Improving seismic hazard approaches for critical infrastructures: a pilot study in the Po Plain

Paper describes the extensive work done in the SIGMA project, aimed at improving knowledge on data, methods and tools to better quantify uncertainties in seismic hazard assessment (SHA). The authors cooperated in the study of potential faults and geological structures, earthquake catalogues, selection of ground motion prediction equations, and methods for site effect evaluation suitable for SHA. All the contributions merged into a probabilistic seismic hazard study conducted for three representative sites of the Po Plain in Northern Italy. Po Plain is a low-to-moderate seismicity region, characterized by some critical features, such as blind faulting and deep alluvium sediments, and by scarcity of strong motion data; these sources of uncertainties in seismic hazard estimation are common to other low seismicity areas around the world. Within SIGMA, special care was devoted to: (a) the use of the single station sigma approach inside the probabilistic SHA, (b) the comparative use of generalized attenuation functions to evaluate the hazard contribution of composite fault systems, and (c) the study of the epistemic uncertainties at play when different modelling approaches to site effects are used.     

Response uncertainty and time-variant reliability analysis for hysteretic MDF structures

Response uncertainty evaluation and dynamic reliability analysis corresponding to classical stochastic dynamic analysis are usually restricted to the uncertainties of the excitation. The inclusion of the parameter uncertainties contained in structural properties and excitation characteristics has become an increasingly important problem in many areas of dynamics. In the present paper, a point estimate procedure is proposed for the evaluation of stochastic response uncertainty, and a response surface approach procedure in standard normal space is proposed for analysis of time-variant reliability analysis for hysteretic MDF structures having parameter uncertainties. Using the proposed procedures, the response uncertainties and time-variant reliability can be easily obtained by several repetitions of stochastic response analysis under given parameters without conducting sensitivity analysis, which is considered to be one of the primary difficulties associated with conventional methods. In the time-variant reliability analysis, the failure probability can be readily obtained by improving the accuracy of the first-order reliability method using the empirical second-order reliability index. The random variables are divided into two groups, those with CDF and those without CDF. The latter are included via the high-order moment standardization technique. A numerical example of a 15F hysteretic MDF structure that takes into account uncertainties of four structural parameters and three excitation characteristics is performed, based on which the proposed procedures are investigated and the effects of parameter uncertainties are discussed. Copyright © 1999 John Wiley & Sons, Ltd.     

Bayesian flood frequency analysis in the light of model and parameter uncertainties

The specific objective of the paper is to propose a new flood frequency analysis method considering uncertainty of both probability distribution selection (model uncertainty) and uncertainty of parameter estimation (parameter uncertainty). Based on Bayesian theory sampling distribution of quantiles or design floods coupling these two kinds of uncertainties is derived, not only point estimator but also confidence interval of the quantiles can be provided. Markov Chain Monte Carlo is adopted in order to overcome difficulties to compute the integrals in estimating the sampling distribution. As an example, the proposed method is applied for flood frequency analysis at a gauge in Huai River, China. It has been shown that the approach considering only model uncertainty or parameter uncertainty could not fully account for uncertainties in quantile estimations, instead, method coupling these two uncertainties should be employed. Furthermore, the proposed Bayesian-based method provides not only various quantile estimators, but also quantitative assessment on uncertainties of flood frequency analysis.     

场地地震反应分析中的不确定性及其处理方法

系统地研究了场地地震反应分析中的不确定性及其产生的根源．利用蒙特卡洛法的有关理论,对影响场地地震反应分析结果的不确定性因素进行了估计与分析．实际应用结果表明,该方法是可行的,而且精度较高     

Estimation of changes in water column velocities and thicknesses from time lapse seismic data

Sea‐bed diffractions are frequently observed for several of the fields in the Norwegian Sea and the Barents Sea. This is a challenge in time lapse seismic analysis, since diffracted multiples are difficult to remove by processing and therefore is a major source of poor time lapse data quality. In this work we test if the diffractions can be used for enhanced 4D interpretation. By analysing the time‐shift of the sea‐bed diffraction hyperbola between the base and monitor it is tested if changes in water velocity and tides can be estimated. Two models using time lapse diffraction analysis are tested: the first one simply adds time‐shifts for the two branches of the diffraction hyperbola and this average time‐shift is then used to estimate the water velocity change. The other method uses an inversion method based on the diffraction equation for a point diffractor to estimate the velocity change. In‐line common‐midpoint shifts are estimated by subtracting the time‐shifts of both hyperbola branches followed by direct inversion. The diffraction based time‐shifts are compared to time‐shifts estimated by standard cross‐correlation of the sea‐bed reflection. The averaging method gives slightly higher uncertainties, while the inversion using an exact traveltime equation gives similar uncertainties compared to the sea‐bed reflection method.     

