Earthquake clusters expected from bare statistics: How bursts and swarms emerge from exogenous and epidemic aftershock processes.

Author(s):  
Jordi Baro

<p>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. </p><p>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‐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.</p><p>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 [Baró, 2020].</p><p>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 α 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 α=b and reproduces bursts. In contrast, by imposing α<0.5b, we recover the properties of swarms, characteristic of regions with high heat flow. </p><p>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 α=0, i.e. a Poisson Galton-Watson process, with similar statistical properties to the ETAS model in the regime α<0.5b.</p><p>Therefore, while bursts are likely to represent actual causal links between events, swarms can either denote causal links with low α/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‐less branching process. </p><p>References:</p><ul><li> <p>Baiesi, M., & Paczuski, M. (2004). <em>Physical Review E</em>, 69, 66,106. doi:10.1103/PhysRevE.69.066106.</p> </li> <li> <p>Baró, J. (2020).  <em>Journal of Geophysical Research: Solid Earth,</em> 125, e2019JB018530. doi:10.1029/2019JB018530.</p> </li> <li> <p>Ogata, Y. (1998) <em>Annals of the Institute of Statistical Mathematics,</em> 50(2), 379–402. doi:10.1023/A:1003403601725.</p> </li> <li> <p>Saichev, A., Helmstetter, A. & Sornette, D. (2005) <em>Pure appl. geophys.</em> 162, 1113–1134. doi:10.1007/s00024-004-2663-6.</p> </li> <li> <p>Turcotte, D. L., Holliday, J. R., and Rundle, J. B. (2007), <em>Geophys. Res. Lett.</em>, 34, L12303, doi:10.1029/2007GL029696.</p> </li> <li> <p>Zaliapin, I., and Ben‐Zion, Y. (2013), <em>J. Geophys. Res. Solid Earth</em>, 118, 2865– 2877, doi:10.1002/jgrb.50178.</p> </li> </ul>

2020 ◽  
Author(s):  
Sebastian Hainzl ◽  
Tomas Fischer

<p>Natural earthquake clusters are often related to a mainshock, which triggers the sequence by its induced stress changes. These clusters are called mainshock-aftershock sequences and statistically well explained by earthquake-earthquake interactions according to the Epidemic Type Aftershock Sequence (ETAS) model. Additionally, aseismic processes such as slow slip, dike propagation or fluid flow might also play a role in the initiation and driving of the earthquake sequence. Earthquake swarms, which lacks a dominant earthquake, are often believed to indicate such transient aseismic forcing signals. However, swarm-type clusters can also occur by chance in ETAS-simulations and thus not necessarily related to aseismic drivers. Thus, more sophisticated quantification of the space-time-magnitude characteristics of earthquake sequences are required for discrimination. Migration patterns are one of those properties which can be indicative for aseismic triggering. We suggest simple measures to identify and quantify migration patterns and test those for synthetic data, data from fluid injection experiments, and natural swarm activity related to fluid flow in NW Bohemia and Long Valley caldera. We analyze their potential to discriminate from ETAS-type clusters and compare it with those of time-magnitude characteristics of the activity such as seismic moment ratios and skewness. Our results are finally used to discriminate earthquake clusters in California and elsewhere.</p>


