@article{FiedlerHainzlZoelleretal.2018, author = {Fiedler, Bernhard and Hainzl, Sebastian and Z{\"o}ller, Gert and Holschneider, Matthias}, title = {Detection of Gutenberg-Richter b-Value Changes in Earthquake Time Series}, series = {Bulletin of the Seismological Society of America}, volume = {108}, journal = {Bulletin of the Seismological Society of America}, number = {5A}, publisher = {Seismological Society of America}, address = {Albany}, issn = {0037-1106}, doi = {10.1785/0120180091}, pages = {2778 -- 2787}, year = {2018}, abstract = {The Gutenberg-Richter relation for earthquake magnitudes is the most famous empirical law in seismology. It states that the frequency of earthquake magnitudes follows an exponential distribution; this has been found to be a robust feature of seismicity above the completeness magnitude, and it is independent of whether global, regional, or local seismicity is analyzed. However, the exponent b of the distribution varies significantly in space and time, which is important for process understanding and seismic hazard assessment; this is particularly true because of the fact that the Gutenberg-Richter b-value acts as a proxy for the stress state and quantifies the ratio of large-to-small earthquakes. In our work, we focus on the automatic detection of statistically significant temporal changes of the b-value in seismicity data. In our approach, we use Bayes factors for model selection and estimate multiple change-points of the frequency-magnitude distribution in time. The method is first applied to synthetic data, showing its capability to detect change-points as function of the size of the sample and the b-value contrast. Finally, we apply this approach to examples of observational data sets for which b-value changes have previously been stated. Our analysis of foreshock and after-shock sequences related to mainshocks, as well as earthquake swarms, shows that only a portion of the b-value changes is statistically significant.}, language = {en} } @article{SalamatZoellerZareetal.2018, author = {Salamat, Mona and Z{\"o}ller, Gert and Zare, Mehdi and Amini, Mortaza}, title = {The maximum expected earthquake magnitudes in different future time intervals of six seismotectonic zones of Iran and its surroundings}, series = {Journal of seismology}, volume = {22}, journal = {Journal of seismology}, number = {6}, publisher = {Springer}, address = {Dordrecht}, issn = {1383-4649}, doi = {10.1007/s10950-018-9780-7}, pages = {1485 -- 1498}, year = {2018}, abstract = {One of the crucial components in seismic hazard analysis is the estimation of the maximum earthquake magnitude and associated uncertainty. In the present study, the uncertainty related to the maximum expected magnitude mu is determined in terms of confidence intervals for an imposed level of confidence. Previous work by Salamat et al. (Pure Appl Geophys 174:763-777, 2017) shows the divergence of the confidence interval of the maximum possible magnitude m(max) for high levels of confidence in six seismotectonic zones of Iran. In this work, the maximum expected earthquake magnitude mu is calculated in a predefined finite time interval and imposed level of confidence. For this, we use a conceptual model based on a doubly truncated Gutenberg-Richter law for magnitudes with constant b-value and calculate the posterior distribution of mu for the time interval T-f in future. We assume a stationary Poisson process in time and a Gutenberg-Richter relation for magnitudes. The upper bound of the magnitude confidence interval is calculated for different time intervals of 30, 50, and 100 years and imposed levels of confidence alpha = 0.5, 0.1, 0.05, and 0.01. The posterior distribution of waiting times T-f to the next earthquake with a given magnitude equal to 6.5, 7.0, and7.5 are calculated in each zone. In order to find the influence of declustering, we use the original and declustered version of the catalog. The earthquake catalog of the territory of Iran and surroundings are subdivided into six seismotectonic zones Alborz, Azerbaijan, Central Iran, Zagros, Kopet Dagh, and Makran. We assume the maximum possible magnitude m(max) = 8.5 and calculate the upper bound of the confidence interval of mu in each zone. The results indicate that for short time intervals equal to 30 and 50 years and imposed levels of confidence 1 - alpha = 0.95 and 0.90, the probability distribution of mu is around mu = 7.16-8.23 in all seismic zones.}, language = {en} } @misc{Zoeller2017, author = {Z{\"o}ller, Gert}, title = {Comment on "Estimation of Earthquake Hazard Parameters from Incomplete Data Files. Part III. Incorporation of Uncertainty of Earthquake-Occurrence Model" by Andrzej Kijko, Ansie Smit, and Markvard A. Sellevoll}, series = {Bulletin of the Seismological Society of America}, volume = {107}, journal = {Bulletin of the Seismological Society of America}, publisher = {Seismological Society of America}, address = {Albany}, issn = {0037-1106}, doi = {10.1785/0120160193}, pages = {1975 -- 1978}, year = {2017}, abstract = {Kijko et al. (2016) present various methods to estimate parameters that are relevant for probabilistic seismic-hazard assessment. One of these parameters, although not the most influential, is the maximum possible earthquake magnitude m(max). I show that the proposed estimation of m(max) is based on an erroneous equation related to a misuse of the estimator in Cooke (1979) and leads to unstable results. So far, reported finite estimations of m(max) arise from data selection, because the estimator in Kijko et al. (2016) diverges with finite probability. This finding is independent of the assumed distribution of earthquake magnitudes. For the specific choice of the doubly truncated Gutenberg-Richter distribution, I illustrate the problems by deriving explicit equations. Finally, I conclude that point estimators are generally not a suitable approach to constrain m(max).