Perfectly matched layer boundary conditions for the second-order acoustic wave equation solved by the rapid expansion method

We derive a governing second-order acoustic wave equation in the time domain with a perfectly matched layer absorbing boundary condition for general inhomogeneous media. Besides, a new scheme to solve the perfectly matched layer equation for absorbing reflections from the model boundaries based on the rapid expansion method is proposed. The suggested scheme can be easily applied to a wide class of wave equations and numerical methods for seismic modelling. The absorbing boundary condition method is formulated based on the split perfectly matched layer method and we employ the rapid expansion method to solve the derived new perfectly matched layer equation. The use of the rapid expansion method allows us to extrapolate wavefields with a time step larger than the ones commonly used by traditional finite-difference schemes in a stable way and free of dispersion noise. Furthermore, in order to demonstrate the efficiency and applicability of the proposed perfectly matched layer scheme, numerical modelling examples are also presented. The numerical results obtained with the put forward perfectly matched layer scheme are compared with results from traditional attenuation absorbing boundary conditions and enlarged models as well. The analysis of the numerical results indicates that the proposed perfectly matched layer scheme is significantly effective and more efficient in absorbing spurious reflections from the model boundaries.     

改进的TTI介质纯P波方程正演模拟与逆时偏移

逆时偏移作为一种高精度偏移方法已成为复杂构造成像的重要技术,描述纵波独立传播的延拓方程是各向异性介质逆时偏移的一个关键问题.在对VTI介质几个经典相速度近似公式回顾的基础上,针对常用于描述纯P波的Harlan近似公式在各向异性参数ε较大情况下近似精度较低的问题,本文对Harlan公式中的非椭圆项进行了修正,在非椭圆项前添加了一个与各向异性参数ε有关的修正系数,得到了三种改进型Harlan公式,并以近似精度最高的改进式为基础,推导了TTI介质纯P波方程.针对该伪微分方程,本文利用伪谱法和有限差分法联合实现波场延拓,对于常密度二阶方程,基于中心网格实现;对于一阶应力-速度方程则基于旋转交错网格实现.通过数值试验分析了TTI介质纯P波一阶应力-速度方程的近似精度,并以一阶纯P波方程为基础进行了TTI介质逆时偏移数值模拟试验.结果表明,本文给出的方法能够较准确地描述TTI介质纯P波波场特征,可以应用至各向异性介质逆时偏移.

     

Seismic response analysis of bridges isolated with friction pendulum bearings

A systematic method is developed for the dynamic analysis of the structures with sliding isolation which is a highly non-linear dynamic problem. According to the proposed method, a unified motion equation can be adapted for both stick and slip modes of the system. Unlike the traditional methods by which the integration interval has to be chopped into infinitesimal pieces during the transition of sliding and non-sliding modes, the integration interval remains constant throughout the whole process of the dynamic analysis by the proposed method so that accuracy and efficiency in the analysis of the non-linear system can be enhanced to a large extent. Moreover, the proposed method is general enough to be adapted for the analysis of the structures with multiple sliding isolators undergoing independent motion conditions simultaneously. The superiority of the proposed method for the analysis of sliding supported structures is verified by a three-span continuous bridge subjected to harmonic motions and real earthquakes. In addition, the side effect of excessive displacement of the superstructure induced by the sliding isolation is eliminated by replacing one of the roller supports on the abutments with hinge support. Therefore, both reductions in the forces of the substructure and the displacements of the superstructure can be achieved simultaneously. © 1998 John Wiley & Sons, Ltd.     

