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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.
Based on an analysis of continuous monitoring of farm animal behavior in the region of the 2016 M6.6 Norcia earthquake in Italy, Wikelski et al., 2020; (Seismol Res Lett, 89, 2020, 1238) conclude that animal activity can be anticipated with subsequent seismic activity and that this finding might help to design a "short-term earthquake forecasting method." We show that this result is based on an incomplete analysis and misleading interpretations. Applying state-of-the-art methods of statistics, we demonstrate that the proposed anticipatory patterns cannot be distinguished from random patterns, and consequently, the observed anomalies in animal activity do not have any forecasting power.
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.
The knowledge of the largest expected earthquake magnitude in a region is one of the key issues in probabilistic seismic hazard calculations and the estimation of worst-case scenarios. Earthquake catalogues are the most informative source of information for the inference of earthquake magnitudes. We analysed the earthquake catalogue for Central Asia with respect to the largest expected magnitudes m(T) in a pre-defined time horizon T-f using a recently developed statistical methodology, extended by the explicit probabilistic consideration of magnitude errors. For this aim, we assumed broad error distributions for historical events, whereas the magnitudes of recently recorded instrumental earthquakes had smaller errors. The results indicate high probabilities for the occurrence of large events (M >= 8), even in short time intervals of a few decades. The expected magnitudes relative to the assumed maximum possible magnitude are generally higher for intermediate-depth earthquakes (51-300 km) than for shallow events (0-50 km). For long future time horizons, for example, a few hundred years, earthquakes with M >= 8.5 have to be taken into account, although, apart from the 1889 Chilik earthquake, it is probable that no such event occurred during the observation period of the catalogue.
Flood loss modeling is a central component of flood risk analysis. Conventionally, this involves univariable and deterministic stage-damage functions. Recent advancements in the field promote the use of multivariable and probabilistic loss models, which consider variables beyond inundation depth and account for prediction uncertainty. Although companies contribute significantly to total loss figures, novel modeling approaches for companies are lacking. Scarce data and the heterogeneity among companies impede the development of company flood loss models. We present three multivariable flood loss models for companies from the manufacturing, commercial, financial, and service sector that intrinsically quantify prediction uncertainty. Based on object-level loss data (n = 1,306), we comparatively evaluate the predictive capacity of Bayesian networks, Bayesian regression, and random forest in relation to deterministic and probabilistic stage-damage functions, serving as benchmarks. The company loss data stem from four postevent surveys in Germany between 2002 and 2013 and include information on flood intensity, company characteristics, emergency response, private precaution, and resulting loss to building, equipment, and goods and stock. We find that the multivariable probabilistic models successfully identify and reproduce essential relationships of flood damage processes in the data. The assessment of model skill focuses on the precision of the probabilistic predictions and reveals that the candidate models outperform the stage-damage functions, while differences among the proposed models are negligible. Although the combination of multivariable and probabilistic loss estimation improves predictive accuracy over the entire data set, wide predictive distributions stress the necessity for the quantification of uncertainty.
The Coulomb failure stress (CFS) criterion is the most commonly used method for predicting spatial distributions of aftershocks following large earthquakes. However, large uncertainties are always associated with the calculation of Coulomb stress change. The uncertainties mainly arise due to nonunique slip inversions and unknown receiver faults; especially for the latter, results are highly dependent on the choice of the assumed receiver mechanism. Based on binary tests (aftershocks yes/no), recent studies suggest that alternative stress quantities, a distance-slip probabilistic model as well as deep neural network (DNN) approaches, all are superior to CFS with predefined receiver mechanism. To challenge this conclusion, which might have large implications, we use 289 slip inversions from SRCMOD database to calculate more realistic CFS values for a layered half-space and variable receiver mechanisms. We also analyze the effect of the magnitude cutoff, grid size variation, and aftershock duration to verify the use of receiver operating characteristic (ROC) analysis for the ranking of stress metrics. The observations suggest that introducing a layered half-space does not improve the stress maps and ROC curves. However, results significantly improve for larger aftershocks and shorter time periods but without changing the ranking. We also go beyond binary testing and apply alternative statistics to test the ability to estimate aftershock numbers, which confirm that simple stress metrics perform better than the classic Coulomb failure stress calculations and are also better than the distance-slip probabilistic model.
