The effect of causal parameter bounds in PSHA‐based ground motion selection

In this paper the effect of causal parameter bounds (e.g. magnitude, source‐to‐site distance, and site condition) on ground motion selection, based on probabilistic seismic hazard analysis (PSHA) results, is investigated. Despite the prevalent application of causal parameter bounds in ground motion selection, present literature on the topic is cast in the context of a scenario earthquake of interest, and thus specific bounds for use in ground motion selection based on PSHA, and the implications of such bounds, is yet to be examined. Thirty‐six PSHA cases, which cover a wide range of causal rupture deaggregation distributions and site conditions, are considered to empirically investigate the effects of various causal parameter bounds on the characteristics of selected ground motions based on the generalized conditional intensity measure (GCIM) approach. It is demonstrated that the application of relatively ‘wide’ bounds on causal parameters effectively removes ground motions with drastically different characteristics with respect to the target seismic hazard and results in an improved representation of the target causal parameters. In contrast, the use of excessively ‘narrow’ bounds can lead to ground motion ensembles with a poor representation of the target intensity measure distributions, typically as a result of an insufficient number of prospective ground motions. Quantitative criteria for specifying bounds for general PSHA cases are provided, which are expected to be sufficient in the majority of problems encountered in ground motion selection for seismic demand analyses. Copyright © 2016 John Wiley & Sons, Ltd.     

Comparison of conventional and Monte Carlo simulation-based probabilistic seismic hazard analyses for Shiraz city,southern Iran

Estimation of ground-motion amplitudes of different hazard levels is of paramount importance in planning of urban development of any metropolis. Such estimation can be computed through a probabilistic seismic hazard analysis (PSHA). This paper concentrates on the PSHA of an area located in Shiraz city, southern Iran. The area includes whole of Shiraz city (i.e., one of the largest and most populous cities of Iran) and its outskirts. Conventional and Monte Carlo simulation-based approaches are utilized to perform the PSHA of the studied area. Two areal seismic source models are delineated, and thence seismicity parameters of all zones associated with their corresponding uncertainties are computed. Uncertainties in ground-motion prediction are accounted for via three ground-motion prediction equations (GMPEs) within the logic tree framework. These GMPEs are applied to estimate bedrock ground shaking (V_s30?=?760 m/s) for several return periods (i.e., 75, 475, 975, and 2475 years). In general, the results of the two abovementioned PSHA approaches show relatively similar results. However, the Monte Carlo simulation-based approach overpredicts bedrock spectral accelerations at periods of 0.4–2.5 s compared to the conventional PSHA approach for return periods of 475, 975, and 2475 years.     

Probabilistic seismic hazard assessment of Italy using kernel estimation methods

A representation of seismic hazard is proposed for Italy based on the zone-free approach developed by Woo (BSSA 86(2):353–362, 1996a), which is based on a kernel estimation method governed by concepts of fractal geometry and self-organized seismicity, not requiring the definition of seismogenic zoning. The purpose is to assess the influence of seismogenic zoning on the results obtained for the probabilistic seismic hazard analysis (PSHA) of Italy using the standard Cornell’s method. The hazard has been estimated for outcropping rock site conditions in terms of maps and uniform hazard spectra for a selected site, with 10 % probability of exceedance in 50 years. Both spectral acceleration and spectral displacement have been considered as ground motion parameters. Differences in the results of PSHA between the two methods are compared and discussed. The analysis shows that, in areas such as Italy, characterized by a reliable earthquake catalog and in which faults are generally not easily identifiable, a zone-free approach can be considered a valuable tool to address epistemic uncertainty within a logic tree framework.     

Probabilistic seismic hazard analysis: Early history

Probabilistic seismic hazard analysis (PSHA) is the evaluation of annual frequencies of exceedence of ground motion levels (typically designated by peak ground acceleration or by spectral accelerations) at a site. The result of a PSHA is a seismic hazard curve (annual frequency of exceedence vs ground motion amplitude) or a uniform hazard spectrum (spectral amplitude vs structural period, for a fixed annual frequency of exceedence). Analyses of this type were first conceived in the 1960s and have become the basis for the seismic design of engineered facilities ranging from common buildings designed according to building codes to critical facilities such as nuclear power plants. This Historical Note traces the early history of PSHA. Copyright © 2007 John Wiley & Sons, Ltd.     

