基于广义帕累托分布的地震震级分布尾部特征分析

极值理论在地震危险性分析中有着重要应用,发震震级超过某一阈值的超出量分布可以近似为广义帕累托分布.基于广义帕累托分布给出了若干地震活动性参数的估计公式,包括强震震级分布、地震复发周期和重现水平、期望重现震级、地震危险性概率和潜在震级上限等;以云南地区震级资料为基础数据,讨论了阈值选取、模型拟合诊断和参数估计;在此基础上计算了该地区的地震活动性参数.结果表明,广义帕累托分布较好地刻画了强震震级分布,通过超阈值(POT)模型计算的复发周期与实际复发间隔统计基本一致,高分位数估计在一定阈值范围内表现稳定,为工程抗震中潜在震级上限的确定提供了一种途径.     

基于广义帕累托分布的地震震级分布尾部特征分析

极值理论在地震危险性分析中有着重要应用, 发震震级超过某一阈值的超出量分布可以近似为广义帕累托分布. 基于广义帕累托分布给出了若干地震活动性参数的估计公式, 包括强震震级分布、 地震复发周期和重现水平、 期望重现震级、 地震危险性概率和潜在震级上限等; 以云南地区震级资料为基础数据, 讨论了阈值选取、 模型拟合诊断和参数估计; 在此基础上计算了该地区的地震活动性参数. 结果表明, 广义帕累托分布较好地刻画了强震震级分布, 通过超阈值(POT)模型计算的复发周期与实际复发间隔统计基本一致, 高分位数估计在一定阈值范围内表现稳定, 为工程抗震中潜在震级上限的确定提供了一种途径.      

基于广义帕累托分布的马尼拉海沟俯冲带地震危险性估计

选取马尼拉海沟俯冲带作为潜源区, 基于广义帕累托分布, 通过对一定时段内超过某一阈值的震级数据进行拟合, 建立该潜源区地震危险性估计模型, 估计强震重现水平和震级上限, 并对估计结果的不确定性进行了分析, 得到马尼拉海沟俯冲带震级上限为9.0级, 10 a、 50 a、 100 a、 200 a马尼拉海沟俯冲带的震级重现水平期望值分别为7.1级、 7.6级、 7.7级、 7.9级。     

中国大陆活动地块边界带强震震级分布特征研究

本文利用基于广义帕累托分布的超阈值分布模型,对中国大陆活动地块边界带强震震级分布特征开展研究,给出了各活动地块边界带强震震级的广义帕累托分布参数估计。结果表明,广义帕累托分布较好地拟合了各边界带强震数据,形状参数估计均为负值,说明对应震级应有上限,因此广义帕累托分布为潜在震级上限提供了一种自然的刻画。在此基础上,估计了震级上限,并给出了分布0.99997高分位数估计,通过与历史最大震级比较发现,高分位数估计相对稳健。在地震发生过程为泊松过程假设下,推导了广义帕累托分布与广义极值分布之间的联系,揭示了一种利用强震数据推断最大震级分布的可能途径。     

基于POT模型的昆仑山地区地震统计特征分析

极值统计是研究较少发生但一旦发生即产生极大影响的随机事件的有效方法。本文以地震活动频繁的昆仑山地区作为研究区域,建立了基于广义帕累托分布的超阈值（POT）模型,并讨论了该地区若干地震活动性参数,包括强震震级分布、潜在震级上限、强震平均复发间隔、一定周期内的强震发震概率、一定时期内的重现水平和超定值重现震级。经统计分析得到:该地区震级阈值选定为M_S5.5,超阈值期望震级为M_S6.81,潜在震级上限高达M_S9.08,M_S8.0的平均复发间隔仅为66.8年,未来3年该地区发生M_S5.5～M_S6.5的概率在80%以上,百年重现水平即可达到历史最大震级M_S8.1。     

龙门山地区的地震活动性广义帕累托模型构建

利用1930—2016年龙门山地区M≥4.5历史地震目录,通过时空窗法减少余震对统计结果的影响,构建了该地区广义帕累托分布的超出量分布模型,估计了龙门山地区震级上限。结果表明:广义帕累托分布较好地拟合了龙门山地区强震数据,形状参数估计均为负值,最大震级分布存在有限上界,震级上限为8.3。     

