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The use of ground-motion-prediction equations to estimate ground shaking has become a very popular approach for seismic-hazard assessment, especially in the framework of a logic-tree approach. Owing to the large number of existing published ground-motion models, however, the selection and ranking of appropriate models for a particular target area often pose serious practical problems. Here we show how observed around-motion records can help to guide this process in a systematic and comprehensible way. A key element in this context is a new, likelihood based, goodness-of-fit measure that has the property not only to quantify the model fit but also to measure in some degree how well the underlying statistical model assumptions are met. By design, this measure naturally scales between 0 and 1, with a value of 0.5 for a situation in which the model perfectly matches the sample distribution both in terms of mean and standard deviation. We have used it in combination with other goodness-of-fit measures to derive a simple classification scheme to quantify how well a candidate ground-rnotion-prediction equation models a particular set of observed-response spectra. This scheme is demonstrated to perform well in recognizing a number of popular ground-motion models from their rock-site- recording, subsets. This indicates its potential for aiding the assignment of logic-tree weights in a consistent and reproducible way. We have applied our scheme to the border region of France, Germany, and Switzerland where the M-w 4.8 St. Die earthquake of 22 February 2003 in eastern France recently provided a small set of observed-response spectra. These records are best modeled by the ground-motion-prediction equation of Berge-Thierry et al. (2003), which is based on the analysis of predominantly European data. The fact that the Swiss model of Bay et al. (2003) is not able to model the observed records in an acceptable way may indicate general problems arising from the use of weak-motion data for strong-motion prediction
Composite ground-motion models and logic trees: Methodology, sensitivities, and uncertainties
(2005)
Logic trees have become a popular tool in seismic hazard studies. Commonly, the models corresponding to the end branches of the complete logic tree in a probabalistic seismic hazard analysis (PSHA) are treated separately until the final calculation of the set of hazard curves. This comes at the price that information regarding sensitivities and uncertainties in the ground-motion sections of the logic tree are only obtainable after disaggregation. Furthermore, from this end-branch model perspective even the designers of the logic tree cannot directly tell what ground-motion scenarios most likely would result from their logic trees for a given earthquake at a particular distance, nor how uncertain these scenarios might be or how they would be affected by the choices of the hazard analyst. On the other hand, all this information is already implicitly present in the logic tree. Therefore, with the ground-motion perspective that we propose in the present article, we treat the ground-motion sections of a complete logic tree for seismic hazard as a single composite model representing the complete state-of-knowledge-and-belief of a particular analyst on ground motion in a particular target region. We implement this view by resampling the ground-motion models represented in the ground-motion sections of the logic tree by Monte Carlo simulation (separately for the median values and the sigma values) and then recombining the sets of simulated values in proportion to their logic-tree branch weights. The quantiles of this resampled composite model provide the hazard analyst and the decision maker with a simple, clear, and quantitative representation of the overall physical meaning of the ground-motion section of a logic tree and the accompanying epistemic uncertainty. Quantiles of the composite model also provide an easy way to analyze the sensitivities and uncertainties related to a given logic-tree model. We illustrate this for a composite ground- motion model for central Europe. Further potential fields of applications are seen wherever individual best estimates of ground motion have to be derived from a set of candidate models, for example, for hazard rnaps, sensitivity studies, or for modeling scenario earthquakes
The most recent intense earthquake swarm in the Vogtland lasted from 6 October 2008 until January 2009. Greatest magnitudes exceeded M3.5 several times in October making it the greatest swarm since 1985/86. In contrast to the swarms in 1985 and 2000, seismic moment release was concentrated near swarm onset. Focal area and temporal evolution are similar to the swarm in 2000. Work hypothysis: uprising upper-mantle fluids trigger swarm earthquakes at low stress level. To monitor the seismicity, the University of Potsdam operated a small aperture seismic array at 10 km epicentral distance between 18 October 2008 and 18 March 2009. Consisting of 12 seismic stations and 3 additional microphones, the array is capable of detecting earthquakes from larger to very low magnitudes (M<-1) as well as associated air waves. We use array techniques to determine properties of the incoming wavefield: noise, direct P and S waves, and converted phases.
In probabilistic seismic-hazard analysis, epistemic uncertainties are commonly treated within a logic-tree framework in which the branch weights express the degree of belief of an expert in a set of models. For the calculation of the distribution of hazard curves, these branch weights represent subjective probabilities. A major challenge for experts is to provide logically consistent weight estimates (in the sense of Kolmogorovs axioms), to be aware of the multitude of heuristics, and to minimize the biases which affect human judgment under uncertainty. We introduce a platform-independent, interactive program enabling us to quantify, elicit, and transfer expert knowledge into a set of subjective probabilities by applying experimental design theory, following the approach of Curtis and Wood (2004). Instead of determining the set of probabilities for all models in a single step, the computer-driven elicitation process is performed as a sequence of evaluations of relative weights for small subsets of models. From these, the probabilities for the whole model set are determined as a solution of an optimization problem. The result of this process is a set of logically consistent probabilities together with a measure of confidence determined from the amount of conflicting information which is provided by the expert during the relative weighting process. We experiment with different scenarios simulating likely expert behaviors in the context of knowledge elicitation and show the impact this has on the results. The overall aim is to provide a smart elicitation technique, and our findings serve as a guide for practical applications.