Physics‐based probabilistic seismic hazard and loss assessment in large urban areas: A simplified application to Istanbul

A set of 3D physics‐based numerical simulations (PBS) of possible earthquakes scenarios in Istanbul along the North Anatolian Fault (Turkey) is considered in this article to provide a comprehensive example of application of PBS to probabilistic seismic hazard (PSHA) and loss assessment in a large urban area. To cope with the high‐frequency (HF) limitations of PBS, numerical results are first postprocessed by a recently introduced technique based on Artificial Neural Networks (ANN), providing broadband waveforms with a proper correlation of HF and low‐frequency (LF) portions of ground motion as well as a proper spatial correlation of peak values also at HF, that is a key feature for the seismic risk application at urban scale. Second, before application to PSHA, a statistical analysis of residuals is carried out to ensure that simulated results provide a set of realizations with a realistic within‐ and between‐event variability of ground motion. PBS results are then applied in a PSHA framework, adopting both the “generalized attenuation function” (GAF) approach, and a novel “footprint” (FP)‐based approach aiming at a convenient and direct application of PBS into PSHA. PSHA results from both approaches are then compared with those obtained from a more standard application of PSHA with empirical ground motion models. Finally, the probabilistic loss assessment of an extended simplified portfolio of buildings is investigated, comparing the results obtained adopting the different approaches: (i) GMPE, (ii) GAF, and (iii) FP. Only FP turned out to have the capability to account for the specific features of source and propagation path, while preserving the proper physically based spatial correlation characteristics, as required for a reliable loss estimate on a building portfolio spatially distributed over a large urban area.     

An energy-based envelope function for the stochastic simulation of earthquake accelerograms

An energy-based envelope function is developed for use in the stochastic simulation of earthquake ground motion. The envelope function is directly related to the Arias intensity of the ground motion as well to the manner in which this Arias intensity is built-up over time. It is shown that this build-up, represented by a Husid plot, can be very well modelled using a simple lognormal distribution. The proposed envelope makes use of parameters that are commonly available in seismic design situations, either following a deterministic scenario-type analysis or following a more comprehensive probabilistic seismic hazard analysis (PSHA), either in terms of Arias intensity or the more common spectral acceleration. The shape parameters of the envelope function are estimated following the calculation of the analytic envelopes for a large number of records from PEER Next Generation of Attenuation (NGA) database. The envelope may also be used to predict the distribution of peak ground acceleration values corresponding to an earthquake scenario. The distribution thus obtained is remarkably consistent with those of the recent NGA models.     

A probabilistic framework for quantification of aftershock ground‐motion hazard in California: Methodology and parametric study

This paper presents a proposed method of aftershock probabilistic seismic hazard analysis (APSHA) similar to conventional ‘mainshock’ PSHA in that it estimates the likelihoods of ground motion intensity (in terms of peak ground accelerations, spectral accelerations or other ground motion intensity measures) due to aftershocks following a mainshock occurrence. This proposed methodology differs from the conventional mainshock PSHA in that mainshock occurrence rates remain constant for a conventional (homogeneous Poisson) earthquake occurrence model, whereas aftershock occurrence rates decrease with increased elapsed time from the initial occurrence of the mainshock. In addition, the aftershock ground motion hazard at a site depends on the magnitude and location of the causative mainshock, and the location of aftershocks is limited to an aftershock zone, which is also dependent on the location and magnitude of the initial mainshock. APSHA is useful for post‐earthquake safety evaluation where there is a need to quantify the rates of occurrence of ground motions caused by aftershocks following the initial rupture. This knowledge will permit, for example, more informed decisions to be made for building tagging and entry of damaged buildings for rescue, repair or normal occupancy. Copyright © 2008 John Wiley & Sons, Ltd.     