The problem of estimating the maximum possible earthquake magnitude m(max) has attracted growing attention in recent years. Due to sparse data, the role of uncertainties becomes crucial. In this work, we determine the uncertainties related to the maximum magnitude in terms of confidence intervals. Using an earthquake catalog of Iran, m(max) is estimated for different predefined levels of confidence in six seismotectonic zones. Assuming the doubly truncated Gutenberg-Richter distribution as a statistical model for earthquake magnitudes, confidence intervals for the maximum possible magnitude of earthquakes are calculated in each zone. While the lower limit of the confidence interval is the magnitude of the maximum observed event, the upper limit is calculated from the catalog and the statistical model. For this aim, we use the original catalog which no declustering methods applied on as well as a declustered version of the catalog. Based on the study by Holschneider et al. (Bull Seismol Soc Am 101(4): 1649-1659, 2011), the confidence interval for m(max) is frequently unbounded, especially if high levels of confidence are required. In this case, no information is gained from the data. Therefore, we elaborate for which settings finite confidence levels are obtained. In this work, Iran is divided into six seismotectonic zones, namely Alborz, Azerbaijan, Zagros, Makran, Kopet Dagh, Central Iran. Although calculations of the confidence interval in Central Iran and Zagros seismotectonic zones are relatively acceptable for meaningful levels of confidence, results in Kopet Dagh, Alborz, Azerbaijan and Makran are not that much promising. The results indicate that estimating mmax from an earthquake catalog for reasonable levels of confidence alone is almost impossible.
Earthquake rates are driven by tectonic stress buildup, earthquake-induced stress changes, and transient aseismic processes. Although the origin of the first two sources is known, transient aseismic processes are more difficult to detect. However, the knowledge of the associated changes of the earthquake activity is of great interest, because it might help identify natural aseismic deformation patterns such as slow-slip events, as well as the occurrence of induced seismicity related to human activities. For this goal, we develop a Bayesian approach to identify change-points in seismicity data automatically. Using the Bayes factor, we select a suitable model, estimate possible change-points, and we additionally use a likelihood ratio test to calculate the significance of the change of the intensity. The approach is extended to spatiotemporal data to detect the area in which the changes occur. The method is first applied to synthetic data showing its capability to detect real change-points. Finally, we apply this approach to observational data from Oklahoma and observe statistical significant changes of seismicity in space and time.
Paleoearthquakes and historic earthquakes are the most important source of information for the estimation of long-term earthquake recurrence intervals in fault zones, because corresponding sequences cover more than one seismic cycle. However, these events are often rare, dating uncertainties are enormous, and missing or misinterpreted events lead to additional problems. In the present study, I assume that the time to the next major earthquake depends on the rate of small and intermediate events between the large ones in terms of a clock change model. Mathematically, this leads to a Brownian passage time distribution for recurrence intervals. I take advantage of an earlier finding that under certain assumptions the aperiodicity of this distribution can be related to the Gutenberg-Richter b value, which can be estimated easily from instrumental seismicity in the region under consideration. In this way, both parameters of the Brownian passage time distribution can be attributed with accessible seismological quantities. This allows to reduce the uncertainties in the estimation of the mean recurrence interval, especially for short paleoearthquake sequences and high dating errors. Using a Bayesian framework for parameter estimation results in a statistical model for earthquake recurrence intervals that assimilates in a simple way paleoearthquake sequences and instrumental data. I present illustrative case studies from Southern California and compare the method with the commonly used approach of exponentially distributed recurrence times based on a stationary Poisson process.
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.
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.
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 Zöller 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 }
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.