}, language = {en} } @article{ShcherbakovZhuangZoelleretal.2019, author = {Shcherbakov, Robert and Zhuang, Jiancang and Z{\"o}ller, Gert and Ogata, Yosihiko}, title = {Forecasting the magnitude of the largest expected earthquake}, series = {Nature Communications}, volume = {10}, journal = {Nature Communications}, publisher = {Nature Publishing Group}, address = {London}, issn = {2041-1723}, doi = {10.1038/s41467-019-11958-4}, pages = {11}, year = {2019}, abstract = {The majority of earthquakes occur unexpectedly and can trigger subsequent sequences of events that can culminate in more powerful earthquakes. This self-exciting nature of seismicity generates complex clustering of earthquakes in space and time. Therefore, the problem of constraining the magnitude of the largest expected earthquake during a future time interval is of critical importance in mitigating earthquake hazard. We address this problem by developing a methodology to compute the probabilities for such extreme earthquakes to be above certain magnitudes. We combine the Bayesian methods with the extreme value theory and assume that the occurrence of earthquakes can be described by the Epidemic Type Aftershock Sequence process. We analyze in detail the application of this methodology to the 2016 Kumamoto, Japan, earthquake sequence. We are able to estimate retrospectively the probabilities of having large subsequent earthquakes during several stages of the evolution of this sequence.}, language = {en} } @article{SalamatZoellerAmini2019, author = {Salamat, Mona and Z{\"o}ller, Gert and Amini, Morteza}, title = {Prediction of the Maximum Expected Earthquake Magnitude in Iran:}, series = {Pure and applied geophysics}, volume = {176}, journal = {Pure and applied geophysics}, number = {8}, publisher = {Springer}, address = {Basel}, issn = {0033-4553}, doi = {10.1007/s00024-019-02141-3}, pages = {3425 -- 3438}, year = {2019}, abstract = {This paper concerns the problem of predicting the maximum expected earthquake magnitude μ in a future time interval Tf given a catalog covering a time period T in the past. Different studies show the divergence of the confidence interval of the maximum possible earthquake magnitude m_{ max } for high levels of confidence (Salamat et al. 2017). Therefore, m_{ max } should be better replaced by μ (Holschneider et al. 2011). In a previous study (Salamat et al. 2018), μ is estimated for an instrumental earthquake catalog of Iran from 1900 onwards with a constant level of completeness ( {m0 = 5.5} ). In the current study, the Bayesian methodology developed by Z{\"o}ller et al. (2014, 2015) is applied for the purpose of predicting μ based on the catalog consisting of both historical and instrumental parts. The catalog is first subdivided into six subcatalogs corresponding to six seismotectonic zones, and each of those zone catalogs is subsequently subdivided according to changes in completeness level and magnitude uncertainty. For this, broad and small error distributions are considered for historical and instrumental earthquakes, respectively. We assume that earthquakes follow a Poisson process in time and Gutenberg-Richter law in the magnitude domain with a priori unknown a and b values which are first estimated by Bayes' theorem and subsequently used to estimate μ. Imposing different values of m_{ max } for different seismotectonic zones namely Alborz, Azerbaijan, Central Iran, Zagros, Kopet Dagh and Makran, the results show considerable probabilities for the occurrence of earthquakes with Mw ≥ 7.5 in short Tf , whereas for long Tf, μ is almost equal to m_{ max }}, language = {en} } @article{HainzlZoellerMain2006, author = {Hainzl, Sebastian and Z{\"o}ller, Gert and Main, Ian}, title = {Introduction to special issue: Dynamics of seismicity patterns and earthquake triggering - Preface}, series = {Tectonophysics : international journal of geotectonics and the geology and physics of the interior of the earth}, volume = {424}, journal = {Tectonophysics : international journal of geotectonics and the geology and physics of the interior of the earth}, number = {Special issue}, publisher = {Elsevier}, address = {Amsterdam}, issn = {0040-1951}, doi = {10.1016/j.tecto.2006.03.034}, pages = {135 -- 138}, year = {2006}, language = {en} } @article{Zoeller2022, author = {Z{\"o}ller, Gert}, title = {A note on the estimation of the maximum possible earthquake magnitude based on extreme value theory for the Groningen Gas Field}, series = {The bulletin of the Seismological Society of America : BSSA}, volume = {112}, journal = {The bulletin of the Seismological Society of America : BSSA}, number = {4}, publisher = {Seismological Society of America}, address = {El Cerito, Calif.