Assessment of ground motion variability and its effects on seismic hazard analysis: a case study for iceland

Probabilistic seismic hazard analysis (PSHA) generally relies on the basic assumption that ground motion prediction equations (GMPEs) developed for other similar tectonic regions can be adopted in the considered area. This implies that observed ground motion and its variability at considered sites could be modelled by the selected GMPEs. Until now ground-motion variability has been taken into account in PSHA by integrating over the standard deviation reported in GMPEs, which significantly affects estimated ground motions, especially at very low probabilities of exceedance. To provide insight on this issue, ground-motion variability in the South Iceland Seismic Zone (SISZ), where many ground-motion records are available, is assessed. Three statistical methods are applied to separate the aleatory variability into source (inter-event), site (inter-site) and residual (intra-event and intra-site) components. Furthermore, the current PSHA procedure that makes the ergodic assumption of equality between spatially and temporal variability is examined. In contrast to the ergodic assumption, several recent studies show that the observed ground-motion variability at an individual location is lower than that implied by the standard deviation of a GMPE. This could imply a mishandling of aleatory uncertainty in PSHA by ignoring spatial variability and by mixing aleatory and epistemic uncertainties in the computation of sigma. Station correction coefficients are introduced in order to capture site effects at different stations. The introduction of the non-ergodic assumption in PSHA leads to larger epistemic uncertainty, although this is not the same as traditional epistemic uncertainty modelled using different GMPEs. The epistemic uncertainty due to the site correction coefficients (i.e. mean residuals) could be better constrained for future events if more information regarding the characteristics of these seismic sources and path dependence could be obtained.     

Updating the Probabilistic Seismic Hazard Values of Northern Algeria with the 21 May 2003 <Emphasis Type="Italic">M</Emphasis> 6.8 Algiers Earthquake Included

The occurrence of the Algiers earthquake (M 6.8) of May 21, 2003, has motivated the necessity to reassess the probabilistic seismic hazard of northern Algeria. The fact that this destructive earthquake took place in an area where there was no evidence of previous significant earthquakes, neither instrumental nor historical, strongly encourages us to review the seismic hazard map of this region. Recently, the probabilistic seismic hazard of northern Algeria was computed using the spatially smoothed seismicity methodology. The catalog used in the previous computation was updated for this review, and not only includes information until June 2003, but also considers a recent re-evaluation of several historical earthquakes. In this paper, the same methodology and seismicity models are utilized in an effort to compare this methodology against an improved and updated seismic catalog. The largest mean peak ground acceleration (PGA) values are obtained in northernmost Algeria, specifically in the central area of the Tell Atlas. These values are of the order of 0.48 g for a return period of 475 years. In the City of Algiers, the capital of Algeria, and approximately 50 km from the reported epicenter of this latest destructive earthquake, a new mean PGA value of 0.23 g is obtained for the same return period. This value is 0.07 g greater than that obtained in the previous computation. In general, we receive greater seismic hazard results in the surrounding area of Algiers, especially to the southwest. The main reason is not this recent earthquake by itself, but the significant increase in the m_max magnitude in the seismic source where the city and the epicenter are included.     

Application-driven ground motion prediction equation for seismic hazard assessments in non-cratonic moderate-seismicity areas

We present a ground motion prediction equation (GMPE) for probabilistic seismic hazard assessments (PSHA) in low-to-moderate seismicity areas, such as Germany. Starting from the NGA-West2 flat-file (Ancheta et al. in Earthquake Spectra 30:989–1005, 2014), we develop a model tailored to the hazard application in terms of data selection and implemented functional form. In light of such hazard application, the GMPE is derived for hypocentral distance (along with the Joyner-Boore one), selecting recordings at sites with vs30 ≥ 360 m/s, distances within 300 km, and magnitudes in the range 3 to 8 (being 7.4 the maximum magnitude for the PSHA in the target area). Moreover, the complexity of the considered functional form is reflecting the availability of information in the target area. The median predictions are compared with those from the NGA-West2 models and with one recent European model, using the Sammon’s map constructed for different scenarios. Despite the simplification in the functional form, the assessed epistemic uncertainty in the GMPE median is of the order of those affecting the NGA-West2 models for the magnitude range of interest of the hazard application. On the other hand, the simplification of the functional form led to an increment of the apparent aleatory variability. In conclusion, the GMPE developed in this study is tailored to the needs for applications in low-to-moderate seismic areas and for short return periods (e.g., 475 years); its application in studies where the hazard is involving magnitudes above 7.4 and for long return periods is not advised.     

