Estimating the ETAS model from an early aftershock sequence

Earthquake catalogs exhibit strong spatio-temporal correlations. As such, earthquakes are often classified into clusters of correlated activity. Clusters themselves are traditionally classified in two different kinds: (i) bursts, with a clear hierarchical structure between a single strong mainshock, preceded by a few foreshocks and followed by a power-law decaying aftershock sequence, and (ii) swarms, exhibiting a non-trivial activity rate that cannot be reduced to such a simple hierarchy between events.&#160;The Epidemic Aftershock Sequence (ETAS) model is a linear Hawkes point process able to reproduce earthquake clusters from empirical statistical laws [Ogata, 1998]. Although not always explicit, the ETAS model is often interpreted as the outcome of a background activity driven by external forces and a Galton-Watson branching process with one-to-one causal links between events [Saichev et al., 2005]. Declustering techniques based on field observations [Baiesi & Paczuski, 2004] can be used to infer the most likely causal links between events in a cluster. Following this method, Zaliapin and Ben&#8208;Zion (2013) determined the statistical properties of earthquake clusters characterizing bursts and swarms, finding a relationship between the predominant cluster-class and the heat flow in seismic regions.Here, I show how the statistical properties of clusters are related to the fundamental statistics of the underlying seismogenic process, modeled in two point-process paradigms [Bar&#243;, 2020].The classification of clusters into bursts and swarms appears naturally in the standard ETAS model with homogeneous rates and are determined by the average branching ratio (nb) and the ratio between exponents &#945; and b characterizing the production of aftershocks and the distribution of magnitudes, respectively. The scale-free ETAS model, equivalent to the BASS model [Turcotte, et al., 2007], and usual in cold active tectonic regions, is imposed by &#945;=b and reproduces bursts. In contrast, by imposing &#945;<0.5b, we recover the properties of swarms, characteristic of regions with high heat flow.&#160;Alternatively, the same declustering methodology applied to a non-homogeneous Poisson process with a non-factorizable intensity, i.e. in absence of causal links, recovers swarms with &#945;=0, i.e. a Poisson Galton-Watson process, with similar statistical properties to the ETAS model in the regime &#945;<0.5b.Therefore, while bursts are likely to represent actual causal links between events, swarms can either denote causal links with low &#945;/b ratio or variations of the background rate caused by exogenous processes introducing local and transient stress changes. Furthermore, the redundancy in the statistical laws can be used to test the hypotheses posed by the ETAS model as a memory&#8208;less branching process.&#160;References:<ul><li> Baiesi, M., & Paczuski, M. (2004). Physical Review E, 69, 66,106. doi:10.1103/PhysRevE.69.066106. </li> <li> Bar&#243;, J. (2020).&#160; Journal of Geophysical Research: Solid Earth, 125, e2019JB018530. doi:10.1029/2019JB018530. </li> <li> Ogata, Y. (1998) Annals of the Institute of Statistical Mathematics, 50(2), 379&#8211;402. doi:10.1023/A:1003403601725. </li> <li> Saichev, A., Helmstetter, A. & Sornette, D. (2005) Pure appl. geophys. 162, 1113&#8211;1134. doi:10.1007/s00024-004-2663-6. </li> <li> Turcotte, D. L., Holliday, J. R., and Rundle, J. B. (2007), Geophys. Res. Lett., 34, L12303, doi:10.1029/2007GL029696. </li> <li> Zaliapin, I., and Ben&#8208;Zion, Y. (2013), J. Geophys. Res. Solid Earth, 118, 2865&#8211; 2877, doi:10.1002/jgrb.50178. </li> </ul>

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Operational Earthquake Forecasting during the 2019 Ridgecrest, California, Earthquake Sequence with the UCERF3-ETAS Model

Seismological Research Letters ◽

10.1785/0220190294 ◽

2020 ◽

Vol 91 (3) ◽

pp. 1567-1578 ◽

Cited By ~ 3

Author(s):

Kevin R. Milner ◽

Edward H. Field ◽

William H. Savran ◽

Morgan T. Page ◽

Thomas H. Jordan

Keyword(s):

