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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.
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).
One of the major challenges related with the current practice in seismic hazard studies is the adjustment of empirical ground motion prediction equations (GMPEs) to different seismological environments. We believe that the key to accommodating differences in regional seismological attributes of a ground motion model lies in the Fourier spectrum. In the present study, we attempt to explore a new approach for the development of response spectral GMPEs, which is fully consistent with linear system theory when it comes to adjustment issues. This approach consists of developing empirical prediction equations for Fourier spectra and for a particular duration estimate of ground motion which is tuned to optimize the fit between response spectra obtained through the random vibration theory framework and the classical way. The presented analysis for the development of GMPEs is performed on the recently compiled reference database for seismic ground motion in Europe (RESORCE-2012). Although, the main motivation for the presented approach is the adjustability and the use of the corresponding model to generate data driven host-to-target conversions, even as a standalone response spectral model it compares reasonably well with the GMPEs of Ambraseys et al. (Bull Earthq Eng 3:1-53, 2005), Akkar and Bommer (Seismol Res Lett 81(2):195-206, 2010) and Akkar and Cagnan (Bull Seismol Soc Am 100(6):2978-2995, 2010).
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.