycles. The independent evaluation of the impact of these factors in the forecast process leads to two-dimensional numerical explorations. Finally, and as a third gradual step in the process of refinement, we combine these factors leading to a three-dimensional exploration. The final improvement in the loss function is about 8.5%.

physics.geo-ph↗

arXiv2003

Error Diagrams and Temporal Correlations in a Fracture Model with Characteristic and Power-Law Distributed Avalanches

Forecasting failure events is one of the most important problems in fracture mechanics and related sciences. In this paper, we use the Molchan scheme to investigate the error diagrams in a fracture model which has the notable advantage of displaying two completely different regimes according to the heterogeneity of the system. In one regime, a characteristic event is observed while for the second regime a power-law spectrum of avalanches is obtained reminiscent of self-organized criticality. We find that both regimes are different when predicting large avalanches and that, in the second regime, there are non-trivial temporal correlations associated to clustering of large events. Finally, we extend the discussion to seismology, where both kinds of avalanche size distributions can be seen.

cond-mat.stat-mech↗

arXiv2001

A Minimalist Model of Characteristic Earthquakes

In a spirit akin to the sandpile model of self-organized criticality, we present a simple statistical model of the cellular-automaton type which produces an avalanche spectrum similar to the characteristic-earthquake behavior of some seismic faults. This model, that has no parameter, is amenable to an algebraic description as a Markov Chain. This possibility illuminates some important results, obtained by Monte Carlo simulations, such as the earthquake size-frequency relation and the recurrence time of the characteristic earthquake.

cond-mat.mtrl-sci↗