High Performance ◽

Aftershock Sequence ◽

Lessons Learned ◽

Ease Of Use ◽

Earthquake Forecasting ◽

Earthquake Rupture ◽

Etas Model ◽

Epidemic Type Aftershock Sequence ◽

Aftershock Sequences ◽

High Performance Computing Cluster

Abstract The first Uniform California Earthquake Rupture Forecast, Version 3–epidemic-type aftershock sequence (UCERF3-ETAS) aftershock simulations were running on a high-performance computing cluster within 33 min of the 4 July 2019 M 6.4 Searles Valley earthquake. UCERF3-ETAS, an extension of the third Uniform California Earthquake Rupture Forecast (UCERF3), is the first comprehensive, fault-based, epidemic-type aftershock sequence (ETAS) model. It produces ensembles of synthetic aftershock sequences both on and off explicitly modeled UCERF3 faults to answer a key question repeatedly asked during the Ridgecrest sequence: What are the chances that the earthquake that just occurred will turn out to be the foreshock of an even bigger event? As the sequence unfolded—including one such larger event, the 5 July 2019 M 7.1 Ridgecrest earthquake almost 34 hr later—we updated the model with observed aftershocks, finite-rupture estimates, sequence-specific parameters, and alternative UCERF3-ETAS variants. Although configuring and running UCERF3-ETAS at the time of the earthquake was not fully automated, considerable effort had been focused in 2018 on improving model documentation and ease of use with a public GitHub repository, command line tools, and flexible configuration files. These efforts allowed us to quickly respond and efficiently configure new simulations as the sequence evolved. Here, we discuss lessons learned during the Ridgecrest sequence, including sensitivities of fault triggering probabilities to poorly constrained finite-rupture estimates and model assumptions, as well as implications for UCERF3-ETAS operationalization.

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Integration of geological and seismological data in earthquakes occurrence models for Italy: towards a unified model for different forecast perspectives

Geophysical Journal International ◽

10.1093/gji/ggz419 ◽

2019 ◽

Vol 219 (3) ◽

pp. 2148-2164

Author(s):

A M Lombardi

Keyword(s):

Aftershock Sequence ◽

Earthquake Forecasting ◽

Short Term ◽

Background Rate ◽

Etas Model ◽

Term Forecast ◽

Earthquake Predictability ◽

Background Seismicity ◽

Different Types

SUMMARY The operational earthquake forecasting (OEF) is a procedure aimed at informing communities on how seismic hazard changes with time. This can help them live with seismicity and mitigate risk of destructive earthquakes. A successful short-term prediction scheme is not yet produced, but the search for it should not be abandoned. This requires more research on seismogenetic processes and, specifically, inclusion of any information about earthquakes in models, to improve forecast of future events, at any spatio-temporal-magnitude scale. The short- and long-term forecast perspectives of earthquake occurrence followed, up to now, separate paths, involving different data and peculiar models. But actually they are not so different and have common features, being parts of the same physical process. Research on earthquake predictability can help to search for a common path in different forecast perspectives. This study aims to improve the modelling of long-term features of seismicity inside the epidemic type aftershock sequence (ETAS) model, largely used for short-term forecast and OEF procedures. Specifically, a more comprehensive estimation of background seismicity rate inside the ETAS model is attempted, by merging different types of data (seismological instrumental, historical, geological), such that information on faults and on long-term seismicity integrates instrumental data, on which the ETAS models are generally set up. The main finding is that long-term historical seismicity and geological fault data improve the pseudo-prospective forecasts of independent seismicity. The study is divided in three parts. The first consists in models formulation and parameter estimation on recent seismicity of Italy. Specifically, two versions of ETAS model are compared: a ‘standard’, previously published, formulation, only based on instrumental seismicity, and a new version, integrating different types of data for background seismicity estimation. Secondly, a pseudo-prospective test is performed on independent seismicity, both to test the reliability of formulated models and to compare them, in order to identify the best version. Finally, a prospective forecast is made, to point out differences and similarities in predicting future seismicity between two models. This study must be considered in the context of its limitations; anyway, it proves, beyond argument, the usefulness of a more sophisticated estimation of background rate, inside short-term modelling of earthquakes.