Aleatory variability in ground-motion prediction, represented by the standard deviation (sigma) of a ground-motion prediction equation, exerts a very strong influence on the results of probabilistic seismic-hazard analysis (PSHA). This is especially so at the low annual exceedance frequencies considered for nuclear facilities; in these cases, even small reductions in sigma can have a marked effect on the hazard estimates. Proper separation and quantification of aleatory variability and epistemic uncertainty can lead to defensible reductions in sigma. One such approach is the single-station sigma concept, which removes that part of sigma corresponding to repeatable site-specific effects. However, the site-to-site component must then be constrained by site-specific measurements or else modeled as epistemic uncertainty and incorporated into the modeling of site effects. The practical application of the single-station sigma concept, including the characterization of the dynamic properties of the site and the incorporation of site-response effects into the hazard calculations, is illustrated for a PSHA conducted at a rock site under consideration for the potential construction of a nuclear power plant.
The PEGASOS project was a major international seismic hazard study, one of the largest ever conducted anywhere in the world, to assess seismic hazard at four nuclear power plant sites in Switzerland. Before the report of this project has become publicly available, a paper attacking both methodology and results has appeared. Since the general scientific readership may have difficulty in assessing this attack in the absence of the report being attacked, we supply a response in the present paper. The bulk of the attack, besides some misconceived arguments about the role of uncertainties in seismic hazard analysis, is carried by some exercises that purport to be validation exercises. In practice, they are no such thing; they are merely independent sets of hazard calculations based on varying assumptions and procedures, often rather questionable, which come up with various different answers which have no particular significance. (C) 2005 Elsevier B.V. All rights reserved
Seismic-hazard assessment is of great importance within the field of engineering seismology. Nowadays, it is common practice to define future seismic demands using probabilistic seismic-hazard analysis (PSHA). Often it is neither obvious nor transparent how PSHA responds to changes in its inputs. In addition, PSHA relies on many uncertain inputs. Sensitivity analysis (SA) is concerned with the assessment and quantification of how changes in the model inputs affect the model response and how input uncertainties influence the distribution of the model response. Sensitivity studies are challenging primarily for computational reasons; hence, the development of efficient methods is of major importance. Powerful local (deterministic) methods widely used in other fields can make SA feasible, even for complex models with a large number of inputs; for example, automatic/algorithmic differentiation (AD)-based adjoint methods. Recently developed derivative-based global sensitivity measures can combine the advantages of such local SA methods with efficient sampling strategies facilitating quantitative global sensitivity analysis (GSA) for complex models. In our study, we propose and implement exactly this combination. It allows an upper bounding of the sensitivities involved in PSHA globally and, therefore, an identification of the noninfluential and the most important uncertain inputs. To the best of our knowledge, it is the first time that derivative-based GSA measures are combined with AD in practice. In addition, we show that first-order uncertainty propagation using the delta method can give satisfactory approximations of global sensitivity measures and allow a rough characterization of the model output distribution in the case of PSHA. An illustrative example is shown for the suggested derivative-based GSA of a PSHA that uses stochastic ground-motion simulations.
Probabilistic seismic-hazard analysis (PSHA) is the current tool of the trade used to estimate the future seismic demands at a site of interest. A modern PSHA represents a complex framework that combines different models with numerous inputs. It is important to understand and assess the impact of these inputs on the model output in a quantitative way. Sensitivity analysis is a valuable tool for quantifying changes of a model output as inputs are perturbed, identifying critical input parameters, and obtaining insight about the model behavior. Differential sensitivity analysis relies on calculating first-order partial derivatives of the model output with respect to its inputs; however, obtaining the derivatives of complex models can be challenging.
In this study, we show how differential sensitivity analysis of a complex framework such as PSHA can be carried out using algorithmic/automatic differentiation (AD). AD has already been successfully applied for sensitivity analyses in various domains such as oceanography and aerodynamics. First, we demonstrate the feasibility of the AD methodology by comparing AD-derived sensitivities with analytically derived sensitivities for a basic case of PSHA using a simple ground-motion prediction equation. Second, we derive sensitivities via AD for a more complex PSHA study using a stochastic simulation approach for the prediction of ground motions. The presented approach is general enough to accommodate more advanced PSHA studies of greater complexity.
