Basic models of seismicity: temporal models

Zhuang, Jian; Harte, David; Werner, M. J.; Hainzl, Sebastian; Zhou, Shiyong

doi:10.5078/corssa-79905851

Cited by 53 publications

(19 citation statements)

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“…Båth’s law is an empirical observation that the average magnitude difference between a mainshock earthquake and its largest aftershock is approximately 1.2 magnitude units 14 . Statistical models of earthquakes 15 , 16 have come to interpret Båth’s law as a probabilistic consequence of two more fundamental observations 17 – 20 . The first being an aftershock law (i.e., Omori’s law), which describes the temporal decay of earthquake rate following a main shock 21 – 23 .…”

Section: Background Information On Tectonic Aftershocks and Båth’s Lawmentioning

confidence: 99%

Statistical bounds on how induced seismicity stops

Schultz

Ellsworth

Beroza

2022

Sci Rep

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Earthquakes caused by human activities receive scrutiny due to the risks and hazards they pose. Seismicity that occurs after the causative anthropogenic operation stops has been particularly problematic—both because of high-profile cases of damage caused by this trailing seismicity and due to the loss of control for risk management. With this motivation, we undertake a statistical examination of how induced seismicity stops. We borrow the concept of Båth’s law from tectonic aftershock sequences. Båth’s law anticipates the difference between magnitudes in two subsets of seismicity as dependent on their population count ratio. We test this concept for its applicability to induced seismicity, including ~ 80 cases of earthquakes caused by hydraulic fracturing, enhanced geothermal systems, and other fluid-injections with clear operational end points. We find that induced seismicity obeys Båth’s law: both in terms of the magnitude-count-ratio relationship and the power law distribution of residuals. Furthermore, the distribution of count ratios is skewed and heavy-tailed, with most earthquakes occurring during stimulation/injection. We discuss potential models to improve the characterization of these count ratios and propose a Seismogenic Fault Injection Test to measure their parameters in situ. We conclude that Båth’s law quantifies the occurrence of earthquake magnitudes trailing anthropogenic operations.

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Section: Background Information On Tectonic Aftershocks and Båth’s Lawmentioning

confidence: 99%

Statistical bounds on how induced seismicity stops

Schultz

Ellsworth

Beroza

2022

Sci Rep

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“…There is considerable debate in the seismological community about the best method to estimate the spatial background rate ρ(x, y) [Ogata (2011), Helmstetter and Werner (2012), Zhuang et al (2012)]. When modeling larger, regional catalogs, ρ is often estimated by smoothing the largest events in the historical catalog [Ogata (1998)], and in such cases a very important open question is how (and how much) to smooth [Schoenberg (2003), Helmstetter, Kagan and Jackson (2007), Helmstetter and Werner (2012), Zhuang et al (2012)]. For a single earthquake-aftershock sequence, however, can one instead simply estimate ρ as constant within a finite, local area, as in Schoenberg (2013)?…”

Section: Voronoi Residualsmentioning

confidence: 99%

Voronoi residual analysis of spatial point process models with applications to California earthquake forecasts

Bray¹,

Wong²,

Barr³

et al. 2014

Ann. Appl. Stat.

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This reprint differs from the original in pagination and typographic detail. 1 2 BRAY, WONG, BARR AND SCHOENBERG project was initiated to create a variety of earthquake forecast models for seismic hazard assessment in California. Unlike previous projects that addressed the assessment of models for seismic hazard, the RELM participants decided to adopt many competing forecasting models and to rigorously and prospectively test their performance in a dedicated testing center ]. With the end of the RELM project, the forecast models became available and the development of the testing center was done within the scope of CSEP. Many point process models, including multiple variants of the Epidemic-Type Aftershock Sequence (ETAS) models of Ogata (1998) have now been proposed and are part of RELM and CSEP, though the problem of how to compare and evaluate the goodness of fit of such models remains quite open. In RELM, a community consensus was reached that all entered models be tested with certain tests, including the Number or N-test that compares the total forecasted rate with the observation, the Likelihood or L-test that assesses the quality of a forecast in terms of overall likelihood, and the Likelihood-Ratio or R-test that assesses the relative performance of two forecast models compared with what is expected under one proposed model ]. However, over time several drawbacks of these tests were discovered [Schorlemmer et al. (2010)] and the need for more powerful tests became clear. The N-test and L-test simply compare the quantiles of the total numbers of events in each bin or likelihood within each bin to those expected under the given model, and the resulting low-power tests are typically unable to discern significant lack of fit unless the overall rate of the model fits extremely poorly. Further, even when the tests do reject a model, they do not typically indicate where or when the model fits poorly, or how it could be improved. Meanwhile, the number of proposed spatial-temporal models for earthquake occurrences has grown, and the need for discriminating which models fit better than others has become increasingly important. Techniques for assessing goodness of fit are needed to pinpoint where existing models may be improved, and residual plots, rather than numerical significance tests, seem preferable for these purposes.This paper proposes a new form of residual analysis for assessing the goodness of fit of spatial point process models. The proposed method compares the normalized observed and expected numbers of points over Voronoi cells generated by the observed point pattern. The method is applied here in particular to the examination of a version of the ETAS model originally proposed by Ogata (1998), and its goodness of fit to a sequence of 520 M ≥ 3 Hector Mine earthquakes occurring between October 1999 and December 2000. In particular, the Voronoi residuals indicate that assumption of a constant background rate ρ in the ETAS model results in excessive smoothing

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“…When ρ < 1 each earthquake is assumed to trigger less than one aftershock, the seismicity diminishes, and eventually the family dies. That means the process is stable and stationary, indicating that the estimated model parameters are rational [48]. On the contrary, a value of ρ > 1 means that the process generates more than one primary aftershock per earthquake, indicating that seismic activity exponentially increases with time.…”

Section: Validation Methodsmentioning

confidence: 99%

An Earthquake-Clustering Model in North Aegean Area (Greece)

Mangira

Console

Papadimitriou

et al. 2022

Axioms

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The investigation of short-term earthquake-clustering features is made feasible through the application of a purely stochastic Epidemic-Type Aftershock Sequence (ETAS) model. The learning period that is used for the estimation of the parameters is composed by earthquakes with M ≥ 2.6 that occurred between January 2008 and May 2017. The model predictability is retrospectively examined for the 12 June 2017 Lesvos earthquake (Mw6.4) and the subsequent events. The construction of time-dependent seismicity maps and comparison between the observed and expected earthquake number are performed in order to temporally and spatially test the evolution of the sequence, respectively. The generation of 127 target events with M ≥ 3.0 in the period June–July 2017, just before the main shock occurrence, is examined in a quantitative evaluation. The statistical criteria used for assessing the model performance are the Relative Operating Characteristic Diagram, the R-score, and the probability gain. Reliable forecasts are provided through the epidemic model testifying its superiority towards a time-invariant Poisson model.

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Basic models of seismicity: temporal models

Cited by 53 publications

References 0 publications

Statistical bounds on how induced seismicity stops

Statistical bounds on how induced seismicity stops

Voronoi residual analysis of spatial point process models with applications to California earthquake forecasts

An Earthquake-Clustering Model in North Aegean Area (Greece)

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