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Testing of the foreshock hypothesis within an epidemic like description of seismicity

Geophysical Journal International ◽

10.1093/gji/ggaa611 ◽

2020 ◽

Author(s):

G Petrillo ◽

E Lippiello

Keyword(s):

Seismic Activity ◽

Good Description ◽

Aftershock Sequence ◽

Short Term ◽

Etas Model ◽

Temporal Clustering ◽

Epidemic Type Aftershock Sequence ◽

Preparatory Phase ◽

Spatio Temporal ◽

The One

Summary The Epidemic Type Aftershock Sequence (ETAS) model provides a good description of the post-seismic spatio-temporal clustering of seismicity and is also able to capture some features of the increase of seismic activity caused by foreshocks. Recent results, however, have shown that the number of foreshocks observed in instrumental catalogs is significantly much larger than the one predicted by the ETAS model. Here we show that it is possible to keep an epidemic description of post-seismic activity and, at the same time, to incorporate pre-seismic temporal clustering, related to foreshocks. Taking also into-account the short-term incompleteness of instrumental catalogs, we present a model which achieves very good description of the southern California seismicity both on the aftershock and on the foreshock side. Our results indicate that the existence of a preparatory phase anticipating mainshocks represents the most plausible explanation for the occurrence of foreshocks.

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Monitoring of anomaly in the aftershock sequence of the 2005 earthquake of M7.0 off coast of the western Fukuoka, Japan, by the ETAS model

Geophysical Research Letters ◽

10.1029/2005gl024405 ◽

2006 ◽

Vol 33 (1) ◽

pp. n/a-n/a ◽

Cited By ~ 19

Author(s):

Yosihiko Ogata

Keyword(s):

Aftershock Sequence ◽

Etas Model

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The Relevance of Foreshocks in Earthquake Triggering: A Statistical Study

10.20944/preprints201810.0679.v1 ◽

2018 ◽

Author(s):

Eugenio Lippiello ◽

Cataldo Godano ◽

Lucilla De Arcangelis

Keyword(s):

Statistical Study ◽

Aftershock Sequence ◽

Statistical Features ◽

Earthquake Triggering ◽

Etas Model ◽

Epidemic Type Aftershock Sequence ◽

The One ◽

Triggering Process ◽

Large Earthquakes ◽

Good Agreement

An increase of seismic activity is often observed before large earthquakes. Events responsible for this increase are usually named foreshock and their occurrence probably represents the most reliable precursory pattern. Many foreshocks statistical features can be interpreted in terms of the standard mainshock-to-aftershock triggering process and are recovered in the Epidemic Type Aftershock Sequence ETAS model. Here we present a statistical study of instrumental seismic catalogs from four different geographic regions. We focus on some common features of foreshocks in the four catalogs which cannot be reproduced by the ETAS model. In particular we find in instrumental catalogs a significantly larger number of foreshocks than the one predicted by the ETAS model. We show that this foreshock excess cannot be attributed to catalog incompleteness. We therefore propose a generalized formulation of the ETAS model, the ETAFS model, which explicitly includes foreshock occurrence. Statistical features of aftershocks and foreshocks in the ETAFS model are in very good agreement with instrumental results.

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The Relevance of Foreshocks in Earthquake Triggering: A Statistical Study

Entropy ◽

10.3390/e21020173 ◽

2019 ◽

Vol 21 (2) ◽

pp. 173 ◽

Cited By ~ 3

Author(s):

Eugenio Lippiello ◽

Cataldo Godano ◽

Lucilla de Arcangelis

Keyword(s):

Statistical Study ◽

Aftershock Sequence ◽

Statistical Features ◽

Earthquake Triggering ◽

Etas Model ◽

Epidemic Type Aftershock Sequence ◽

The One ◽

Triggering Process ◽

Large Earthquakes ◽

Good Agreement

An increase of seismic activity is often observed before large earthquakes. Events responsible for this increase are usually named foreshock and their occurrence probably represents the most reliable precursory pattern. Many foreshocks statistical features can be interpreted in terms of the standard mainshock-to-aftershock triggering process and are recovered in the Epidemic Type Aftershock Sequence ETAS model. Here we present a statistical study of instrumental seismic catalogs from four different geographic regions. We focus on some common features of foreshocks in the four catalogs which cannot be reproduced by the ETAS model. In particular we find in instrumental catalogs a significantly larger number of foreshocks than the one predicted by the ETAS model. We show that this foreshock excess cannot be attributed to catalog incompleteness. We therefore propose a generalized formulation of the ETAS model, the ETAFS model, which explicitly includes foreshock occurrence. Statistical features of aftershocks and foreshocks in the ETAFS model are in very good agreement with instrumental results.

