A homogeneous stochastic model for earthquake occurrences

Kiremidjian, Anne S.; Anagnos, Thalia

doi:10.3133/ofr801153

Cited by 20 publications

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“…When an earthquake finally occurs, it resets the renewal process to its initial state. Several well-known statistical distributions (such as the gamma, 21 log-normal, 22 and Weibull 16,21,23,24 ) have been used to describe the duration of the seismic cycle and to calculate the conditional probabilities of future earthquakes. These distributions also have been used as failure models for reliability and time-to-failure problems.…”

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confidence: 99%

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

González

Gómez

Pacheco

2005

American Journal of Physics

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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.

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confidence: 99%

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

González

Gómez

Pacheco

2005

American Journal of Physics

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“…The simplest such schemes make use of only the magnitude or time of occurrence of the last large event, and are referred to as the time-predictable and slip-predictable models for hazard assessment [Shimazaki and Nakata, 1980]. Various applications of both time-predictable [Scholz, 1985;Bakun and McEvilly, 1984] and slip-predictable [Kiremidjian and Anagnos, 1984] models to real faults have been made. Historical records and geological information are used to construct plots of accumulated slip as a function of time for a particular fault or fault segment.…”

Section: Long Term Prediction: Results Based On Recurrence Intervalsmentioning

confidence: 99%

Prediction of large events on a dynamical model of a fault

Pepke¹,

Carlson²,

Shaw³

1994

J. Geophys. Res.

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We present results for long term and intermediate term prediction algorithms applied to a simple mechanical model of a fault. We use long term prediction methods based, for example, on the distribution of repeat times between large events to establish a benchmark for predictability in the model. In comparison, intermediate term prediction techniques, analogous to the pattern recognition algorithms CN and M8 introduced and studied by Keilis-Borok et al., are more effective at predicting coming large events. We consider the implications of several different quality functions Q which can be used to optimize the algorithms with respect to features such as space, time, and magnitude windows, and find that our results are not overly sensitive to variations in these algorithm parameters. We also study the intrinsic uncertainities which are associated with seismicity catalogs of restricted lengths.

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“…There are numerous papers indicating the non-Poissonian character of tectonic (e.g. Shlien and Toksöz 1970;Vere-Jones 1970;Kiremidjian and Anagnos 1984;Cornell and Winterstein 1988;Parvez and Ram 1997;Lana et al 2005;Xu and Burton 2006;Chang et al 2006;Jimenez 2011;Martin-Montoya et al 2015) as well as anthropogenic seismic processes (e.g. Lasocki 1992;Weglarczyk and Lasocki 2009;Marcak 2013).…”

Section: Introductionmentioning

confidence: 99%

Interval Estimation of Seismic Hazard Parameters

Orlecka‐Sikora

Lasocki

2016

Pure Appl. Geophys.

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Abstract-The paper considers Poisson temporal occurrence of earthquakes and presents a way to integrate uncertainties of the estimates of mean activity rate and magnitude cumulative distribution function in the interval estimation of the most widely used seismic hazard functions, such as the exceedance probability and the mean return period. The proposed algorithm can be used either when the Gutenberg-Richter model of magnitude distribution is accepted or when the nonparametric estimation is in use. When the Gutenberg-Richter model of magnitude distribution is used the interval estimation of its parameters is based on the asymptotic normality of the maximum likelihood estimator. When the nonparametric kernel estimation of magnitude distribution is used, we propose the iterated bias corrected and accelerated method for interval estimation based on the smoothed bootstrap and secondorder bootstrap samples. The changes resulted from the integrated approach in the interval estimation of the seismic hazard functions with respect to the approach, which neglects the uncertainty of the mean activity rate estimates have been studied using Monte Carlo simulations and two real dataset examples. The results indicate that the uncertainty of mean activity rate affects significantly the interval estimates of hazard functions only when the product of activity rate and the time period, for which the hazard is estimated, is no more than 5.0. When this product becomes greater than 5.0, the impact of the uncertainty of cumulative distribution function of magnitude dominates the impact of the uncertainty of mean activity rate in the aggregated uncertainty of the hazard functions. Following, the interval estimates with and without inclusion of the uncertainty of mean activity rate converge. The presented algorithm is generic and can be applied also to capture the propagation of uncertainty of estimates, which are parameters of a multiparameter function, onto this function.Key words: Aggregated uncertainty in the activity rate and magnitude, magnitude cumulative distribution function, interval estimation of seismic hazard functions, resampling methods, bootstrap, jackknife.

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A homogeneous stochastic model for earthquake occurrences

Cited by 20 publications

References 0 publications

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

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

Prediction of large events on a dynamical model of a fault

Interval Estimation of Seismic Hazard Parameters

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