Response spectra are of fundamental importance in earthquake engineering and represent a standard measure in seismic design for the assessment of structural performance. However, unlike Fourier spectral amplitudes, the relationship of response spectral amplitudes to seismological source, path, and site characteristics is not immediately obvious and might even be considered counterintuitive for high oscillator frequencies. The understanding of this relationship is nevertheless important for seismic-hazard analysis. The purpose of the present study is to comprehensively characterize the variation of response spectral amplitudes due to perturbations of the causative seismological parameters. This is done by calculating the absolute parameter sensitivities (sensitivity coefficients) defined as the partial derivatives of the model output with respect to its input parameters. To derive sensitivities, we apply algorithmic differentiation (AD). This powerful approach is extensively used for sensitivity analysis of complex models in meteorology or aerodynamics. To the best of our knowledge, AD has not been explored yet in the seismic-hazard context. Within the present study, AD was successfully implemented for a proven and extensively applied simulation program for response spectra (Stochastic Method SIMulation [SMSIM]) using the TAPENADE AD tool. We assess the effects and importance of input parameter perturbations on the shape of response spectra for different regional stochastic models in a quantitative way. Additionally, we perform sensitivity analysis regarding adjustment issues of groundmotion prediction equations.
The ellipticity of Rayleigh surface waves, which is an important parameter characterizing the propagation medium, is studied for several models with increasing complexity. While the main focus lies on theory, practical implications of the use of the horizontal to vertical component ratio (H/V-ratio) to Study the subsurface structure are considered as well. Love's approximation of the ellipticity for an incompressible layer over an incompressible half-space is critically discussed especially concerning its applicability for different impedance contrasts. The main result is an analytically exact formula of H/V for a 2-layer model of compressible media, which is a generalization of Love's formula. It turns out that for a limited range of models Love's approximation can be used also in the general case. (C) 2003 Elsevier B.V. All rights reserved
Empirical ground-motion models used in seismic hazard analysis are commonly derived by regression of observed ground motions against a chosen set of predictor variables. Commonly, the model building process is based on residual analysis and/or expert knowledge and/or opinion, while the quality of the model is assessed by the goodness-of-fit to the data. Such an approach, however, bears no immediate relation to the predictive power of the model and with increasing complexity of the models is increasingly susceptible to the danger of overfitting. Here, a different, primarily data-driven method for the development of ground-motion models is proposed that makes use of the notion of generalization error to counteract the problem of overfitting. Generalization error directly estimates the average prediction error on data not used for the model generation and, thus, is a good criterion to assess the predictive capabilities of a model. The approach taken here makes only few a priori assumptions. At first, peak ground acceleration and response spectrum values are modeled by flexible, nonphysical functions (polynomials) of the predictor variables. The inclusion of a particular predictor and the order of the polynomials are based on minimizing generalization error. The approach is illustrated for the next generation of ground-motion attenuation dataset. The resulting model is rather complex, comprising 48 parameters, but has considerably lower generalization error than functional forms commonly used in ground-motion models. The model parameters have no physical meaning, but a visual interpretation is possible and can reveal relevant characteristics of the data, for example, the Moho bounce in the distance scaling. In a second step, the regression model is approximated by an equivalent stochastic model, making it physically interpretable. The resulting resolvable stochastic model parameters are comparable to published models for western North America. In general, for large datasets generalization error minimization provides a viable method for the development of empirical ground-motion models.
Bayesian networks are a powerful and increasingly popular tool for reasoning under uncertainty, offering intuitive insight into (probabilistic) data-generating processes. They have been successfully applied to many different fields, including bioinformatics. In this paper, Bayesian networks are used to model the joint-probability distribution of selected earthquake, site, and ground-motion parameters. This provides a probabilistic representation of the independencies and dependencies between these variables. In particular, contrary to classical regression, Bayesian networks do not distinguish between target and predictors, treating each variable as random variable. The capability of Bayesian networks to model the ground-motion domain in probabilistic seismic hazard analysis is shown for a generic situation. A Bayesian network is learned based on a subset of the Next Generation Attenuation (NGA) dataset, using 3342 records from 154 earthquakes. Because no prior assumptions about dependencies between particular parameters are made, the learned network displays the most probable model given the data. The learned network shows that the ground-motion parameter (horizontal peak ground acceleration, PGA) is directly connected only to the moment magnitude, Joyner-Boore distance, fault mechanism, source-to-site azimuth, and depth to a shear-wave horizon of 2: 5 km/s (Z2.5). In particular, the effect of V-S30 is mediated by Z2.5. Comparisons of the PGA distributions based on the Bayesian networks with the NGA model of Boore and Atkinson (2008) show a reasonable agreement in ranges of good data coverage.