Median floor acceleration spectra of linear structures with uncertain properties

Response parameters used to estimate nonstructural damage differ depending on whether deformation‐sensitive or acceleration‐sensitive components are considered. In the latter case, seismic demand is usually represented through floor spectra, that is response spectra in terms of pseudo‐acceleration, which are calculated at the floor levels of the structure where the nonstructural components are attached to. Objective of this paper is to present a new spectrum‐to‐spectrum method for calculating floor acceleration spectra, which is able to explicitly account for epistemic uncertainties in the modal properties of the supporting structure. By using this method, effects on the spectra of possible variations from nominal values of the periods of vibration of the structure can be estimated. The method derives from the extension of closed‐form equations recently proposed by the authors to predict uniform hazard floor acceleration spectra. These equations are built to rigorously account for the input ground motion uncertainty, that is the record‐to‐record variability of the nonstructural response. In order to evaluate the proposed method, comparisons with exact spectra obtained from a standard probabilistic seismic demand analysis, as well as spectra calculated using the Eurocode 8 equation, are finally shown. Copyright © 2017 John Wiley & Sons, Ltd.     

An analysis of the Chow-Kulandaiswamy GHS model

The Chow-Kulandaiswamy general hydrologic system (GHS) model is revisited. Based on a mathematical study by Singh and McCann the GHS model is simplified. Explicit solutions are obtained for special cases which can satisfactorily determine watershed surface runoff response due to given rainfall excess. A rational criterion is developed to determine the number of derivative terms to be retained in the model. In order to determine the coefficients in the GHS model the method of moments is proposed. Criteria are developed to determine complex roots and oscillations for these coefficients. By analysing Chow-Kulandaiswamy's results it is found that in a majority of cases which they studied roots are complex. Moreover, for the cases which have complex roots, a majority of the solutions oscillate. A brief sensitivity analysis of the GHS model is performed with regard to: (a) its leading coefficient, and (b) the order of the differential equation. Finally, the peak characteristics are specified for the second order case and their qualitative properties are shown for the third order case.     

A method for generating fully non-stationary and spectrum-compatible ground motion vector processes

Earthquake ground motion spatial variability can influence significantly the response of certain structures. In order to accurately evaluate probabilistic characteristics of the seismic response of structures, the Monte Carlo simulation technique is still the only universal method of analysis when strong nonlinearities and input uncertainties are involved. Consequently, realizations of ground motion time histories taking into account both time and spatial variability need to be generated. Furthermore, for some design applications, the generated time histories must also satisfy the provision imposed by certain seismic codes stating that they have to be also response-spectrum-compatible. For these purposes, a spectral-representation-based methodology for generating fully non-stationary and spectrum-compatible ground motion vector processes at a number of locations on the ground surface is proposed in this paper. The simulated time histories do not require any iterations on the individual generated sample functions so that Gaussianity and prescribed coherence are suitably preserved. The methodology has also the advantage of providing the fully non-stationary and spectrum-compatible cross-spectral density matrix of the ground motion time-histories that can be used for reliability studies in an analytic stochastic fashion.     

Facies-constrained prestack seismic probabilistic inversion driven by rock physics

Seismic Rock physics plays a bridge role between the rock moduli and physical properties of the hydrocarbon reservoirs. Prestack seismic inversion is an important method for the quantitative characterization of elasticity, physical properties, lithology and fluid properties of subsurface reservoirs. In this paper, a high order approximation of rock physics model for clastic rocks is established and one seismic AVO reflection equation characterized by the high order approximation(Jacobian and Hessian matrix) of rock moduli is derived. Besides, the contribution of porosity, shale content and fluid saturation to AVO reflectivity is analyzed. The feasibility of the proposed AVO equation is discussed in the direct estimation of rock physical properties. On the basis of this, one probabilistic AVO inversion based on differential evolution-Markov chain Monte Carlo stochastic model is proposed on the premise that the model parameters obey Gaussian mixture probability prior model. The stochastic model has both the global optimization characteristics of the differential evolution algorithm and the uncertainty analysis ability of Markov chain Monte Carlo model. Through the cross parallel of multiple Markov chains, multiple stochastic solutions of the model parameters can be obtained simultaneously, and the posterior probability density distribution of the model parameters can be simulated effectively. The posterior mean is treated as the optimal solution of the model to be inverted.Besides, the variance and confidence interval are utilized to evaluate the uncertainties of the estimated results, so as to realize the simultaneous estimation of reservoir elasticity, physical properties, discrete lithofacies and dry rock skeleton. The validity of the proposed approach is verified by theoretical tests and one real application case in eastern China.     