龙门山地区地震活动性广义极值模型构建

以龙门山地区为研究区, 利用1931年至2010年历史地震数据, 时限取80年, 时间间隔取10年, 构建地震活动性广义极值模型, 估计龙门山地区震级上限和强震重现水平。 结果表明龙门山地区地震活动性广义极值模型服从具有有限上界的Weibull分布, 震级上限为8.3, 未来20年、 50年、 100年龙门山地区的强震重现水平分别为7.9、 8.1、 8.1。 起始年由1930年至1933年逐年平移, 时间间隔不变, 震级上限及强震重现水平的计算结果相差不到0.2级, 表明本文构建的龙门山地区广义极值模型具有一定程度的稳定性, 可为地震区划以及地震危险性分析研究提供参考。     

基于轮廓似然估计的广义极值分布在地震中长期预测中的应用

为描述强震预测的不确定性,在地震预报极值分析模型的参数估计中,引入轮廓似然估计法。对广义极值分布中形状参数和地震重现水平的轮廓似然估计原理及数值算法进行了详细地阐述,并利用构建的广义极值分布模型对东昆仑地震带进行了地震危险性分析。关于形状参数和重现水平的点估计,以及10年以内的重现水平置信区间的估计,轮廓似然估计法与极大似然估计法效果基本相同,但在中长期地震重现水平置信区间的预测中,轮廓似然估计法得到的关于置信水平不对称的置信区间,在强震水平下对预测震级的不确定性表达更准确,预测结果更加有效。      

完整资料的地震危险性参数估计及敏感性分析

应用考虑震级不确定笥和资料完整性估计地震危险性参数的极大似然法，分别采用１９４０年和１０７０年至１９９３年完整的地震资料，计算了汾渭地震带及陕南地区的地震危险性参数。结果表明：利用近几十年来的完整地震资料结合研究区历史上发生的最大地震，可以得到较为可靠的地震危险性参数；参数敏感性分析表明，完整震级不确定性对β的影响较小；随震级不确定性的增大地震年发生率减小；在资料完整的前提下，震级下限在一定范围内     

根据不完整数据文件估计地震危险性参数第Ⅲ部分:引入地震发生模型的不确定性

大多数概率地震危险性分析方法要求知道至少3个震源参数,即平均地震活动率λ、古登堡—里克特b值和地区特征(孕震源)的最大可能震级mmax。目前,所有使用这3个参数的地震危险性评估方法几乎都明确地假定这3个参数在时间和空间上保持不变。但是,对大多数地震目录更细致的分析表明,地震活动率λ和古登堡—里克特b值都存在显著的时空变化。本文,这些地震危险性参数的最大似然估计考虑目录的不完整性、震级测定的不确定性以及所用地震发生模型的不确定性。通过假定平均地震活动率λ和古登堡—里克特b值为伽马分布的随机变量引入地震发生模型的不确定性。该方法扩展了经典的古登堡—里克特的频度—震级关系,地震数量按对应的复合量泊松分布(Benjamin,1968;Campbell,1982,1983)。使用所提出的方法估计了在南非当代历史上经历最强、破坏性最大地震,即1969年9月29日M_W6.3塞里斯—塔尔巴赫地震地区的地震活动性参数。结果表明引入地震发生模型的不确定性会减小平均复发周期,使所估计的地震危险性增大。此外,研究证实考虑震级的不确定性则作用相反,即那会增大复发周期或等效地减小估计的地震危险性。     

Effects of seismic declustering on seismic hazard assessment: a sensitivity study using the Turkish earthquake catalogue

Earthquakes trigger other earthquakes and build up clusters in space and time that in turn create a bias in seismic catalogues. Therefore, declustering is considered as a prerequisite in seismic studies, particularly for probabilistic seismic hazard analysis, not only to eliminate the bias but also to decouple mainshocks and triggered events. However, a declustering process is not a straightforward task due to the complex nature of earthquake phenomena. There exist several declustering methods that mostly employ subjective rules to distinguish between background seismicity and offsprings. Eventually, the final declustered catalogues usually deviate significantly according to the employed method. This issue is raising some concerns, such as how to select the most suitable declustering algorithm, or to assess how this selection affects seismic hazard assessment. In consequence, the main goal of this paper is to quantify the sensitivity of seismic hazard assessments to different declustering techniques. Accordingly, the recently compiled Turkish earthquake catalogue was declustered by making use of three declustering algorithms. A total of six declustered catalogues, two catalogues per method, one by implementing the default input parameters, and one by altering the free input parameters of the employed methods, were produced. The clusters of selected earthquakes were studied in terms of the spatial–temporal distribution of earthquake sequences. A sensitivity analysis was conducted through the major steps of seismic hazard assessment for Istanbul metropolitan city. The seismicity of Istanbul and surroundings was modeled on the basis of four areal source zones. Comparative studies showed that, while the selected declustering algorithm did not significantly affect the completeness periods of moderate to large size earthquakes, it considerably altered those of small magnitude events (e.g. M_w 4.3–5.2) and consequently the recurrence parameters of the source zones. Depending on the declustering algorithm and input parameters, the activity rate was observed to vary up to a factor of two. The differences in the declustered catalogues obtained from different declustering approaches resulted in considerable variations in seismic hazard estimations. The hazard maps at return periods of 475 and 2475 years indicated that peak ground acceleration values may vary up to 20% at some locations. Moreover, the differences in 5% damped elastic spectral accelerations at T = 0.2 for the return periods of 475 and 2475 years are about 18 and 12%, respectively, on the southern shores of Istanbul where the highest hazard levels are observed.     