An exploration of incorporating site response into PSHA—Part I: Issues related to site response analysis methods

This paper presents a series of analyses for the evaluation of the ground response of two NEHRP class D sites, subjected to shaking by a large number of strong ground-motion records. The two investigated sites have very distinct profiles, but they are characterised by almost identical V_s30 values. The site response analyses are performed using various methods of analysis and input parameters in order to explore the sensitivity of the ground response estimates and to identify the dominating parameters. Equivalent linear analysis is performed using different sets of dynamic soil properties curves, while nonlinear analysis is performed using different target dynamic soil curves, viscous damping formulations and fitting procedures for the constitutive model parameters. Particular focus is given to the sensitivity of the response when soil sites are subjected to high-intensity shaking, a subject of particular interest when the prediction of surface ground motions with low annual probabilities of exceedance is the target of probabilistic seismic hazard analyses (PSHA). The site response analysis results of this paper are incorporated into the probabilistic framework of Bazzurro and Cornell [1] in our companion paper in order to assess their impact on the final soil surface hazard calculation.     

Ground-motion intensity measure correlations observed in Italian strong-motion records

Ground-motion models (GMMs) are widely used in probabilistic seismic hazard analysis (PSHA) to estimate the probability distributions of earthquake-induced ground-motion intensity measures (IMs) at a site, given an earthquake of a certain magnitude occurring at a nearby location. Accounting for spatial and cross-IM correlations in earthquake-induced ground motions has important implications on probabilistic seismic hazard and loss estimates. This study first develops a new Italian GMM with spatial correlation for 31 amplitude-related IMs, including peak ground acceleration (PGA), peak ground velocity (PGV), and 5%-damped elastic pseudo-spectral accelerations (PSAs) at 29 periods ranging from 0.01 to 4 seconds. The model estimation is performed through a recently developed one-stage nonlinear regression algorithm proposed by the authors, known as the Scoring estimation approach. In fact, current state-of-practice approaches estimate spatial correlation separately from the GMM estimation, resulting in inconsistent and statistically inefficient estimators of interevent and intraevent variances and parameters in the spatial correlation model. We test whether this affects the subsequent cross-IM correlation analysis. To this aim, based on the newly developed GMM, the empirical correlation coefficients from interevent and intraevent residuals are investigated. Finally, a set of analytical correlation models between the selected IMs are proposed. This is of special interest as several correlation models between different IMs have been calibrated and validated based on advanced GMMs and global datasets, lacking earthquakes in extensional regions; however, modeling the correlation between different IM types has not been adequately addressed by current, state-of-the-art GMMs and recent ground-motion records for Italy.     

Empirical equations for the prediction of displacement spectrum intensity and its correlation with other intensity measures

Displacement spectrum intensity (DSI), defined as the integral of a ground motion's displacement response spectrum from 2.0 to 5.0 s, is proposed as an indicator of the severity of the long period content of a ground motion. It is demonstrated how the distribution of DSI can be predicted using existing ground motion prediction equations for (pseudo) spectral accelerations, which is necessary for it to be a useful intensity measure (IM) in either probabilistic or deterministic seismic hazard analysis. Empirical correlation equations between DSI and other common ground motion IMs are developed for active shallow crustal earthquakes using a dataset of ground motions from active shallow crustal earthquakes. The ability of DSI to account for near-source ground motions exhibiting forward directivity, potentially damaging far-source long-period ground motion, and its use with other spectrum intensity parameters to characterise short, medium, and long period severity of ground motions is discussed. The developed ground motion prediction and correlation equations enable DSI to be utilised in rigorous ground motion selection frameworks such as the generalised conditional intensity measure (GCIM) approach.     

地震危险性概率分析方法:存在的问题和纠正

地震危险性概率分析(PSHA)是目前最广泛应用于地震灾害与风险性评估的方法。然而它在计算中却存在着一个错误:把强地面运动衰减关系(一个函数)的条件超越概率等同于强地面运动误差(一个变量)的超越概率。这个错误导致了运用强地面运动误差(空间分布特征)去外推强地面运动的发生(时间分布特征)或称之为遍历性假设,同时也造成了对PSHA理解和应用上的困难。本文推导出新的灾害计算方法(称之为KY-PSHA)来纠正这种错误。     

History of Modern Earthquake Hazard Mapping and Assessment in California Using a Deterministic or Scenario Approach