Application of random sets to model uncertainties of natural entities extracted from remote sensing images

Remotely sensed images as a major data source to observe the earth, have been extensively integrated into spatial-temporal analysis in environmental research. Information on spatial distribution and spatial-temporal dynamic of natural entities recorded by series of images, however, usually bears various kinds of uncertainties. To deepen our insight into the uncertainties that are inherent in these observations of natural phenomena from images, a general data modeling methodology is developed to embrace different kinds of uncertainties. The aim of this paper is to propose a random set method for uncertainty modeling of spatial objects extracted from images in environmental study. Basic concepts of random set theory are introduced and primary random spatial data types are defined based on them. The method has been applied to dynamic wetland monitoring in the Poyang Lake national nature reserve in China. Four Landsat images have been used to monitor grassland and vegetation patches. Their broad gradual boundaries are represented by random sets, and their statistical mean and median are estimated. Random sets are well suited to estimate these boundaries. We conclude that our method based on random set theory has a potential to serve as a general framework in uncertainty modeling and is applicable in a spatial environmental analysis.     

Risk management of BTEX contamination in ground water--an integrated fuzzy approach

An integrated fuzzy simulation-assessment method (FSAM) was developed for assessing environmental risks from petroleum hydrocarbon contamination in ground water. In the FSAM, techniques of fuzzy simulation and fuzzy risk assessment were coupled into a general framework to reflect a variety of system uncertainties. A petroleum-contaminated site located in western Canada was selected as a study case for demonstrating applicability of the proposed method. The risk assessment results demonstrated that system uncertainties would significantly impact expressions of risk-level outputs. A relatively deterministic expression of the risks would have clearer representations of the study problem but may miss valuable uncertain information; conversely, an assessment under vaguer system conditions would help reveal potential consequences of adverse effects but would suffer from a higher degree of fuzziness in presenting the modeling outputs. Based on the risk assessment results, a decision analysis procedure was used to calculate a general risk index (GRI) to help identify proper responsive actions. The proposed method was useful for evaluating risks within a system containing multiple factors with complicated uncertainties and interactions and providing support for identifying proper site management strategies.     

Ground motion characterization and seismic hazard assessment in Spain: context,problems and recent developments

This article points out some particular features conditioning seismic hazard assessments (SHA) in Spain, a region with low–moderate seismicity. Although sized earthquakes occurred in the past, as evidenced by historical documents and neotectonic studies, no large events occurred during the last decades. The absence of strong motion records corresponding to earthquakes with magnitude larger than 5.5 is an important obstacle for the development of ground motion models constrained by local data, with the consequent difficulty in SHA studies. In this paper, some recent developments aiming at providing solutions to these difficulties are presented. Specifically, a strong motion databank containing a massive collection of accelerograms and response spectra from different configurations source-path-site corresponding to earthquakes all over the world is introduced, together with software utilities for its management. A first application of this databank is the development of specific ground motion models for Spain and for the Mediterranean region that predict peak ground accelerations as a function of several definitions of magnitude, distance and soil class. The predictive power of these ground motion models is tested by contrasting their estimates with recently recorded ground motions. The comparison between our ground-motion models with others proposed in the literature for other areas reveals a regular overestimation of the expected ground motions at Spanish sites by the non-local models. Consequently, SHA studies based in external models may overestimate the predicted hazard at the Iberian sites. In the last part of the paper a method for checking whether the response spectra proposed in the Spanish Building Code (NCSE-02) are consistent with actual accelerometric data from recent low magnitude earthquakes is applied. The spectral shapes of the Spanish Building Code NCSE-02 are compared with the response spectral shapes deduced from the available accelerograms by normalising the response spectra with the recorded PGA. It is appreciated that the NCSE-02 spectral shapes are exceeded by a large number of actual spectral shapes for short periods (around 0.2 s), a result to be taken into account in further revisions of the NCSE-02 code. The issues tackled in this work constitute not only an improvement for ground-motion characterisation in Spain, but also provide guidelines of general interest for potential applications in other regions with similar seismicity.     