Probabilistic seismic hazard assessment for Romania and sensitivity analysis: A case of joint consideration of intermediate-depth (Vrancea) and shallow (crustal) seismicity

The earthquake risk on Romania is one of the highest in Europe, and seismic hazard for almost half of the territory of Romania is determined by the Vrancea seismic region, which is situated beneath the southern Carpathian Arc. The region is characterized by a high rate of occurrence of large earthquakes in a narrow focal volume at depth from 70 to 160 km. Besides the Vrancea area, several zones of shallow seismicity located within and outside the Romanian territory are considered as seismically dangerous. We present the results of probabilistic seismic hazard analysis, which implemented the “logic tree” approach, and which considered both the intermediate-depth and the shallow seismicity. Various available models of seismicity and ground-motion attenuation were used as the alternative variants. Seismic hazard in terms of macroseismic intensities, peak ground acceleration, and response spectra was evaluated for various return periods. Sensitivity study was performed to analyze the impact of variation of input parameters on the hazard results. The uncertainty on hazard estimates may be reduced by better understanding of parameters of the Vrancea source zone and the zones of crustal seismicity. Reduction of uncertainty associated with the ground-motion models is also very important issue for Romania.     

Earthquake Hazard Parameters Estimated in Crete Island and the Adjacent Area

—?Earthquake hazard parameters are estimated by the application of the maximum likelihood method. The technique is based on a procedure which utilizes data of different quality, e.g., those in which the uncertainty in the assessment of the magnitudes is great and those in which the magnitudes are computed with great precision. In other words the data were extracted from both historical (incomplete) and recorded (complete) files. The historical part of the catalogue contains only the strongest events, whereas the complete part can be divided into several sub-catalogues; each one assumed to be complete above a specified magnitude threshold. Uncertainty in the determination of magnitudes has also been taken into account. The method allows us to estimate the earthquake hazard parameters which are the maximum regional magnitude, M _max, the activity rate, λ, of the seismic events and the well known value β (b=β?log?e), which is the slope of the magnitude-frequency relationship. All these parameters are of physical significance. The mean return periods, RP, of earthquakes with a certain lower magnitude M?≥?m are also determined. The method is applied in the Island of Crete and the adjacent area, where catastrophic earthquakes are known from the historical era. The earthquake hazard of the whole area is divided in a cellular manner which allow the analysis of the localized hazard parameters and the representation of their regional variation. The seismic hazard analysis, which is expressed by: (a) The annual probability of exceedance of a specified value of magnitude and (b) the return periods (in years) that are expected for given magnitudes, for shallow events is finally performed for shallow events. This hazard analysis is useful for both theoretical and practical reasons and provides a tool for earthquake resistant design in both areas of low and high seismicity.     

The application of seismic data with different precision in the determination of seismicity parameters

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A Probabilistic Assessment of Earthquake Hazard Parameters in NW Himalaya and the Adjoining Regions

The maximum likelihood estimation method is applied to study the geographical distribution of earthquake hazard parameters and seismicity in 28 seismogenic source zones of NW Himalaya and the adjoining regions. For this purpose, we have prepared a reliable, homogeneous and complete earthquake catalogue during the period 1500–2010. The technique used here allows the data to contain either historical or instrumental era or even a combination of the both. In this study, the earthquake hazard parameters, which include maximum regional magnitude (M _max), mean seismic activity rate (λ), the parameter b (or β?=?b/log e) of Gutenberg–Richter (G–R) frequency-magnitude relationship, the return periods of earthquakes with a certain threshold magnitude along with their probabilities of occurrences have been calculated using only instrumental earthquake data during the period 1900–2010. The uncertainties in magnitude have been also taken into consideration during the calculation of hazard parameters. The earthquake hazard in the whole NW Himalaya region has been calculated in 28 seismogenic source zones delineated on the basis of seismicity level, tectonics and focal mechanism. The annual probability of exceedance of earthquake (activity rate) of certain magnitude is also calculated for all seismogenic source zones. The obtained earthquake hazard parameters were geographically distributed in all 28 seismogenic source zones to analyze the spatial variation of localized seismicity parameters. It is observed that seismic hazard level is high in Quetta-Kirthar-Sulaiman region in Pakistan, Hindukush-Pamir Himalaya region and Uttarkashi-Chamoli region in Himalayan Frontal Thrust belt. The source zones that are expected to have maximum regional magnitude (M _max) of more than 8.0 are Quetta, southern Pamir, Caucasus and Kashmir-Himanchal Pradesh which have experienced such magnitude of earthquakes in the past. It is observed that seismic hazard level varies spatially from one zone to another which suggests that the examined regions have high crustal heterogeneity and seismotectonic complexity.     

