@article{ZoellerHolschneiderHainzl2013, author = {Z{\"o}ller, Gert and Holschneider, Matthias and Hainzl, Sebastian}, title = {The Maximum Earthquake Magnitude in a Time Horizon: Theory and Case Studies}, series = {Bulletin of the Seismological Society of America}, volume = {103}, journal = {Bulletin of the Seismological Society of America}, number = {2A}, publisher = {Seismological Society of America}, address = {Albany}, issn = {0037-1106}, doi = {10.1785/0120120013}, pages = {860 -- 875}, year = {2013}, abstract = {We show how the maximum magnitude within a predefined future time horizon may be estimated from an earthquake catalog within the context of Gutenberg-Richter statistics. The aim is to carry out a rigorous uncertainty assessment, and calculate precise confidence intervals based on an imposed level of confidence a. In detail, we present a model for the estimation of the maximum magnitude to occur in a time interval T-f in the future, given a complete earthquake catalog for a time period T in the past and, if available, paleoseismic events. For this goal, we solely assume that earthquakes follow a stationary Poisson process in time with unknown productivity Lambda and obey the Gutenberg-Richter law in magnitude domain with unknown b-value. The random variables. and b are estimated by means of Bayes theorem with noninformative prior distributions. Results based on synthetic catalogs and on retrospective calculations of historic catalogs from the highly active area of Japan and the low-seismicity, but high-risk region lower Rhine embayment (LRE) in Germany indicate that the estimated magnitudes are close to the true values. Finally, we discuss whether the techniques can be extended to meet the safety requirements for critical facilities such as nuclear power plants. For this aim, the maximum magnitude for all times has to be considered. In agreement with earlier work, we find that this parameter is not a useful quantity from the viewpoint of statistical inference.}, language = {en} } @article{ZoellerHolschneiderHainzletal.2014, author = {Z{\"o}ller, Gert and Holschneider, Matthias and Hainzl, Sebastian and Zhuang, Jiancang}, title = {The largest expected earthquake magnitudes in Japan: The statistical perspective}, series = {Bulletin of the Seismological Society of America}, volume = {104}, journal = {Bulletin of the Seismological Society of America}, number = {2}, publisher = {Seismological Society of America}, address = {Albany}, issn = {0037-1106}, doi = {10.1785/0120130103}, pages = {769 -- 779}, year = {2014}, abstract = {Earthquake catalogs are probably the most informative data source about spatiotemporal seismicity evolution. The catalog quality in one of the most active seismogenic zones in the world, Japan, is excellent, although changes in quality arising, for example, from an evolving network are clearly present. Here, we seek the best estimate for the largest expected earthquake in a given future time interval from a combination of historic and instrumental earthquake catalogs. We extend the technique introduced by Zoller et al. (2013) to estimate the maximum magnitude in a time window of length T-f for earthquake catalogs with varying level of completeness. In particular, we consider the case in which two types of catalogs are available: a historic catalog and an instrumental catalog. This leads to competing interests with respect to the estimation of the two parameters from the Gutenberg-Richter law, the b-value and the event rate lambda above a given lower-magnitude threshold (the a-value). The b-value is estimated most precisely from the frequently occurring small earthquakes; however, the tendency of small events to cluster in aftershocks, swarms, etc. violates the assumption of a Poisson process that is used for the estimation of lambda. We suggest addressing conflict by estimating b solely from instrumental seismicity and using large magnitude events from historic catalogs for the earthquake rate estimation. Applying the method to Japan, there is a probability of about 20\% that the maximum expected magnitude during any future time interval of length T-f = 30 years is m >= 9.0. Studies of different subregions in Japan indicates high probabilities for M 8 earthquakes along the Tohoku arc and relatively low probabilities in the Tokai, Tonankai, and Nankai region. Finally, for scenarios related to long-time horizons and high-confidence levels, the maximum expected magnitude will be around 10.