Modern earthquake ground motion hazard mapping in California began following the 1971 San Fernando earthquake in the Los Angeles metropolitan area of southern California. Earthquake hazard assessment followed a traditional approach, later called Deterministic Seismic Hazard Analysis (DSHA) in order to distinguish it from the newer Probabilistic Seismic Hazard Analysis (PSHA). In DSHA, seismic hazard in the event of the Maximum Credible Earthquake (MCE) magnitude from each of the known seismogenic faults within and near the state are assessed. The likely occurrence of the MCE has been assumed qualitatively by using late Quaternary and younger faults that are presumed to be seismogenic, but not when or within what time intervals MCE may occur. MCE is the largest or upper-bound potential earthquake in moment magnitude, and it supersedes and automatically considers all other possible earthquakes on that fault. That moment magnitude is used for estimating ground motions by applying it to empirical attenuation relationships, and for calculating ground motions as in neo-DSHA (Zuccolo et al., 2008). The first deterministic California earthquake hazard map was published in 1974 by the California Division of Mines and Geology (CDMG) which has been called the California Geological Survey (CGS) since 2002, using the best available fault information and ground motion attenuation relationships at that time. The California Department of Transportation (Caltrans) later assumed responsibility for printing the refined and updated peak acceleration contour maps which were heavily utilized by geologists, seismologists, and engineers for many years. Some engineers involved in the siting process of large important projects, for example, dams and nuclear power plants, continued to challenge the map(s). The second edition map was completed in 1985 incorporating more faults, improving MCE??s estimation method, and using new ground motion attenuation relationships from the latest published results at that time. CDMG eventually published the second edition map in 1992 following the Governor??s Board of Inquiry on the 1989 Loma Prieta earthquake and at the demand of Caltrans. The third edition map was published by Caltrans in 1996 utilizing GIS technology to manage data that includes a simplified three-dimension geometry of faults and to facilitate efficient corrections and revisions of data and the map. The spatial relationship of fault hazards with highways, bridges or any other attribute can be efficiently managed and analyzed now in GIS at Caltrans. There has been great confidence in using DSHA in bridge engineering and other applications in California, and it can be confidently applied in any other earthquake-prone region. Earthquake hazards defined by DSHA are: (1) transparent and stable with robust MCE moment magnitudes; (2) flexible in their application to design considerations; (3) can easily incorporate advances in ground motion simulations; and (4) economical. DSHA and neo-DSHA have the same approach and applicability. The accuracy of DSHA has proven to be quite reasonable for practical applications within engineering design and always done with professional judgment. In the final analysis, DSHA is a reality-check for public safety and PSHA results. Although PSHA has been acclaimed as a better approach for seismic hazard assessment, it is DSHA, not PSHA, that has actually been used in seismic hazard assessment for building and bridge engineering, particularly in California.     

Peak-over-threshold: Quantifying ground motion beyond design

In performance-based seismic design, as adopted by several building codes worldwide, the structural performance is verified against ground motions that have predetermined exceedance return periods at the site of interest. Such a return period is evaluated by means of probabilistic seismic hazard analysis (PSHA), and the corresponding ground motion is often represented by the uniform hazard spectrum (UHS). The structural performance for ground motions larger than those considered in this design approach is, typically, not explicitly controlled under the assumption that they are sufficiently rare. On one hand, this does not achieve uniform safety at sites characterized by different design ground motions corresponding to the same return period; on the other hand, exceedances of the design spectra are systematically observed over large areas, for example in Italy. The latter issue is because of the nature of UHS, the exceedance of which is likely-to-almost-certain when the construction site is in the epicentral area of moderate-to-high magnitude earthquakes (ie, the design spectrum may be not conservative at these locations), especially if PSHA is based on seismic source zones. The former is partially because of the systematic difference of ground motions for return periods larger than the design one at the different sites. Quantification of the expected ground motion given the exceedance of the design ground motions (ie, the recently introduced as the expected peak-over-threshold or POT) can be of help in quantitatively assessing these issues. In the study, a procedure to compute the POT distribution is derived first; second, POT spectra are introduced and used to help understanding why and how seismic structural reliability of code-conforming structures decreases as the seismic hazard of the site increases; third, expected and 95^th percentile POT maps are shown for Italy to discuss how much high hazard sites are exposed to much larger peak-over-threshold with respect to mid-hazard and low-hazard sites; finally the POT is discussed with respect to the slope of the hazard curve (in log-log scale) at the threshold, a known proxy for ground motion beyond design. All data presented in the maps are made available for the interested reader as a supplemental archive.     