Seismic hazard in the Northwestern Apennines

A study of the seismic hazard for the Northwestern Apennines, based on seismotectonic and seismicity data, is presented. Starting from a seismotectonic analysis, showing the complex structural evolution of the region, the seismic activity in the period 1000–1975 has been modeled by some seismic source zones justified by geostructural and seismological considerations. The recurrence statistical parameters and the attenuation laws have been determined for all these sources. With an appropriate analysis method, maps of seismic hazard for return periods of 50, 200, and 500 years were elaborated. Finally, a comparison with the map of maximum felt intensity and with hazard values calculated by a different approach is presented.     

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．      

Assessment of <Emphasis Type="Italic">pre-crisis</Emphasis> and <Emphasis Type="Italic">syn-crisis</Emphasis> seismic hazard at Campi Flegrei and Mt. Vesuvius volcanoes,Campania, southern Italy

In this study, we address the issue of short-term to medium-term probabilistic seismic hazard analysis for two volcanic areas, Campi Flegrei caldera and Mt. Vesuvius in the Campania region of southern Italy. Two different phases of the volcanic activity are considered. The first, which we term the pre-crisis phase, concerns the present quiescent state of the volcanoes that is characterized by low-to-moderate seismicity. The second phase, syn-crisis, concerns the unrest phase that can potentially lead to eruption. For the Campi Flegrei case study, we analyzed the pattern of seismicity during the 1982–1984 ground uplift episode (bradyseism). For Mt. Vesuvius, two different time-evolutionary models for seismicity were adopted, corresponding to different ways in which the volcano might erupt. We performed a site-specific analysis, linked with the hazard map, to investigate the effects of input parameters, in terms of source geometry, mean activity rate, periods of data collection, and return periods, for the syn-crisis phase. The analysis in the present study of the pre-crisis phase allowed a comparison of the results of probabilistic seismic hazard analysis for the two study areas with those provided in the Italian national hazard map. For the Mt. Vesuvius area in particular, the results show that the hazard can be greater than that reported in the national hazard map when information at a local scale is used. For the syn-crisis phase, the main result is that the data recorded during the early months of the unrest phase are substantially representative of the seismic hazard during the whole duration of the crisis.     

A probabilistic seismic hazard assessment for the Turkish territory: part II—fault source and background seismicity model

Over the years, several local and regional seismic hazard studies have been conducted for the estimation of the seismic hazard in Turkey using different statistical processing tools for instrumental and historical earthquake data and modeling the geologic and tectonic characteristics of the region. Recently developed techniques, increased knowledge and improved databases brought the necessity to review the national active fault database and the compiled earthquake catalogue for the development of a national earthquake hazard map. A national earthquake strategy and action plan were conceived and accordingly with the collaboration of the several institutions and expert researchers, the Revision of Turkish Seismic Hazard Map Project (UDAP-Ç-13-06) was initiated, and finalized at the end of 2014. The scope of the project was confined to the revision of current national seismic hazard map, using the state of the art technologies and knowledge of the active fault, earthquake database, and ground motion prediction equations. The following two seismic source zonation models are developed for the probabilistic earthquake hazard analysis: (1) Area source model, (2) Fault and spatial smoothing seismic source model (FSBCK). In this study, we focus on the development and the characterization of the Fault Source model, the background spatially smoothed seismicity model and intrinsic uncertainty on the earthquake occurrence-rates-estimation. Finally, PSHA results obtained from the fault and spatial smoothed seismic source model are presented for 43, 72, 475 and 2475 years return periods (corresponding to 69, 50, 10, and 2% probability of exceedance in 50 years) for PGA and 5% damped spectral accelerations at 0.2 and 1.0 s.