Copula joint function and its application in probability seismic hazard analysis

A mature mathematical technique called copula joint function is introduced in this paper, which is commonly used in the financial risk analysis to estimate uncertainty. The joint function is generalized to the n-dimensional Frank’s copula. In addition, we adopt two attenuation models proposed by YU and Boore et al, respectively, and construct a two-dimensional copula joint probabilistic function as an example to illustrate the uncertainty treatment at low probability. The results show that copula joint function gives us a better prediction of peak ground motion than that resultant from the simple linear weight technique which is commonly used in the traditional logic-tree treatment of model uncertainties. In light of widespread application in the risk analysis from financial investment to insurance assessment, we believe that the copula-based technique will have a potential application in the seismic hazard analysis.

Probabilistic seismic landslide hazard assessment: a case study in Tianshui, Northwest China

Probabilistic analysis in the field of seismic landslide hazard assessment is often based on an estimate of uncertainties of geological, geotechnical,geomorphological and seismological parameters.However, real situations are very complex and thus uncertainties of some parameters such as water content conditions and critical displacement are difficult to describe with accurate mathematical models. In this study, we present a probabilistic methodology based on the probabilistic seismic hazard analysis method and the Newmark’s displacement model. The Tianshui seismic zone(105°00′-106°00′ E, 34°20′-34°40′ N) in the northeastern Tibetan Plateau were used as an example. Arias intensity with three standard probabilities of exceedance(63%, 10%, and 2% in 50 years) in accordance with building design provisions were used to compute Newmark displacements by incorporating the effects of topographic amplification.Probable scenarios of water content condition were considered and three water content conditions(dry,wet and saturated) were adopted to simulate the effect of pore-water on slope. The influence of 5 cm and 10 cm critical displacements were investigated in order to analyze the sensitivity of critical displacement to the probabilities of earthquake-induced landslide occurrence. The results show that water content in particular, have a great influence on the distribution of high seismic landslide hazard areas. Generally, the dry coverage analysis represents a lower bound for susceptibility and hazard assessment, and the saturated coverage analysis represents an upper bound to some extent. Moreover, high seismic landslide hazard areas are also influenced by the critical displacements. The slope failure probabilities during future earthquakes with critical displacements of 5 cm can increase by a factor of 1.2 to 2.3 as compared to that of 10 cm. It suggests that more efforts are required in order to obtain reasonable threshold values for slope failure. Considering the probable scenarios of water content condition which is varied with seasons, seismic landslide hazard assessments are carried out for frequent, occasional and rare earthquake occurrences in the Tianshui region, which can provide a valuable reference for landslide hazard management and infrastructure design in mountainous seismic zones.

Inferring seismic hazard in Sichuan-Yunnan region of China based on the modern earthquake catalogue (1980-2019)

Based on the modern earthquake catalogue,the incomplete centroidal voronoi tessellation(ICVT)method was used in this study to estimate the seismic hazard in Sichuan-Yunnan region of China.We calculated spatial distributions of the total seismic hazard and background seismic hazard in this area.The Bayesian delaunay tessellation smoothing method put forward by Ogata was used to calculate the spatial distributions of b-value.The results show that seismic hazards in Sichuan-Yunan region are high,and areas with relatively high hazard values are distributed along the main faults,while seismic hazards in Sichuan basin are relatively low.

Mapping Seismic Hazard for Canadian Sites Using Spatially Smoothed Seismicity Model

The estimated seismic hazard based on the delineated seismic source model is used as the basis to assign the seismic design loads in Canadian structural design codes.An alternative for the estimation is based on a spatially smoothed source model.However,a quantification of differences in the Canadian seismic hazard maps(CanSHMs)obtained based on the delineated seismic source model and spatially smoothed model is unavailable.The quantification is valuable to identify epistemic uncertainty in the estimated seismic hazard and the degree of uncertainty in the CanSHMs.In the present study,we developed seismic source models using spatial smoothing and historical earthquake catalogue.We quantified the differences in the estimated Canadian seismic hazard by considering the delineated source model and spatially smoothed source models.For the development of the spatially smoothed seismic source models,we considered spatial kernel smoothing techniques with or without adaptive bandwidth.The results indicate that the use of the delineated seismic source model could lead to under or over-estimation of the seismic hazard as compared to those estimated based on spatially smoothed seismic source models.This suggests that an epistemic uncertainty caused by the seismic source models should be considered to map the seismic hazard.