}, language = {en} } @article{BeauvalHainzlScherbaum2006, author = {Beauval, Celine and Hainzl, Sebastian and Scherbaum, Frank}, title = {The impact of the spatial uniform distribution of seismicity on probabilistic seismic-hazard estimation}, series = {Bulletin of the Seismological Society of America}, volume = {96}, journal = {Bulletin of the Seismological Society of America}, number = {6}, publisher = {GeoScienceWorld}, address = {Alexandria, Va.}, issn = {0037-1106}, doi = {10.1785/0120060073}, pages = {2465 -- 2471}, year = {2006}, abstract = {The first step in the estimation of probabilistic seismic hazard in a region commonly consists of the definition and characterization of the relevant seismic sources. Because in low-seismicity regions seismicity is often rather diffuse and faults are difficult to identify, large areal source zones are mostly used. The corresponding hypothesis is that seismicity is uniformly distributed inside each areal seismic source zone. In this study, the impact of this hypothesis on the probabilistic hazard estimation is quantified through the generation of synthetic spatial seismicity distributions. Fractal seismicity distributions are generated inside a given source zone and probabilistic hazard is computed for a set of sites located inside this zone. In our study, the impact of the spatial seismicity distribution is defined as the deviation from the hazard value obtained for a spatially uniform seismicity distribution. From the generation of a large number of synthetic distributions, the correlation between the fractal dimension D and the impact is derived. The results show that the assumption of spatially uniform seismicity tends to bias the hazard to higher values. The correlation can be used to determine the systematic biases and uncertainties for hazard estimations in real cases, where the fractal dimension has been determined. We apply the technique in Germany (Cologne area) and in France (Alps).}, language = {en} } @article{EngbertHainzlZoelleretal.1998, author = {Engbert, Ralf and Hainzl, Sebastian and Z{\"o}ller, Gert and Kurths, J{\"u}rgen}, title = {Testing for unstable periodic orbits to characterize spatiotemporal dynamics}, year = {1998}, language = {en} } @article{RichterHainzlDahmetal.2020, author = {Richter, Gudrun and Hainzl, Sebastian and Dahm, Torsten and Z{\"o}ller, Gert}, title = {Stress-based, statistical modeling of the induced seismicity at the Groningen gas field}, series = {Environmental earth sciences}, volume = {79}, journal = {Environmental earth sciences}, number = {11}, publisher = {Springer}, address = {New York}, issn = {1866-6280}, doi = {10.1007/s12665-020-08941-4}, pages = {15}, year = {2020}, abstract = {Groningen is the largest onshore gas field under production in Europe. The pressure depletion of the gas field started in 1963. In 1991, the first induced micro-earthquakes have been located at reservoir level with increasing rates in the following decades. Most of these events are of magnitude less than 2.0 and cannot be felt. However, maximum observed magnitudes continuously increased over the years until the largest, significant event with ML=3.6 was recorded in 2014, which finally led to the decision to reduce the production. This causal sequence displays the crucial role of understanding and modeling the relation between production and induced seismicity for economic planing and hazard assessment. Here we test whether the induced seismicity related to gas exploration can be modeled by the statistical response of fault networks with rate-and-state-dependent frictional behavior. We use the long and complete local seismic catalog and additionally detailed information on production-induced changes at the reservoir level to test different seismicity models. Both the changes of the fluid pressure and of the reservoir compaction are tested as input to approximate the Coulomb stress changes. We find that the rate-and-state model with a constant tectonic background seismicity rate can reproduce the observed long delay of the seismicity onset. In contrast, so-called Coulomb failure models with instantaneous earthquake nucleation need to assume that all faults are initially far from a critical state of stress to explain the delay. Our rate-and-state model based on the fluid pore pressure fits the spatiotemporal pattern of the seismicity best, where the fit further improves by taking the fault density and orientation into account. Despite its simplicity with only three free parameters, the rate-and-state model can reproduce the main statistical features of the observed activity.