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Declustering of Iran earthquake catalog (1983–2017) using the epidemic-type aftershock sequence (ETAS) model

Acta Geophysica ◽

10.1007/s11600-018-0211-5 ◽

2018 ◽

Vol 66 (6) ◽

pp. 1359-1373 ◽

Cited By ~ 4

Author(s):

Nader Davoudi ◽

Hamid Reza Tavakoli ◽

Mehdi Zare ◽

Abdollah Jalilian

Keyword(s):

Aftershock Sequence ◽

Earthquake Catalog ◽

Etas Model ◽

Epidemic Type Aftershock Sequence

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Seismicity Declustering and Hazard Analysis of the Oklahoma–Kansas Region

Bulletin of the Seismological Society of America ◽

10.1785/0120190111 ◽

2019 ◽

Vol 109 (6) ◽

pp. 2356-2366 ◽

Cited By ~ 5

Author(s):

Ganyu Teng ◽

Jack W. Baker

Keyword(s):

Induced Seismicity ◽

Hazard Analysis ◽

Aftershock Sequence ◽

Eastern United States ◽

Etas Model ◽

Epidemic Type Aftershock Sequence ◽

Window Method ◽

Seismicity Declustering ◽

Hazard Level ◽

Seismicity Catalog

Abstract This study is an evaluation of the suitability of several declustering method for induced seismicity and their impacts on hazard analysis of the Oklahoma–Kansas region. We considered the methods proposed by Gardner and Knopoff (1974), Reasenberg (1985), Zaliapin and Ben‐Zion (2013), and the stochastic declustering method (Zhuang et al., 2002) based on the epidemic‐type aftershock sequence (ETAS) model (Ogata, 1988, 1998). The results show that the choice of declustering method has a significant impact on the declustered catalog and the resulting hazard analysis of the Oklahoma–Kansas region. The Gardner and Knopoff method, which is currently implemented in the U.S. Geological Survey one‐year seismic‐hazard forecast for the central and eastern United States, has unexpected features when used for this induced seismicity catalog. It removes 80% of earthquakes and fails to reflect the changes in background rates that have occurred in the past few years. This results in a slight increase in the hazard level from 2016 to 2017, despite a decrease in seismic activities in 2017. The Gardner and Knopoff method also frequently identifies aftershocks with much stronger shaking intensities than their associated mainshocks. These features are mostly due to the window method implemented in the Gardner and Knopoff method. Compared with the Gardner and Knopoff method, the other three methods are able to capture the changing hazard level in the region. However, the ETAS model potentially overestimates the foreshock effect and generates negligible probabilities of large earthquakes being mainshocks. The Reasenberg and Zaliapin and Ben‐Zion methods have similar performance on catalog declustering and hazard analysis. Compared with the ETAS method, these two methods are easier to implement and faster to generate the declustered catalog. The results from this study suggest that both Reasenberg and Zaliapin and Ben‐Zion declustering methods are suitable for declustering and hazard analysis for induced seismicity in the Oklahoma–Kansas region.

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Occurrence of earthquake doublets in the light of the ETAS model

10.5194/egusphere-egu2020-5242 ◽

2020 ◽

Author(s):

Christian Grimm ◽

Martin Käser ◽

Helmut Küchenhoff

Keyword(s):

Explanatory Power ◽

Aftershock Sequence ◽

Probabilistic Seismic Hazard Assessment ◽

Model Parameters ◽

Damage Potential ◽

Plate Interface ◽

Earthquake Catalogues ◽

Etas Model ◽

Aftershock Sequences ◽

Triggering Process

While Probabilistic Seismic Hazard Assessment is commonly based on earthquake catalogues in a declustered form, ongoing seismicity in aftershock sequences is known to be able to add significant hazard, which can also increase the damage potential to already affected structures in risk assessment. Especially so-called earthquake doublets (multiplets), i.e. a cluster mainshock being followed or preceded by one (or more) events with a similarly strong magnitude occurring within pre-defined temporal and spatial limits, can cause loss multiplication effects to the insurance industry, which therefore has a pronounced interest in investigating the frequency of earthquake doublets to happen worldwide. A widely used method to analyse and simulate the triggering process of earthquake sequences is the Epidemic Type Aftershock Sequence (ETAS) model. We estimate the ETAS model parameters for some regional areas and produce synthetic catalogues, which are then analysed particularly with respect to the occurrence of earthquake doublets and compared to the observed history. Also, different seismic subduction-type regions in the world are pointed out to have shown differing relative frequencies of earthquake doublets. Regression models are used to study whether certain mainshock and local, geophysical properties such as magnitude, dip and rake angle, depth, distance to subduction plate interface and velocity of converging subduction plates nearby show explanatory power for the probability of a cluster containing an earthquake doublet.

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