Integration of Geological, Geophysical and Seismological Data for Seismic Hazard Assessment Using Spatial Matching Index

Probabilistic seismic hazard assessment (PSHA) takes into account as much data as possible for defining the initial seismic source zone model. In response to this, an algorithm has been developed for integration of geological, geophysical and seismological data through a spatial index showing the presence or absence of a potential seismic source feature in the input data. The spatial matching index (SMI) is calculated to define the coincidence of independent data showing any indications for existence of a fault structure. It is applied for hazard assessment of Bulgaria through quantification of the seismic potential of 416 square blocks, 20 × 20 km in size covering the entire territory of Bulgaria and extended by 20 km outside of the country borders. All operations are carried out in GIS environment using its capabilities to work with different types of georeferenced spatial data. Results show that the highest seismic potential (largest SMI) is observed in 56 block elements (13% of the territory) clearly delineating cores of the source zones. Partial match is registered in 98 block elements when one of the features is missing. Not any evidence for earthquake occurrence is predicted by our calculation in 117 elements, comprising 28% of the examined area. The quantitative parameter for spatial data integration which is obtained in the present research may be used to analyze information regardless of its type and purpose.

Seismic Hazard Analysis of China's Mainland Based on a New Seismicity Model

Based on the seismic source model in the Fifth Generation Seismic Ground Motion Parameters Zonation Map of China(FGSGMPZMC),a new seismic fault model,the new zonation of seismic risk areas(SRAs),and the estimation of seismicity rates for 2021-2030,this study constructed a new time-dependent seismic source model of China’s mainland,and used the probabilistic seismic hazard analysis method to calculate seismic hazard by selecting the ground motion models(GMMs)suitable for seismic sources in China.It also provided the probabilities of China’s mainland being affected by earthquakes of modified Mercalli intensity(MMI)Ⅵ,Ⅶ,Ⅷ,Ⅸ,and≥Ⅹin 2021-2030.The spatial pattern of seismic hazards presented in this article is similar to the pattern of the FGSGMPZMC,but shows more details.The seismic hazards in this study are higher than those in the FGSGMPZMC in the SRAs and fault zones that can produce large earthquakes.This indicates that the seismic source model construction in this study is scientific and reasonable.There are certain similarities between the results in this study and those of Rong et al.(2020)and Feng et al.(2020),but also disparities for specific sites due to differences in seismic source models,seismicity parameters,and GMMs.The results of seismic hazard may serve as parameter input for future seismic risk assessments.The hazard results can also be used as a basis for the formulation of earthquake prevention and mitigation policies for China’s mainland.

Strong motion simulation by the composite source modeling:A case study of 1679 M8.0 Sanhe-Pinggu earthquake

In this study, a composite source model has been used to calculate the realistic strong ground motions in Beijing area, caused by 1679 Ms8.0 earthquake in Sanhe-Pinggu. The results could provide us the useful physical parameters for the future seismic hazard analysis in this area. Considering the regional geological/geophysical background, we simulated the scenario earthquake with an associated ground motions in the area ranging from 39.3°N to 41. 1°N in latitude and from 115.35°E to 117.55°E in longitude. Some of the key factors which could influence the characteristics of strong ground motion have been discussed, and the resultant peak ground acceleration （PGA） distribution and the peak ground velocity （PGV） distribution around Beijing area also have been made as well. A comparison of the simulated result with the results derived from the attenuation relation has been made, and a sufficient discussion about the advantages and disadvantages of composite source model also has been given in this study. The numerical results, such as the PGA, PGV, peak ground displacement （PGD）, and the three-component time-histories developed for Beijing area, have a potential application in earthquake engineering field and building code design, especially for the evaluation of critical constructions, government decision making and the seismic hazard assessment by financial/insurance companies.

A practical framework for performance-based reliability analysis of subway stations based on a faultestructure combined system

It is necessary to pay particular attention to the uncertainties that exist in an engineering problem to reduce the risk of seismic damage of infrastructures against natural hazards.Moreover,certain structural performance levels should be satisfied during strong earthquakes.However,these performance levels have been only well described for aboveground structures.This study investigates the main uncertainties involved in the performance-based seismic analysis of a multi-story subway station.More than 100 pulse-like and no pulse-like ground motions have been selected.In this regard,an effective framework is presented,based on a set of nonlinear static and dynamic analyses performed by OpenSees code.The probabilistic seismic demand models for computing the free-field shear strain of soil and racking ratio of structure are proposed.These models result in less variability compared with existing relations,and make it possible to evaluate a wider range of uncertainties through reliability analysis in Rtx software using the Monte Carlo sampling method.This work is performed for three different structural performance levels(denoted as PL1ePL3).It is demonstrated that the error terms related to the magnitude and location of earthquake excitations and also the corresponding attenuation relationships have been the most important parameters.Therefore,using a faultestructure model would be inevitable for the reliability analysis of subway stations.It is found that the higher performance level(i.e.PL3)has more sensitivity to random variables than the others.In this condition,the pulse-like ground motions have a major contribution to the vulnerability of subway stations.