A Bayesian ground-motion model is presented that directly estimates the coefficients of the model and the correlation between different ground-motion parameters of interest. The model is developed as a multi-level model with levels for earthquake, station and record terms. This separation allows to estimate residuals for each level and thus the estimation of the associated aleatory variability. In particular, the usually estimated within-event variability is split into a between-station and between-record variability. In addition, the covariance structure between different ground-motion parameters of interest is estimated for each level, i.e. directly the between-event, between-station and between-record correlation coefficients are available. All parameters of the model are estimated via Bayesian inference, which allows to assess their epistemic uncertainty in a principled way. The model is developed using a recently compiled European strong-motion database. The target variables are peak ground velocity, peak ground acceleration and spectral acceleration at eight oscillator periods. The model performs well with respect to its residuals, and is similar to other ground-motion models using the same underlying database. The correlation coefficients are similar to those estimated for other parts of the world, with nearby periods having a high correlation. The between-station, between-event and between-record correlations follow generally a similar trend.
The combined passive and active seismic TRANSALP experiment produced an unprecedented high-resolution crustal image of the Eastern Alps between Munich and Venice. The European and Adriatic Mohos (EM and AM, respectively) are clearly imaged with different seismic techniques: near-vertical incidence reflections and receiver functions (RFs). The European Moho dips gently southward from 35 km beneath the northern foreland to a maximum depth of 55 km beneath the central part of the Eastern Alps, whereas the Adriatic Moho is imaged primarily by receiver functions at a relatively constant depth of about 40 km. In both data sets, we have also detected first-order Alpine shear zones, such as the Helvetic detachment, Inntal fault and SubTauern ramp in the north. Apart from the Valsugana thrust, receiver functions in the southern part of the Eastern Alps have also observed a north dipping interface, which may penetrate the entire Adriatic crust [Adriatic Crust Interface (ACI)]. Deep crustal seismicity may be related to the ACI. We interpret the ACI as the currently active retroshear zone in the doubly vergent Alpine collisional belt. (C) 2004 Elsevier B.V. All rights reserved
In the estimate of dispersion with the help of wavelet analysis considerable emphasis has been put on the extraction of the group velocity using the modulus of the wavelet transform. In this paper we give an asymptotic expression of the full propagator in wavelet space that comprises the phase velocity as well. This operator establishes a relationship between the observed signals at two different stations during wave propagation in a dispersive and attenuating medium. Numerical and experimental examples are presented to show that the method accurately models seismic wave dispersion and attenuation
A partially non-ergodic ground-motion prediction equation is estimated for Europe and the Middle East. Therefore, a hierarchical model is presented that accounts for regional differences. For this purpose, the scaling of ground-motion intensity measures is assumed to be similar, but not identical in different regions. This is achieved by assuming a hierarchical model, where some coefficients are treated as random variables which are sampled from an underlying global distribution. The coefficients are estimated by Bayesian inference. This allows one to estimate the epistemic uncertainty in the coefficients, and consequently in model predictions, in a rigorous way. The model is estimated based on peak ground acceleration data from nine different European/Middle Eastern regions. There are large differences in the amount of earthquakes and records in the different regions. However, due to the hierarchical nature of the model, regions with only few data points borrow strength from other regions with more data. This makes it possible to estimate a separate set of coefficients for all regions. Different regionalized models are compared, for which different coefficients are assumed to be regionally dependent. Results show that regionalizing the coefficients for magnitude and distance scaling leads to better performance of the models. The models for all regions are physically sound, even if only very few earthquakes comprise one region.
The Ceres earthquake of 29 September 1969 is the largest known earthquake in southern Africa. Digitized analog recordings from Worldwide Standardized Seismographic Network stations (Powell and Fries, 1964) are used to retrieve the point source moment tensor and the most likely centroid depth of the event using full waveform modeling. A scalar seismic moment of 2.2-2.4 x 10(18) N center dot m corresponding to a moment magnitude of 6.2-6.3 is found. The analysis confirms the pure strike-slip mechanism previously determined from onset polarities by Green and Bloch (1971). Overall good agreement with the fault orientation previously estimated from local aftershock recordings is found. The centroid depth can be constrained to be less than 15 km. In a second analysis step, we use a higher order moment tensor based inversion scheme for simple extended rupture models to constrain the lateral fault dimensions. We find rupture propagated unilaterally for 4.7 s from east-southwest to west-northwest for about 17 km ( average rupture velocity of about 3: 1 km/s).