}, issn = {0037-1106}, doi = {10.1785/0120210307}, pages = {1825 -- 1831}, year = {2022}, abstract = {Extreme value statistics is a popular and frequently used tool to model the occurrence of large earthquakes. The problem of poor statistics arising from rare events is addressed by taking advantage of the validity of general statistical properties in asymptotic regimes. In this note, I argue that the use of extreme value statistics for the purpose of practically modeling the tail of the frequency-magnitude distribution of earthquakes can produce biased and thus misleading results because it is unknown to what degree the tail of the true distribution is sampled by data. Using synthetic data allows to quantify this bias in detail. The implicit assumption that the true M-max is close to the maximum observed magnitude M-max,M-observed restricts the class of the potential models a priori to those with M-max = M-max,M-observed + Delta M with an increment Delta M approximate to 0.5... 1.2. This corresponds to the simple heuristic method suggested by Wheeler (2009) and labeled :M-max equals M-obs plus an increment." The incomplete consideration of the entire model family for the frequency-magnitude distribution neglects, however, the scenario of a large so far unobserved earthquake.}, language = {en} } @misc{ZoellerHolschneider2018, author = {Z{\"o}ller, Gert and Holschneider, Matthias}, title = {Reply to "Comment on 'The Maximum Possible and the Maximum Expected Earthquake Magnitude for Production-Induced Earthquakes at the Gas Field in Groningen, The Netherlands' by Gert Z{\"o}ller and Matthias Holschneider" by Mathias Raschke}, series = {Bulletin of the Seismological Society of America}, volume = {108}, journal = {Bulletin of the Seismological Society of America}, number = {2}, publisher = {Seismological Society of America}, address = {Albany}, issn = {0037-1106}, doi = {10.1785/0120170131}, pages = {1029 -- 1030}, year = {2018}, language = {en} } @article{ZollerHolschneiderBenZion2005, author = {Zoller, Gert and Holschneider, Matthias and Ben-Zion, Yehuda}, title = {The role of heterogeneities as a tuning parameter of earthquake dynamics}, issn = {0033-4553}, year = {2005}, abstract = {We investigate the influence of spatial heterogeneities on various aspects of brittle failure and seismicity in a model of a large strike-slip fault. The model dynamics is governed by realistic boundary conditions consisting of constant velocity motion of regions around the fault, static/kinetic friction laws, creep with depth-dependent coefficients, and 3-D elastic stress transfer. The dynamic rupture is approximated on a continuous time scale using a finite stress propagation velocity ("quasidynamic model''). The model produces a "brittle- ductile'' transition at a depth of about 12.5 km, realistic hypocenter distributions, and other features of seismicity compatible with observations. Previous work suggested that the range of size scales in the distribution of strength-stress heterogeneities acts as a tuning parameter of the dynamics. Here we test this hypothesis by performing a systematic parameter-space study with different forms of heterogeneities. In particular, we analyze spatial heterogeneities that can be tuned by a single parameter in two distributions: ( 1) high stress drop barriers in near- vertical directions and ( 2) spatial heterogeneities with fractal properties and variable fractal dimension. The results indicate that the first form of heterogeneities provides an effective means of tuning the behavior while the second does not. In relatively homogeneous cases, the fault self-organizes to large-scale patches and big events are associated with inward failure of individual patches and sequential failures of different patches. The frequency-size event statistics in such cases are compatible with the characteristic earthquake distribution and large events are quasi-periodic in time. In strongly heterogeneous or near-critical cases, the rupture histories are highly discontinuous and consist of complex migration patterns of slip on the fault. In such cases, the frequency-size and temporal statistics follow approximately power-law relations}, language = {en} } @article{ZollerHainzlHolschneideretal.2005, author = {Zoller, Gert and Hainzl, Sebastian and Holschneider, Matthias and Ben-Zion, Yehuda}, title = {Aftershocks resulting from creeping sections in a heterogeneous fault}, issn = {0094-8276}, year = {2005}, abstract = {We show that realistic aftershock sequences with space-time characteristics compatible with observations are generated by a model consisting of brittle fault segments separated by creeping zones. The dynamics of the brittle regions is governed by static/kinetic friction, 3D elastic stress transfer and small creep deformation. The creeping parts are characterized by high ongoing creep velocities. These regions store stress during earthquake failures and then release it in the interseismic periods. The resulting postseismic deformation leads to aftershock sequences following the modified Omori law. The ratio of creep coefficients in the brittle and creeping sections determines the duration of the postseismic transients and the exponent p of the modified Omori law}, language = {en} }