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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.