This study presents results of ambient noise measurements from temporary single station and small-scale array deployments in the northeast of Basle. H/V spectral ratios were determined along various profiles crossing the eastern masterfault of the Rhine Rift Valley and the adjacent sedimentary rift fills. The fundamental H/V peak frequencies are decreasing along the profile towards the eastern direction being consistent with the dip of the tertiary sediments within the rift. Using existing empirical relationships between H/V frequency peaks and the depth of the dominant seismic contrast, derived on basis of the lambda/4-resonance hypothesis and a power law depth dependence of the S-wave velocity, we obtain thicknesses of the rift fill from about 155 m in the west to 280 in in the east. This is in agreement with previous studies. The array analysis of the ambient noise wavefield yielded a stable dispersion relation consistent with Rayleigh wave propagation velocities. We conclude that a significant amount of surface waves is contained in the observed wavefield. The computed ellipticity for fundamental mode Rayleigh waves for the velocity depth models used for the estimation of the sediment thicknesses is in agreement with the observed H/V spectra over a large frequency band
This study presents an unsupervised feature selection and learning approach for the discovery and intuitive imaging of significant temporal patterns in seismic single-station or network recordings. For this purpose, the data are parametrized by real-valued feature vectors for short time windows using standard analysis tools for seismic data, such as frequency-wavenumber, polarization, and spectral analysis. We use Self-Organizing Maps (SOMs) for a data-driven feature selection, visualization and clustering procedure, which is in particular suitable for high-dimensional data sets. Our feature selection method is based on significance testing using the Wald-Wolfowitz runs test for-individual features and on correlation hunting with SOMs in feature subsets. Using synthetics composed of Rayleigh and Love waves and real-world data, we show the robustness and the improved discriminative power of that approach compared to feature subsets manually selected from individual wavefield parametrization methods. Furthermore, the capability of the clustering and visualization techniques to investigate the discrimination of wave phases is shown by means of synthetic waveforms and regional earthquake recordings.
In probabilistic seismic hazard analysis, different ground-motion prediction equations (GMPEs) are commonly combined within a logic tree framework. The selection of appropriate GMPEs, however, is a non-trivial task, especially for regions where strong motion data are sparse and where no indigenous GMPE exists because the set of models needs to capture the whole range of ground-motion uncertainty. In this study we investigate the aggregation of GMPEs into a mixture model with the aim to infer a backbone model that is able to represent the center of the ground-motion distribution in a logic tree analysis. This central model can be scaled up and down to obtain the full range of ground-motion uncertainty. The combination of models into a mixture is inferred from observed ground-motion data. We tested the new approach for Northern Chile, a region for which no indigenous GMPE exists. Mixture models were calculated for interface and intraslab type events individually. For each source type we aggregated eight subduction zone GMPEs using mainly new strong-motion data that were recorded within the Plate Boundary Observatory Chile project and that were processed within this study. We can show that the mixture performs better than any of its component GMPEs, and that it performs comparable to a regression model that was derived for the same dataset. The mixture model seems to represent the median ground motions in that region fairly well. It is thus able to serve as a backbone model for the logic tree.
Slow fourier transform
(2013)
In recent years, H/V measurements have been increasingly used to map the thickness of sediment fill in sedimentary basins in the context of seismic hazard assessment. This parameter is believed to be an important proxy for the site effects in sedimentary basins (e.g. in the Los Angeles basin). Here we present the results of a test using this approach across an active normal fault in a structurally well known situation. Measurements on a 50 km long profile with 1 km station spacing clearly show a change in the frequency of the fundamental peak of H/V ratios with increasing thickness of the sediment layer in the eastern part of the Lower Rhine Embayment. Subsequently, a section of 10 km length across the Erft-Sprung system, a normal fault with ca. 750 m vertical offset, was measured with a station distance of 100 m. Frequencies of the first and second peaks and the first trough in the H/V spectra are used in a simple resonance model to estimate depths of the bedrock. While the frequency of the first peak shows a large scatter for sediment depths larger than ca. 500 m, the frequency of the first trough follows the changing thickness of the sediments across the fault. The lateral resolution is in the range of the station distance of 100 m. A power law for the depth dependence of the S-wave velocity derived from down hole measurements in an earlier study [Budny, 1984] and power laws inverted from dispersion analysis of micro array measurements [Scherbaum et al., 2002] agree with the results from the H/V ratios of this study
The most recent intense earthquake swarm in West Bohemia lasted from 6 October 2008 to January 2009. Starting 12 days after the onset, the University of Potsdam monitored the swarm by a temporary small-aperture seismic array at 10 km epicentral distance. The purpose of the installation was a complete monitoring of the swarm including micro-earthquakes (M (L) < 0). We identify earthquakes using a conventional short-term average/long-term average trigger combined with sliding-window frequency-wavenumber and polarisation analyses. The resulting earthquake catalogue consists of 14,530 earthquakes between 19 October 2008 and 18 March 2009 with magnitudes in the range of -aEuro parts per thousand 1.2 a parts per thousand currency signaEuro parts per thousand M (L) a parts per thousand currency signaEuro parts per thousand 2.7. The small-aperture seismic array substantially lowers the detection threshold to about M (c) = -aEuro parts per thousand 0.4, when compared to the regional networks operating in West Bohemia (M (c) > 0.0). In the course of this work, the main temporal features (frequency-magnitude distribution, propagation of back azimuth and horizontal slowness, occurrence rate of aftershock sequences and interevent-time distribution) of the recent 2008/2009 earthquake swarm are presented and discussed. Temporal changes of the coefficient of variation (based on interevent times) suggest that the swarm earthquake activity of the 2008/2009 swarm terminates by 12 January 2009. During the main phase in our studied swarm period after 19 October, the b value of the Gutenberg-Richter relation decreases from 1.2 to 0.8. This trend is also reflected in the power-law behavior of the seismic moment release. The corresponding total seismic moment release of 1.02x10(17) Nm is equivalent to M (L,max) = 5.4.
