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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
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.
A SSHAC Level 3 Probabilistic Seismic Hazard Analysis for a New-Build Nuclear Site in South Africa
(2015)
A probabilistic seismic hazard analysis has been conducted for a potential nuclear power plant site on the coast of South Africa, a country of low-to-moderate seismicity. The hazard study was conducted as a SSHAC Level 3 process, the first application of this approach outside North America. Extensive geological investigations identified five fault sources with a non-zero probability of being seismogenic. Five area sources were defined for distributed seismicity, the least active being the host zone for which the low recurrence rates for earthquakes were substantiated through investigations of historical seismicity. Empirical ground-motion prediction equations were adjusted to a horizon within the bedrock at the site using kappa values inferred from weak-motion analyses. These adjusted models were then scaled to create new equations capturing the range of epistemic uncertainty in this region with no strong motion recordings. Surface motions were obtained by convolving the bedrock motions with site amplification functions calculated using measured shear-wave velocity profiles.
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.
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
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 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
Enhancing the resolution and accuracy of surface ground-penetrating radar (GPR) reflection data by inverse filtering to recover a zero-phased band-limited reflectivity image requires a deconvolution technique that takes the mixed-phase character of the embedded wavelet into account. In contrast, standard stochastic deconvolution techniques assume that the wavelet is minimum phase and, hence, often meet with limited success when applied to GPR data. We present a new general-purpose blind deconvolution algorithm for mixed-phase wavelet estimation and deconvolution that (1) uses the parametrization of a mixed-phase wavelet as the convolution of the wavelet's minimum-phase equivalent with a dispersive all-pass filter, (2) includes prior information about the wavelet to be estimated in a Bayesian framework, and (3) relies on the assumption of a sparse reflectivity. Solving the normal equations using the data autocorrelation function provides an inverse filter that optimally removes the minimum-phase equivalent of the wavelet from the data, which leaves traces with a balanced amplitude spectrum but distorted phase. To compensate for the remaining phase errors, we invert in the frequency domain for an all-pass filter thereby taking advantage of the fact that the action of the all-pass filter is exclusively contained in its phase spectrum. A key element of our algorithm and a novelty in blind deconvolution is the inclusion of prior information that allows resolving ambiguities in polarity and timing that cannot be resolved using the sparseness measure alone. We employ a global inversion approach for non-linear optimization to find the all-pass filter phase values for each signal frequency. We tested the robustness and reliability of our algorithm on synthetic data with different wavelets, 1-D reflectivity models of different complexity, varying levels of added noise, and different types of prior information. When applied to realistic synthetic 2-D data and 2-D field data, we obtain images with increased temporal resolution compared to the results of standard processing.
Modern natural hazards research requires dealing with several uncertainties that arise from limited process knowledge, measurement errors, censored and incomplete observations, and the intrinsic randomness of the governing processes. Nevertheless, deterministic analyses are still widely used in quantitative hazard assessments despite the pitfall of misestimating the hazard and any ensuing risks.
In this paper we show that Bayesian networks offer a flexible framework for capturing and expressing a broad range of uncertainties encountered in natural hazard assessments. Although Bayesian networks are well studied in theory, their application to real-world data is far from straightforward, and requires specific tailoring and adaptation of existing algorithms. We offer suggestions as how to tackle frequently arising problems in this context and mainly concentrate on the handling of continuous variables, incomplete data sets, and the interaction of both. By way of three case studies from earthquake, flood, and landslide research, we demonstrate the method of data-driven Bayesian network learning, and showcase the flexibility, applicability, and benefits of this approach.
Our results offer fresh and partly counterintuitive insights into well-studied multivariate problems of earthquake-induced ground motion prediction, accurate flood damage quantification, and spatially explicit landslide prediction at the regional scale. In particular, we highlight how Bayesian networks help to express information flow and independence assumptions between candidate predictors. Such knowledge is pivotal in providing scientists and decision makers with well-informed strategies for selecting adequate predictor variables for quantitative natural hazard assessments.
In this paper, we propose a method of surface waves characterization based on the deformation of the wavelet transform of the analysed signal. An estimate of the phase velocity (the group velocity) and the attenuation coefficient is carried out using a model-based approach to determine the propagation operator in the wavelet domain, which depends nonlinearly on a set of unknown parameters. These parameters explicitly define the phase velocity, the group velocity and the attenuation. Under the assumption that the difference between waveforms observed at a couple of stations is solely due to the dispersion characteristics and the intrinsic attenuation of the medium, we then seek to find the set of unknown parameters of this model. Finding the model parameters turns out to be that of an optimization problem, which is solved through the minimization of an appropriately defined cost function. We show that, unlike time-frequency methods that exploit only the square modulus of the transform, we can achieve a complete characterization of surface waves in a dispersive and attenuating medium. Using both synthetic examples and experimental data, we also show that it is in principle possible to separate different modes in both the time domain and the frequency domain
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
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.
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.
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
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.
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.