基于ETAS模型的余震概率性地震危险性分析

余震概率性地震危险性分析对主震发生后的地震风险评估至关重要。经典的余震概率性地震危险性分析框架基于Reasenberg-Jones(R-J)模型建立,但R-J模型对复杂的地震序列可能存在预测失效的问题,因此,将对真实余震序列描述较好的传染型余震序列模型(epidemic-type aftershock sequence,ETAS)结合到余震概率性地震危险性分析框架中,以2008年汶川7.9级余震序列和2014年鲁甸6.2级余震序列为例,评估余震危险性的重要性以及探讨ETAS模型相对于R-J模型在余震概率性地震危险性分析中的差异。结果表明:余震危险性水平与主震震级大小有关,主震震级越大,余震危险性水平越高,持续时间越久,对于震级较大的强主震事件,主震发生后早期的余震危险性不容忽略。对于汶川7.9级和鲁甸6.2级地震事件,在余震发生率预测效能上ETAS模型优于R-J模型,而在余震危险性评估中,余震危险性的大小取决于余震发生率,基于R-J模型计算的余震发生率大于ETAS模型计算的余震发生率,因此,在余震危险性评估中使用R-J模型相比于ETAS模型会造成对余震危险性水平的高估,ETAS模型可用于改进余震概率性地震危险性评估框架。

考虑地震事件内空间相关性的区域概率地震危险性分析

一次地震事件不同地点的地震动强度参数与结构响应参数之间是空间相关的,相关的地震效应将导致地震损失急剧集中与积累,从而造成灾难性事件,但是现有的区域尺度地震风险评估并没有考虑地震动的空间相关性。该文采用地统计学方法表征地震事件内地震动强度参数的空间相关性,提出了理论半变异函数的几何稳健估计方法,并采用加权最小二乘法实现对短距离空间相关性的准确高效评估。以新潟越冲地震为例,基于指数半变异函数模型,采用加权最小二乘法对几何稳健估计半变异函数值进行拟合,得到了PGA、PGV和0 s~10 s谱加速度的空间相关性函数,提出了变程b值的预测模型,结果表明:相比于短周期谱加速度,长周期谱加速度的空间相关性衰减速率更小,且在T=0.45 s处存在拐点。将所开发的空间相关性模型应用于区域概率地震危险性分析,采用Monte Carlo方法实现了空间相关随机场的区域地震动强度参数的模拟,改进了传统区域地震危险性分析的方法,发现绝大多数情况下考虑空间相关性的年超越概率大于未考虑空间相关性的年超越概率,表明考虑空间相关性对于建筑群落及基础设施风险评估、韧性城市建设等具有重要的指导意义。

基于广义条件强度参数的水平和竖向地震动联合选取研究

为了合理地考虑竖向地震作用和实现水平和竖向地震动的联合选取,提出了基于广义条件强度参数的水平和竖向地震动联合选取方法:扩展广义条件强度参数的基本理论,提出水平和竖向地震动广义条件强度参数分布的构建方法,并与“无条件分布”对比,提出基于广义条件强度参数的水平和竖向地震动联合选取方法的基本理论,给出以水平强度参数作为条件的实际算例,利用现有水平-水平、水平-竖向强度参数相关系数模型构建水平和竖向地震动广义条件强度参数目标分布,对目标地震动数据库进行联合选取,将选取结果与传统选取方法进行对比,说明该方法的合理性。结果表明:构建出的水平和竖向广义条件强度参数分布与“无条件”分布之间存在一定差异;水平和竖向地震动联合选取结果与目标理论分布匹配良好;与仅考虑水平向广义条件强度参数地震动选取方法相比,联合选取方法能够考虑竖向地震动特性,并且不会对水平向造成影响,提出的水平和竖向地震动联合选取方法能够更加合理地、全面地考虑水平和竖向地震动特性,为工程结构在水平和竖向地震动作用下的抗震性能研究提供地震动输入基础。