River floods are among the most damaging natural hazards that frequently occur in Germany. Flooding causes high economic losses and impacts many residents. In 2016, several southern German municipalities were hit by flash floods after unexpectedly severe heavy rainfall, while in 2013 widespread river flooding had occurred. This study investigates and compares the psychological impacts of river floods and flash floods and potential consequences for precautionary behaviour. Data were collected using computer-aided telephone interviews that were conducted among flood-affected households around 9 months after each damaging event. This study applies Bayesian statistics and negative binomial regressions to test the suitability of psychological indicators to predict the precaution motivation of individuals. The results show that it is not the particular flood type but rather the severity and local impacts of the event that are crucial for the different, and potentially negative, impacts on mental health. According to the used data, however, predictions of the individual precaution motivation should not be based on the derived psychological indicators – i.e. coping appraisal, threat appraisal, burden and evasion – since their explanatory power was generally low and results are, for the most part, non-significant. Only burden reveals a significant positive relation to planned precaution regarding weak flash floods. In contrast to weak flash floods and river floods, the perceived threat of strong flash floods is significantly lower although feelings of burden and lower coping appraisals are more pronounced. Further research is needed to better include psychological assessment procedures and to focus on alternative data sources regarding floods and the connected precaution motivation of affected residents.
River floods are among the most damaging natural hazards that frequently occur in Germany. Flooding causes high economic losses and impacts many residents. In 2016, several southern German municipalities were hit by flash floods after unexpectedly severe heavy rainfall, while in 2013 widespread river flooding had occurred. This study investigates and compares the psychological impacts of river floods and flash floods and potential consequences for precautionary behaviour. Data were collected using computer-aided telephone interviews that were conducted among flood-affected households around 9 months after each damaging event. This study applies Bayesian statistics and negative binomial regressions to test the suitability of psychological indicators to predict the precaution motivation of individuals. The results show that it is not the particular flood type but rather the severity and local impacts of the event that are crucial for the different, and potentially negative, impacts on mental health. According to the used data, however, predictions of the individual precaution motivation should not be based on the derived psychological indicators – i.e. coping appraisal, threat appraisal, burden and evasion – since their explanatory power was generally low and results are, for the most part, non-significant. Only burden reveals a significant positive relation to planned precaution regarding weak flash floods. In contrast to weak flash floods and river floods, the perceived threat of strong flash floods is significantly lower although feelings of burden and lower coping appraisals are more pronounced. Further research is needed to better include psychological assessment procedures and to focus on alternative data sources regarding floods and the connected precaution motivation of affected residents.
Introduction to special issue: Dynamics of seismicity patterns and earthquake triggering - Preface
(2006)
Stress drop is a key factor in earthquake mechanics and engineering seismology. However, stress drop calculations based on fault slip can be significantly biased, particularly due to subjectively determined smoothing conditions in the traditional least-square slip inversion. In this study, we introduce a mechanically constrained Bayesian approach to simultaneously invert for fault slip and stress drop based on geodetic measurements. A Gaussian distribution for stress drop is implemented in the inversion as a prior. We have done several synthetic tests to evaluate the stability and reliability of the inversion approach, considering different fault discretization, fault geometries, utilized datasets, and variability of the slip direction, respectively. We finally apply the approach to the 2010 M8.8 Maule earthquake and invert for the coseismic slip and stress drop simultaneously. Two fault geometries from the literature are tested. Our results indicate that the derived slip models based on both fault geometries are similar, showing major slip north of the hypocenter and relatively weak slip in the south, as indicated in the slip models of other studies. The derived mean stress drop is 5-6 MPa, which is close to the stress drop of similar to 7 MPa that was independently determined according to force balance in this region Luttrell et al. (J Geophys Res, 2011). These findings indicate that stress drop values can be consistently extracted from geodetic data.
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).
In the present study, we summarize and evaluate the endeavors from recent years to estimate the maximum possible earthquake magnitude m(max) from observed data. In particular, we use basic and physically motivated assumptions to identify best cases and worst cases in terms of lowest and highest degree of uncertainty of m(max). In a general framework, we demonstrate that earthquake data and earthquake proxy data recorded in a fault zone provide almost no information about m(max) unless reliable and homogeneous data of a long time interval, including several earthquakes with magnitude close to m(max), are available. Even if detailed earthquake information from some centuries including historic and paleoearthquakes are given, only very few, namely the largest events, will contribute at all to the estimation of m(max), and this results in unacceptably high uncertainties. As a consequence, estimators of m(max) in a fault zone, which are based solely on earthquake-related information from this region, have to be dismissed.