Institut für Geowissenschaften
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The first step in the estimation of probabilistic seismic hazard in a region commonly consists of the definition and characterization of the relevant seismic sources. Because in low-seismicity regions seismicity is often rather diffuse and faults are difficult to identify, large areal source zones are mostly used. The corresponding hypothesis is that seismicity is uniformly distributed inside each areal seismic source zone. In this study, the impact of this hypothesis on the probabilistic hazard estimation is quantified through the generation of synthetic spatial seismicity distributions. Fractal seismicity distributions are generated inside a given source zone and probabilistic hazard is computed for a set of sites located inside this zone. In our study, the impact of the spatial seismicity distribution is defined as the deviation from the hazard value obtained for a spatially uniform seismicity distribution. From the generation of a large number of synthetic distributions, the correlation between the fractal dimension D and the impact is derived. The results show that the assumption of spatially uniform seismicity tends to bias the hazard to higher values. The correlation can be used to determine the systematic biases and uncertainties for hazard estimations in real cases, where the fractal dimension has been determined. We apply the technique in Germany (Cologne area) and in France (Alps).
First comparison of array-derived rotational ground motions with direct ring laser measurements
(2006)
Recently, ring laser technology has provided the first consistent observations of rotational ground motions around a vertical axis induced by earthquakes. "Consistent," in this context, implies that the observed waveforms and amplitudes are compatible with collocated recordings of translational ground motions. In particular, transverse accelerations should be in phase with rotation rate and their ratio proportional to local horizontal phase velocity assuming plane-wave propagation. The ring laser installed at the Fundamental station Wettzell in the Bavarian Forest, Southeast Germany, is recording the rotation rate around a vertical axis, theoretically a linear combination of the space derivatives of the horizontal components of motion. This suggests that, in principle, rotation can be derived from seismic-array experiments by "finite differencing." This has been attempted previously in several studies; however, the accuracy of these observations could never be tested in the absence of direct measurements. We installed a double cross-shaped array of nine stations from December 2003 to March 2004 around the ring laser instrument and observed several large earthquakes on both the ring laser and the seismic array. Here we present for the first time a comparison of array-derived rotations with direct measurements of rotations for ground motions induced by the M 6.3 Al Hoceima, Morocco, earthquake of 24 February 2004. With complete 3D synthetic seismograms calculated for this event we show that even low levels of noise may considerably influence the accuracy of the array-derived rotations when the minimum number of required stations (three) is used. Nevertheless, when using all nine stations, the overall fit between direct and array-derived measurements is surprisingly good (maximum correlation coefficient of 0.94).
The functional form of empirical response spectral ground-motion prediction equations (GMPEs) is often derived using concepts borrowed from Fourier spectral modeling of ground motion. As these GMPEs are subsequently calibrated with empirical observations, this may not appear to pose any major problems in the prediction of ground motion for a particular earthquake scenario. However, the assumption that Fourier spectral concepts persist for response spectra can lead to undesirable consequences when it comes to the adjustment of response spectral GMPEs to represent conditions not covered in the original empirical data set. In this context, a couple of important questions arise, for example, what are the distinctions and/or similarities between Fourier and response spectra of ground motions? And, if they are different, then what is the mechanism responsible for such differences and how do adjustments that are made to Fourier amplitude spectrum (FAS) manifest in response spectra? The present article explores the relationship between the Fourier and response spectrum of ground motion by using random vibration theory (RVT). With a simple Brune (1970, 1971) source model, RVT-generated acceleration spectra for a fixed magnitude and distance scenario are used. The RVT analyses reveal that the scaling of low oscillator-frequency response spectral ordinates can be treated as being equivalent to the scaling of the corresponding Fourier spectral ordinates. However, the high oscillator-frequency response spectral ordinates are controlled by a rather wide band of Fourier spectral ordinates. In fact, the peak ground acceleration, counter to the popular perception that it is a reflection of the high-frequency characteristics of ground motion, is controlled by the entire Fourier spectrum of ground motion. Additionally, this article demonstrates how an adjustment made to FAS is similar or different to the same adjustment made to response spectral ordinates. For this purpose, two cases: adjustments to the stress parameter (Delta sigma) (source term), and adjustments to the attributes reflecting site response (V-S - kappa(0)) are considered.
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.
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.
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.
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.
Empirical ground-motion prediction equations (GMPEs) require adjustment to make them appropriate for site-specific scenarios. However, the process of making such adjustments remains a challenge. This article presents a holistic framework for the development of a response spectral GMPE that is easily adjustable to different seismological conditions and does not suffer from the practical problems associated with adjustments in the response spectral domain. The approach for developing a response spectral GMPE is unique, because it combines the predictions of empirical models for the two model components that characterize the spectral and temporal behavior of the ground motion. Essentially, as described in its initial form by Bora et al. (2014), the approach consists of an empirical model for the Fourier amplitude spectrum (FAS) and a model for the ground-motion duration. These two components are combined within the random vibration theory framework to obtain predictions of response spectral ordinates. In addition, FAS corresponding to individual acceleration records are extrapolated beyond the useable frequencies using the stochastic FAS model, obtained by inversion as described in Edwards and Fah (2013a). To that end, a (oscillator) frequency-dependent duration model, consistent with the empirical FAS model, is also derived. This makes it possible to generate a response spectral model that is easily adjustable to different sets of seismological parameters, such as the stress parameter Delta sigma, quality factor Q, and kappa kappa(0). The dataset used in Bora et al. (2014), a subset of the RESORCE-2012 database, is considered for the present analysis. Based upon the range of the predictor variables in the selected dataset, the present response spectral GMPE should be considered applicable over the magnitude range of 4 <= M-w <= 7.6 at distances <= 200 km.
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.
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.