基于改进云图法的结构概率地震需求分析

概率地震需求分析是美国太平洋地震工程研究中心(Pacific Earthquake Engineering ResearchCenter,PEER)提出的新一代"性能化地震工程(Performance-Based Earthquake Engineering,PBEE)"理论框架的重要一环。传统的概率地震需求分析方法称为"云图法",这种方法针对确定性结构进行一系列地震动作用下的非线性动力分析,从而得到地震动强度参数与结构地震需求的"云图"。然而,传统的云图法只能考虑地震动的不确定性,而无法考虑结构的不确定性。为此,结合拉丁超立方体抽样技术,提出一种能综合考虑地震动不确定性和结构不确定性的改进云图法,并将传统的概率地震需求分析内容拓展为概率地震需求模型、概率地震需求易损性分析、概率地震需求危险性分析三个层次。以一榀五层三跨钢筋混凝土框架结构为例,分别采用传统云图法和改进云图法对其进行概率地震需求分析,得到了该结构的概率地震需求模型、地震需求易损性曲线和地震需求危险性曲线。分析结果表明:提出的方法可以有效地考虑地震动与结构的不确定性,避免不考虑结构的不确定性而低估结构的地震风险性。

新版地震区划图地震活动性模型与参数确定

地震活动性模型和地震动预测模型是概率地震危险性分析的两个核心。在新版地震区划图中,依据板内地震活动空间不均匀性分布的特点,在概率地震危险性分析方法(CPSHA)中采用了由地震统计区、背景潜在震源区和构造潜在震源区构成的三级层次性潜在震源区模型,并构建了相应的地震活动性模型。本文在论述CPSHA方法及其地震活动性模型基本概念的基础上,重点介绍了新版地震区划图地震活动性模型的三级潜在震源区模型的构成、地震活动性假定和基本特点,同时,也对新版地震区划图地震活动性模型的重要参数确定思路、方法与结果进行了介绍。本文将为更好地认识与理解我国新版地震动参数区划图提供有益的参考。

中国地震滑坡危险性评估及其对国土空间规划的影响研究

中国是世界上地震滑坡灾害最为严重的国家之一。考虑地质构造、地形地貌、地层岩性、河流、地震动参数等6类影响因素,针对50年超越概率10%的抗震设防水准,分别开展了基于信息量模型和Newmark模型的地震滑坡危险性评估。基于最不利原则对两项结果进行地震滑坡危险性综合分区,揭示了中国地震滑坡高危险区集中在南北构造带、青藏高原周缘、鄂尔多斯周缘、天山山脉、台湾山脉等5个活动地块边界或地貌过渡带的空间分布特征。通过地震滑坡危险对主要山区城市的影响分析,显示:34个省级行政单元中的云南、四川、甘肃、台湾4省区受影响严重;370个主要城市中的48个城市受影响严重,其中44个城市有活动断裂穿越;9类主体功能规划区中,国家和省级优化开发区域总体较适于城市开发建设;25个经济区与城市群中,总体较适于开发建设,但是滇中、关天、成渝、兰西等4个经济区与城市群受影响严重;14个集中连片特困地区中,滇西边境、乌蒙、秦巴、六盘等4个地区受影响严重,深度贫困区的“三州”受影响严重。这些区域需要在地质灾害防治和国土空间规划中予以特别关注。

以空间光滑的地震活动性模型为空间分布函数的地震危险性分析方法

根据华北地区的地震目录,建立了4个空间光滑的地震活动性模型,并以这些模型为空间分布函数,将华北地震区每个地震带的地震年发生率分配到空间格点中,计算这一地区的地震危险性.结果表明,采用仪器记录地震计算得到的地震活动性模型和地震危险性结果能够反映华北地区现今的地震活动水平和地震危险性水平,符合人们对现今华北地区地震危险性的认识;采用历史破坏性地震(M≥4.7)计算的地震活动性模型和地震危险性结果,较好地反映了华北地区中强地震活动区的地震危险性水平;以地震应变计算地震活动率,并根据点椭圆模型和线椭圆模型计算得到的地震活动性模型,能够较好地反映大地震的活动水平和空间构造特征.将根据4个模型计算得到的50年超越概率10%峰值加速度(PGA)分布加权平均,得到综合的华北地区PGA分布,并将该PGA分布与根据《中国地震动参数区划图》中综合潜源方案计算得到的50年超越概率10%的PGA分布做了比较,发现二者无本质差别,均能反映华北地震区的地震危险性水平.当然,二者也具有一定的差异:前者计算得到的符合PGA≥100cm/s2条件的区域面积明显要比后者的大,而符合PGA≥250cm/s2条件的区域面积则比后者的要小.这主要是由于潜在震源区类型和空间分布函数不同造成的.