Magnitude estimation for microseismicity induced during the KTB 2004/2005 injection experiment
(2011)
We determined the magnitudes of 2540 microseismic events measured at one single 3C borehole geophone at the German Deep Drilling Site (known by the German acronym, KTB) during the injection phase 2004/2005. For this task we developed a three-step approach. First, we estimated local magnitudes of 104 larger events with a standard method based on amplitude measurements at near-surface stations. Second, we investigated a series of parameters to characterize the size of these events using the seismograms of the borehole sensor, and we compared them statistically with the local magnitudes. Third, we extrapolated the regression curve to obtain the magnitudes of 2436 events that were only measured at the borehole geophone. This method improved the magnitude of completeness for the KTB data set by more than one order down to M = -2.75. The resulting b-value for all events was 0.78, which is similar to the b-value obtained from taking only the greater events with standard local magnitude estimation from near-surface stations, b = 0.86. The more complete magnitude catalog was required to study the magnitude distribution with time and to characterize the seismotectonic state of the KTB injection site. The event distribution with time was consistent with prediction from theory assuming pore pressure diffusion as the underlying mechanism to trigger the events. The value we obtained for the seismogenic index of -4 suggested that the seismic hazard potential at the KTB site is comparatively low.
Interdisziplinäres Zentrum für Musterdynamik und Angewandte Fernerkundung Workshop vom 9. - 10. Februar 2006
The statistics of time delays between successive earthquakes has recently been claimed to be universal and to show the existence of clustering beyond the duration of aftershock bursts. We demonstrate that these claims are unjustified. Stochastic simulations with Poissonian background activity and triggered Omori-type aftershock sequences are shown to reproduce the interevent-time distributions observed on different spatial and magnitude scales in California. Thus the empirical distribution can be explained without any additional long-term clustering. Furthermore, we find that the shape of the interevent-time distribution, which can be approximated by the gamma distribution, is determined by the percentage of main-shocks in the catalog. This percentage can be calculated by the mean and variance of the interevent times and varies between 5% and 90% for different regions in California. Our investigation of stochastic simulations indicates that the interevent-time distribution provides a nonparametric reconstruction of the mainshock magnitude-frequency distribution that is superior to standard declustering algorithm
Inferring a ground-motion prediction equation (GMPE) for a region in which only a small number of seismic events has been observed is a challenging task. A response to this data scarcity is to utilise data from other regions in the hope that there exist common patterns in the generation of ground motion that can contribute to the development of a GMPE for the region in question. This is not an unreasonable course of action since we expect regional GMPEs to be related to each other. In this work we model this relatedness by assuming that the regional GMPEs occupy a common low-dimensional manifold in the space of all possible GMPEs. As a consequence, the GMPEs are fitted in a joint manner and not independent of each other, borrowing predictive strength from each other's regional datasets. Experimentation on a real dataset shows that the manifold assumption displays better predictive performance over fitting regional GMPEs independent of each other. (C) 2014 Elsevier Ltd. All rights reserved.
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.