Seismic microzonation of Chania,Crete (Greece) based on SASW measurements and non-linear site response analyses

Following a brief overview of past applications of, and more recent advances on seismic microzonation, the results of a seismic microzonation study for the city of Chania, Greece, are presented. The study was based on V_s vs. depth profiles obtained at 19 sites of the urban area by performing SASW measurements. The spatial distribution of V_s values was utilized in estimating V_s30 values, depth to bedrock and the fundamental ground period variation across the area of the city as well as for conducting 1-D finite element non-linear inelastic site response analyses. The input earthquake excitations employed in the response analyses were based on the results of an available seismic hazard study for the Chania Area. The results of analyses were utilized for establishing the spatial distribution of rock motion amplification, the expected ground motions and spectral values in the area of the city. Contour maps providing values of the expected ground motion in the urban area are given which may become a practical tool in assessing the seismic risk and expected damage in the Chania area. The maps can also be used in the design of new earthquake resistant structures or the seismic retrofitting of existing ones. Finally, the results were utilized to demonstrate the inadequacy of using V_s,30 values for classifying the soil conditions in the Chania area.     

A unified framework for earthquake risk assessment of transportation networks and gross regional product

Natural threats like earthquakes, hurricanes or tsunamis have had serious impacts on communities. In the past, major earthquakes in the United States like Loma Prieta 1989, Northridge 1994, or recent events in Italy like L’Aquila 2009 or Emilia 2012 emphasized the importance of preparedness and awareness to reduce social impacts. In addition to that, earthquake damaged businesses dramatically reduced the gross regional product. Generating scenario earthquakes in a proper way is important to suitably assess the risk in bridge networks and social losses in terms of gross regional product reduction. Seismic hazard is traditionally assessed by means of probabilistic seismic hazard analysis (PSHA). Although PSHA well represents the hazard at a specific location it is not suitable for spatially distributed systems. Scenario earthquakes can overcome this problem; they represent the actual distribution of ground shaking for a spatially distributed system while being hazard consistent. In this work a methodology to generate scenario earthquakes has been proposed using a novel approach with the aim of being the basic step for investigating possible earthquake consequences in seismic areas and contributing to reduce losses.     

Seismic hazard assessment of Tehran,Iran with emphasis on near-fault rupture directivity effects

Many destructive earthquakes happened in Tehran, Iran in the last centuries. The existence of active faults like the North Tehran is the main cause of seismicity in this city. According to past investigations, it is estimated that in the scenario of activation of the North Tehran fault, many structures in Tehran will collapse. Therefore, it is necessary to incorporate the near field rupture directivity effects of this fault into the seismic hazard assessment of important sites in Tehran. In this study, using calculations coded in MATLAB,Probabilistic Seismic Hazard Analysis(PSHA) is conducted for an important site in Tehran. Following that, deaggregation technique is performed on PSHA and the contribution of seismic scenarios to hazard is obtained in the range of distance and magnitude. After identifying the North Tehran fault as the most hazardous source affecting the site in 10000-year return period, rupture directivity effects of this fault is incorporated into the seismic hazard assessment using Somerville et al.(1997) model with broadband approach and Shahi and Baker(2011) model with narrowband approach. The results show that the narrowband approach caused a 27% increase in the peak of response spectrum in 10000-year return period compared with the conventional PSHA. Therefore, it is necessary to incorporate the near fault rupture directivity effects into the higher levels of seismic hazard assessment attributed to important sites.     

Application of a Monte‐Carlo simulation approach for the probabilistic assessment of seismic hazard for geographically distributed portfolio

The conventional integral approach is very well established in probabilistic seismic hazard assessment (PSHA). However, Monte‐Carlo (MC) simulations can become an efficient and flexible alternative against conventional PSHA when more complicated factors (e.g. spatial correlation of ground shaking) are involved. This study aims at showing the implementation of MC simulation techniques for computing the annual exceedance rates of dynamic ground‐motion intensity measures (GMIMs) (e.g. peak ground acceleration and spectral acceleration). We use multi‐scale random field technique to incorporate spatial correlation and near‐fault directivity while generating MC simulations to assess the probabilistic seismic hazard of dynamic GMIMs. Our approach is capable of producing conditional hazard curves as well. We show various examples to illustrate the potential use of the proposed procedures in the hazard and risk assessment of geographically distributed structural systems. Copyright © 2015 John Wiley & Sons, Ltd.