复合地震源模拟强地面运动——以1679年三河—平谷Ms8.0地震为例

利用复合震源模型和人工合成地震图的算法，以1679年三河—平谷Ms8．0地震为例，计算了北京地区的宽频带强地面运动．其结果可为今后该地区的地震危险性评估和工程抗震提供一定的物理参数．通过考察该地区的地质与地球物理区域背景，利用计算机数值模拟的方法，对北纬39．3°～41．1°、东经115．35°～117．55°所围限的北京范围进行了设定地震的仿真模拟，并合成了强地面运动．通过分析影响强地面运动的几个关键因素，给出了北京地区强地面运动峰值加速度和速度分布特征，比较了合成强地面运动记录与通过衰减关系计算所得的结果．同时，还对复合震源模型的优点和局限性给出了充分的讨论．利用数值模拟方法所得的较为真实的强地面运动参数，即加速度、速度、位移和时程特征，可为北京地区工程建设的抗震设计、救援设施的选址、以及金融及保险部门的风险性评估提供一定的依据．

基于MAPGIS的概率性地震危险性分析

对工程场地的地震危险性分析是地震安全性评价的主要方法,并且为工程师提供抗震参数.在分析国内概率性地震危险性分析(PSHA)方法基础上,提出了基于GIS的概率性地震危险性分析的可行性方案.通过MAPGIS二次开发编写了地震危险性分析程序,并以三峡坝区某工程场地为例对程序进行了测试.基于MAPGIS的概率性地震危险性分析程序提供友好的人机交互界面,提高了地震危险性分析的可操作性,更重要的是帮助用户从空间数据中挖掘更多的信息.

余震时空丛集对概率地震危险性分析的影响

本文以东北、华北及川滇地区为例,系统研究了余震时空丛集对概率地震危险性分析的影响.采用基于传染型余震序列模型(ETAS)的蒙特卡罗模拟方法,模拟了包含余震和不包含余震的两套地震序列,然后以模拟地震目录为基础输入,采用基于空间光滑地震活动性模型的地震危险性分析方法计算了两套地震危险性结果——PGA(Peak Ground Acceleration,峰值加速度),通过分析比较这两套PGA的绝对差值和相对差值来研究余震时空丛集对概率地震危险性分析的影响.研究结果表明余震对50年超越概率10%地震危险性计算结果的影响均值为6%左右,最大可达10%,并且随着超越概率水平的提高,余震影响也越大.弱地震活动区余震对概率地震危险性分析的影响要高于强地震活动区.研究结果还进一步揭示两套PGA结果绝对差值的最大值约为15 cm·s^(-2),且出现在高PGA区,这意味着余震对概率地震危险性计算结果不会产生显著影响.因此在地震区划或一般性地震危险性分析中可考虑不用删除余震.

空间光滑地震活动性模型中光滑函数的比较研究

使用Frankel提出的基于空间光滑地震活动性模型的地震危险性分析方法,选择华南、华北、川滇3个地区的地震记录,比较分析了高斯、幂律和地震分形分布光滑函数3种光滑函数在不同地区的适用性.结果表明,使用交叉验证法可以为高斯光滑函数选取合适的相关距离c值,光滑得到的地震活动性模型能够真实反映研究区域的地震活动特征,根据活动性模型计算得出的峰值加速度(PGA)分布也符合人们对研究区域地震危险性的认识.幂律光滑函数适用于地震活动性较强的地区,且具有容易求取光滑参数的优点.光滑程度较低的幂律光滑函数不适用于地震活动性弱的地区,在该类地区应选择光滑程度较高的高斯光滑函数.地震分形分布光滑函数不适用于地震活动较强且地震活动强度差异较大的地区,其容易过分高估高震级地震对地震危险性的影响,而忽略了低震级地震对地震危险性的贡献.但对于地震活动较弱且地震活动强度差异较小的地区,可使用地震分形分布光滑函数,且同样具有容易求取光滑参数的优点.

大跨结构多维多点输入抗震研究进展

对于大跨度结构来说,应该考虑地震动的多维多点效应。从国内外发展现状及取得的主要研究进展和近期的发展动向等角度,对大跨度结构多维多点输入抗震的研究现状进行了系统的综述和总结。首先论述了多维地震动及其相关性,从地震动的各个分量之间的强度比、频率、持时及相关性等方面说明地震动分量的特性;然后论述地震动时空模型,侧重于反映地震动空间变化的相关函数模型的研究现状;最后比较了大跨度结构考虑多维多点输入的抗震计算方法,包括反应谱法、时程分析法以及随机振动分析法。对今后关于这一问题所应开展的研究提出了建议。