Deriving fragility functions from bilinearized capacity curves for earthquake scenario modelling using the conditional spectrum

The development of fragility curves to perform seismic scenario-based risk assessment requires a fully probabilistic procedure in order to account for uncertainties at each step of the computation. This is especially true when developing fragility curves conditional on an Intensity Measure that is directly available from a ground-motion prediction equation. In this study, we propose a new derivation method that uses realistic spectra instead of design spectral shapes or uniform hazard spectra and allows one to easily account for the features of the site-specific hazard that influences the fragility, without using non-linear dynamic analysis. The proposed method has been applied to typical school building types in the city of Basel (Switzerland) and the results have been compared to the standard practice in Europe. The results confirm that fragility curves are scenario dependent and are particularly sensitive to the magnitude of the earthquake scenario. The same background theory used for the derivation of the fragility curves has allowed an innovative method to be proposed for the conversion of fragility curves to a common IM (i.e. spectral acceleration or PGA). This conversion is the only way direct comparisons of fragility curves can be made and is useful when inter-period correlation cannot be used in scenario loss assessment. Moreover, such conversion is necessary to compare and verify newly developed curves against those from previous studies. Conversion to macroseismic intensity is also relevant for the comparison between mechanical-based and empirical fragility curves, in order to detect possible biases.     

Vector-intensity measure based seismic vulnerability analysis of bridge structures

This paper presents a method for seismic vulnerability analysis of bridge structures based on vector-valued intensity measure(v IM), which predicts the limit-state capacities efficiently with multi-intensity measures of seismic event. Accounting for the uncertainties of the bridge model, ten single-bent overpass bridge structures are taken as samples statistically using Latin hypercube sampling approach. 200 earthquake records are chosen randomly for the uncertainties of ground motions according to the site condition of the bridges. The uncertainties of structural capacity and seismic demand are evaluated with the ratios of demand to capacity in different damage state. By comparing the relative importance of different intensity measures, Sa(T1) and Sa(T2) are chosen as v IM. Then, the vector-valued fragility functions of different bridge components are developed. Finally, the system-level vulnerability of the bridge based on v IM is studied with DunnettSobel class correlation matrix which can consider the correlation effects of different bridge components. The study indicates that an increment IMs from a scalar IM to v IM results in a significant reduction in the dispersion of fragility functions and in the uncertainties in evaluating earthquake risk. The feasibility and validity of the proposed vulnerability analysis method is validated and the bridge is more vulnerable than any components.     

Merging energy‐based design criteria and reliability‐based methods: exploring a new concept

This paper examines the potential development of a probabilistic design methodology, considering hysteretic energy demand, within the framework of performance‐based seismic design of buildings. This article does not propose specific energy‐based criteria for design guidelines, but explores how such criteria can be treated from a probabilistic design perspective. Uniform hazard spectra for normalized hysteretic energy are constructed to characterize seismic demand at a specific site. These spectra, in combination with an equivalent systems methodology, are used to estimate hysteretic energy demand on real building structures. A design checking equation for a (hypothetical) probabilistic energy‐based performance criterion is developed by accounting for the randomness of the earthquake phenomenon, the uncertainties associated with the equivalent system analysis technique, and with the site soil factor. The developed design checking equation itself is deterministic, and requires no probabilistic analysis for use. The application of the proposed equation is demonstrated by applying it to a trial design of a three‐storey steel moment frame. The design checking equation represents a first step toward the development of a performance‐based seismic design procedure based on energy criterion, and additional works needed to fully implement this are discussed in brief at the end of the paper. Copyright © 2006 John Wiley & Sons, Ltd.     

Deriving a practical form of IDF formula using transformed rainfall intensities

A general form of formula is presented for the rainfall Intensity–Duration–Frequency (IDF) relationship. This formula is derived from the nearly normal probability distribution function of transformed intensities. In order to transform the raw intensities, a correcting non‐constant spread technique, the Kruskal–Wallis statistic, and the Box–Cox transformation are adopted. These transformations enable to express a simpler model for the IDF formula that agrees well with traditional IDF relationships. Since the proposed method allows the estimation of any percentile value of intensities with a single equation, the intensity percentile at arbitrary duration can be generated easily. The validity of the formula derived by means of the proposed method is assessed using data from major weather stations in Korea. The results show that the percentile intensities produced using the proposed method are in good agreement with those of traditional frequency analysis. Copyright © 2013 John Wiley & Sons, Ltd.