2021 ◽  
Author(s):  
Shubham Sharma ◽  
Shyam Nandan ◽  
Sebastian Hainzl

<p>Currently, the Epidemic Type Aftershock Sequence (ETAS) model is state-of-the-art for forecasting aftershocks. However, the under-performance of ETAS in forecasting the spatial distribution of aftershocks following a large earthquake make us adopt alternative approaches for the modelling of the spatial ETAS-kernel. Here we develop a hybrid physics and statics based forecasting model. The model uses stress changes, calculated from inverted slip models of large earthquakes, as the basis of the spatial kernel in the ETAS model in order to get more reliable estimates of spatiotemporal distribution of aftershocks. We evaluate six alternative approaches of stress-based ETAS-kernels and rank their performance against the base ETAS model. In all cases, an expectation maximization (EM) algorithm is used to estimate the ETAS parameters. The model approach has been tested on synthetic data to check if the known parameters can be inverted successfully. We apply the proposed method to forecast aftershocks of mainshocks available in SRCMOD database, which includes 192 mainshocks with magnitudes in the range between 4.1 and 9.2 occurred from 1906 to 2020. The probabilistic earthquake forecasts generated by the hybrid model have been tested using established CSEP test metrics and procedures. We show that the additional stress information, provided to estimate the spatial probability distribution, leads to more reliable spatiotemporal ETAS-forecasts of aftershocks as compared to the base ETAS model.</p>


2020 ◽  
Vol 91 (3) ◽  
pp. 1567-1578 ◽  
Author(s):  
Kevin R. Milner ◽  
Edward H. Field ◽  
William H. Savran ◽  
Morgan T. Page ◽  
Thomas H. Jordan

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.


2019 ◽  
Vol 219 (3) ◽  
pp. 2148-2164
Author(s):  
A M Lombardi

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.


Author(s):  
G Petrillo ◽  
E Lippiello

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.


2001 ◽  
Vol 38 (A) ◽  
pp. 232-242 ◽  
Author(s):  
Masajiro Imoto

A point process procedure can be used to study reservoir-induced seismicity (RIS), in which the intensity function representing earthquake hazard is a combination of three terms: a constant background term, an ETAS (epidemic-type aftershock sequence) term for aftershocks, and a time function derived from observation of water levels of a reservoir. This paper presents the results of such a study of the seismicity in the vicinity of the Tarbela reservoir in Pakistan. Making allowance for changes in detection capability and the background seismicity related to tectonic activity, earthquakes of magnitude ≥ 2.0, occurring between May 1978 and January 1982 and whose epicentres were within 100 km of the reservoir, were used in this analysis. Several different intensities were compared via their Akaike information criterion (AIC) values relative to those of a Poisson process. The results demonstrate that the seismicity within 20 km of the reservoir correlates with water levels of the reservoir, namely, active periods occur about 250 days after the appearance of low water levels. This suggests that unloading the reservoir activates the seismicity beneath it. Seasonal variations of the seismicity in an area up to 100 km from the reservoir were also found, but these could not be adequately interpreted by an appropriate RIS mechanism.


2014 ◽  
Vol 41 (3) ◽  
pp. 850-857 ◽  
Author(s):  
Takahiro Omi ◽  
Yosihiko Ogata ◽  
Yoshito Hirata ◽  
Kazuyuki Aihara

1982 ◽  
Vol 19 (03) ◽  
pp. 609-618 ◽  
Author(s):  
J. S. Willie

Let {X(t), N(t)}, – ∞< t <∞, be a stationary bivariate stochastic process where X(t) is an ordinary time series and N(t) is an orderly point process counting the number of points in (0, t]. Suppose values of {X(t), N(t)} are available for 0< t ≦T and let σ1, σ2, ···, σ N (T) denote the jump points of N(t) in (0, T]. For |v| < T, define m T 12(υ)=∑ X (σj+υ)/T and μ T 12(υ)=∑ X (σ j +υ)/∑1 where all summations are over indices j such that 0<σ j , σ j +υ≦T for some σj. The functions M T 12(υ) and μ T 12(υ) are often useful in analyzing the covariation of the time series and point process. In this paper, we shall develop some statistical properties of the functions M T 12(υ) and μ T 12(υ) and discuss some specific situations where it is useful to consider these functions.


1996 ◽  
Vol 33 (04) ◽  
pp. 940-948 ◽  
Author(s):  
Peter Olofsson

A general multi-type branching process where new individuals immigrate according to some point process is considered. An intrinsic submartingale is defined and a convergence result for processes counted with random characteristics is obtained. Some examples are given.


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