The deterministic calculation of earthquake scenarios using complete waveform modelling plays an increasingly important role in estimating shaking hazard in seismically active regions. Here we apply 3-D numerical modelling of seismic wave propagation to M 6+ earthquake scenarios in the area of the Lower Rhine Embayment, one of the seismically most active regions in central Europe. Using a 3-D basin model derived from geology, borehole information and seismic experiments, we aim at demonstrating the strong dependence of ground shaking on hypocentre location and basin structure. The simulations are carried out up to frequencies of ca. 1 Hz. As expected, the basin structure leads to strong lateral variations in peak ground motion, amplification and shaking duration. Depending on source-basin-receiver geometry, the effects correlate with basin depth and the slope of the basin flanks; yet, the basin also affects peak ground motion and estimated shaking hazard thereof outside the basin. Comparison with measured seismograms for one of the earthquakes shows that some of the main characteristics of the wave motion are reproduced. Cumulating the derived seismic intensities from the three modelled earthquake scenarios leads to a predominantly basin correlated intensity distribution for our study area
In this article, we address the question of how observed ground-motion data can most effectively be modeled for engineering seismological purposes. Toward this goal, we use a data-driven method, based on a deep-learning autoencoder with a variable number of nodes in the bottleneck layer, to determine how many parameters are needed to reconstruct synthetic and observed ground-motion data in terms of their median values and scatter. The reconstruction error as a function of the number of nodes in the bottleneck is used as an indicator of the underlying dimensionality of ground-motion data, that is, the minimum number of predictor variables needed in a ground-motion model. Two synthetic and one observed datasets are studied to prove the performance of the proposed method. We find that mapping ground-motion data to a 2D manifold primarily captures magnitude and distance information and is suited for an approximate data reconstruction. The data reconstruction improves with an increasing number of bottleneck nodes of up to three and four, but it saturates if more nodes are added to the bottleneck.
In this paper, two sets of earthquake ground-motion relations to estimate peak ground and response spectral acceleration are developed for sites in southern Spain and in southern Norway using a recently published composite approach. For this purpose seven empirical ground-motion relations developed from recorded strong-motion data from different parts of the world were employed. The different relations were first adjusted based on a number of transformations to convert the differing choices of independent parameters to a single one. After these transformations, which include the scatter introduced, were performed, the equations were modified to account for differences between the host and the target regions using the stochastic method to compute the host-to-target conversion factors. Finally functions were fitted to the derived ground-motion estimates to obtain sets of seven individual equations for use in probabilistic seismic hazard assessment for southern Spain and southern Norway. The relations are compared with local ones published for the two regions. The composite methodology calls for the setting up of independent logic trees for the median values and for the sigma values, in order to properly separate epistemic and aleatory uncertainties after the corrections and the conversions
This article presents comparisons among the five ground-motion models described in other articles within this special issue, in terms of data selection criteria, characteristics of the models and predicted peak ground and response spectral accelerations. Comparisons are also made with predictions from the Next Generation Attenuation (NGA) models to which the models presented here have similarities (e.g. a common master database has been used) but also differences (e.g. some models in this issue are nonparametric). As a result of the differing data selection criteria and derivation techniques the predicted median ground motions show considerable differences (up to a factor of two for certain scenarios), particularly for magnitudes and distances close to or beyond the range of the available observations. The predicted influence of style-of-faulting shows much variation among models whereas site amplification factors are more similar, with peak amplification at around 1s. These differences are greater than those among predictions from the NGA models. The models for aleatory variability (sigma), however, are similar and suggest that ground-motion variability from this region is slightly higher than that predicted by the NGA models, based primarily on data from California and Taiwan.
Characterization of polarization attributes of seismic waves using continuous wavelet transforms
(2006)
Complex-trace analysis is the method of choice for analyzing polarized data. Because particle motion can be represented by instantaneous attributes that show distinct features for waves of different polarization characteristics, it can be used to separate and characterize these waves. Traditional methods of complex-trace analysis only give the instantaneous attributes as a function of time or frequency. However. for transient wave types or seismic events that overlap in time, an estimate of the polarization parameters requires analysis of the time-frequency dependence of these attributes. We propose a method to map instantaneous polarization attributes of seismic signals in the wavelet domain and explicitly relate these attributes with the wavelet-transform coefficients of the analyzed signal. We compare our method with traditional complex-trace analysis using numerical examples. An advantage of our method is its possibility of performing the complete wave-mode separation/ filtering process in the wavelet domain and its ability to provide the frequency dependence of ellipticity, which contains important information on the subsurface structure. Furthermore, using 2-C synthetic and real seismic shot gathers, we show how to use the method to separate different wave types and identify zones of interfering wave modes
We introduce a method for computing instantaneous-polarization attributes from multicomponent signals. This is an improvement on the standard covariance method (SCM) because it does not depend on the window size used to compute the standard covariance matrix. We overcome the window-size problem by deriving an approximate analytical formula for the cross-energy matrix in which we automatically and adaptively determine the time window. The proposed method uses polarization analysis as applied to multicomponent seismic by waveform separation and filtering.