}, language = {en} } @article{WangHainzlZoelleretal.2012, author = {Wang, Lifeng and Hainzl, Sebastian and Z{\"o}ller, Gert and Holschneider, Matthias}, title = {Stress- and aftershock-constrained joint inversions for coseismic and postseismic slip applied to the 2004 M6.0 Parkfield earthquake}, series = {Journal of geophysical research : Solid earth}, volume = {117}, journal = {Journal of geophysical research : Solid earth}, publisher = {American Geophysical Union}, address = {Washington}, issn = {2169-9313}, doi = {10.1029/2011JB009017}, pages = {18}, year = {2012}, abstract = {Both aftershocks and geodetically measured postseismic displacements are important markers of the stress relaxation process following large earthquakes. Postseismic displacements can be related to creep-like relaxation in the vicinity of the coseismic rupture by means of inversion methods. However, the results of slip inversions are typically non-unique and subject to large uncertainties. Therefore, we explore the possibility to improve inversions by mechanical constraints. In particular, we take into account the physical understanding that postseismic deformation is stress-driven, and occurs in the coseismically stressed zone. We do joint inversions for coseismic and postseismic slip in a Bayesian framework in the case of the 2004 M6.0 Parkfield earthquake. We perform a number of inversions with different constraints, and calculate their statistical significance. According to information criteria, the best result is preferably related to a physically reasonable model constrained by the stress-condition (namely postseismic creep is driven by coseismic stress) and the condition that coseismic slip and large aftershocks are disjunct. This model explains 97\% of the coseismic displacements and 91\% of the postseismic displacements during day 1-5 following the Parkfield event, respectively. It indicates that the major postseismic deformation can be generally explained by a stress relaxation process for the Parkfield case. This result also indicates that the data to constrain the coseismic slip model could be enriched postseismically. For the 2004 Parkfield event, we additionally observe asymmetric relaxation process at the two sides of the fault, which can be explained by material contrast ratio across the fault of similar to 1.15 in seismic velocity.}, language = {en} } @article{FaenzaHainzlScherbaum2009, author = {Faenza, Licia and Hainzl, Sebastian and Scherbaum, Frank}, title = {Statistical analysis of the Central-Europe seismicity}, issn = {0040-1951}, doi = {10.1016/j.tecto.2008.04.030}, year = {2009}, abstract = {The aim of this paper is to characterize the spatio-temporal distribution of Central-Europe seismicity. Specifically, by using a non-parametric statistical approach, the proportional hazard model, leading to an empirical estimation of the hazard function, we provide some constrains on the time behavior of earthquake generation mechanisms. The results indicate that the most conspicuous characteristics of M-w 4.0+ earthquakes is a temporal clustering lasting a couple of years. This suggests that the probability of occurrence increases immediately after a previous event. After a few years, the process becomes almost time independent. Furthermore, we investigate the cluster properties of the seismicity of Central-Europe, by comparing the obtained result with the one of synthetic catalogs generated by the epidemic type aftershock sequences (ETAS) model, which previously have been successfully applied for short term clustering. Our results indicate that the ETAS is not well suited to describe the seismicity as a whole, while it is able to capture the features of the short- term behaviour. Remarkably, similar results have been previously found for Italy using a higher magnitude threshold.}, language = {en} } @inproceedings{HainzlScherbaumZoeller2006, author = {Hainzl, Sebastian and Scherbaum, Frank and Z{\"o}ller, Gert}, title = {Spatiotemporal earthquake patterns}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-7267}, year = {2006}, abstract = {Interdisziplin{\"a}res Zentrum f{\"u}r Musterdynamik und Angewandte Fernerkundung Workshop vom 9. - 10. Februar 2006}, language = {en} } @article{HainzlZoellerKurths1999, author = {Hainzl, Sebastian and Z{\"o}ller, Gert and Kurths, J{\"u}rgen}, title = {Similar power laws for foreshock and aftershock sequences in a spring block model for earthquakes}, year = {1999}, language = {en} } @article{HainzlZoellerKurths1999, author = {Hainzl, Sebastian and Z{\"o}ller, Gert and Kurths, J{\"u}rgen}, title = {Self-organized criticality model for earthquakes : Quiescence, foreshocks and aftershocks}, year = {1999}, language = {en} }