Large research initiatives such as the Global Earthquake Model (GEM) or the Seismic HAzard haRmonization in Europe (SHARE) projects concentrate a great collaborative effort on defining a global standard for seismic hazard estimations. In this context, there is an increasing need for identifying ground-motion prediction equations (GMPEs) that can be applied at both global and regional scale. With increasing amounts of strong-motion records that are now available worldwide, observational data can provide a valuable resource to tackle this question. Using the global dataset of Allen and Wald (2009), we evaluate the ability of 11 GMPEs to predict ground-motion in different active shallow crustal regions worldwide. Adopting the approach of Scherbaum et al. (2009), we rank these GMPEs according to their likelihood of having generated the data. In particular, we estimate how strongly data support or reject the models with respect to the state of noninformativeness defined by a uniform weighting. Such rankings derived from this particular global dataset enable us to explore the potential of GMPEs to predict ground motions in their host region and also in other regions depending on the magnitude and distance considered. In the ranking process, we particularly focus on the influence of the distribution of the testing dataset compared with the GMPE's native dataset. One of the results of this study is that some nonindigenous models present a high degree of consistency with the data from a target region. Two models in particular demonstrated a strong power of geographically wide applicability in different geographic regions with respect to the testing dataset: the models of Akkar and Bommer (2010) and Chiou et al. (2010).
Considering the increasing number and complexity of ground-motion prediction equations available for seismic hazard assessment, there is a definite need for an efficient, quantitative, and robust method to select and rank these models for a particular region of interest. In a recent article, Scherbaum et al. (2009) have suggested an information- theoretic approach for this purpose that overcomes several shortcomings of earlier attempts at using data-driven ground- motion prediction equation selection procedures. The results of their theoretical study provides evidence that in addition to observed response spectra, macroseismic intensity data might be useful for model selection and ranking. We present here an applicability study for this approach using response spectra and macroseismic intensities from eight Californian earthquakes. A total of 17 ground-motion prediction equations, from different regions, for response spectra, combined with the equation of Atkinson and Kaka (2007) for macroseismic intensities are tested for their relative performance. The resulting data-driven rankings show that the models that best estimate ground motion in California are, as one would expect, Californian and western U. S. models, while some European models also perform fairly well. Moreover, the model performance appears to be strongly dependent on both distance and frequency. The relative information of intensity versus response spectral data is also explored. The strong correlation we obtain between intensity-based rankings and spectral-based ones demonstrates the great potential of macroseismic intensities data for model selection in the context of seismic hazard assessment.
The Seismic Hazard Harmonization in Europe (SHARE) project, which began in June 2009, aims at establishing new standards for probabilistic seismic hazard assessment in the Euro-Mediterranean region. In this context, a logic tree for ground-motion prediction in Europe has been constructed. Ground-motion prediction equations (GMPEs) and weights have been determined so that the logic tree captures epistemic uncertainty in ground-motion prediction for six different tectonic regimes in Europe. Here we present the strategy that we adopted to build such a logic tree. This strategy has the particularity of combining two complementary and independent approaches: expert judgment and data testing. A set of six experts was asked to weight pre-selected GMPEs while the ability of these GMPEs to predict available data was evaluated with the method of Scherbaum et al. (Bull Seismol Soc Am 99:3234-3247, 2009). Results of both approaches were taken into account to commonly select the smallest set of GMPEs to capture the uncertainty in ground-motion prediction in Europe. For stable continental regions, two models, both from eastern North America, have been selected for shields, and three GMPEs from active shallow crustal regions have been added for continental crust. For subduction zones, four models, all non-European, have been chosen. Finally, for active shallow crustal regions, we selected four models, each of them from a different host region but only two of them were kept for long periods. In most cases, a common agreement has been also reached for the weights. In case of divergence, a sensitivity analysis of the weights on the seismic hazard has been conducted, showing that once the GMPEs have been selected, the associated set of weights has a smaller influence on the hazard.
Shallowly situated evaporites in built-up areas are of relevance for urban and cultural development and hydrological regulation. The hazard of sinkholes, subrosion depressions and gypsum karst is often difficult to evaluate and may quickly change with anthropogenic influence. The geophysical exploration of evaporites in metropolitan areas is often not feasible with active industrial techniques. We collect and combine different passive geophysical data as microgravity, ambient vibrations, deformation and hydrological information to study the roof morphology of shallow evaporites beneath Hamburg, Northern Germany. The application of a novel gravity inversion technique leads to a 3-D depth model of the salt diapir under study. We compare the gravity-based depth model to pseudo-depths from H/V measurements and depth estimates from small-scale seismological array data. While the general range and trend of the diapir roof is consistent, a few anomalous regions are identified where H/V pseudo-depths indicate shallower structures not observed in gravity or array data. These are interpreted by shallow residual caprock floaters and zones of increased porosity. The shallow salt structure clearly correlates with a relative subsidence in the order of 2 mm yr(-1). The combined interpretation of roof morphology, yearly subsidence rates, chemical analyses of groundwater and of hydraulic head in aquifers indicates that the salt diapir beneath Hamburg is subject to significant ongoing dissolution that may possibly affect subrosion depressions, sinkhole distribution and land usage. The combined analysis of passive geophysical data may be exemplary for the study of shallow evaporites beneath other urban areas.