Three-parameter generalized exponential distribution in earthquake recurrence interval estimation

The purpose of this article is to study the three-parameter (scale, shape, and location) generalized exponential (GE) distribution and examine its suitability in probabilistic earthquake recurrence modeling. The GE distribution shares many physical properties of the gamma and Weibull distributions. This distribution, unlike the exponential distribution, overcomes the burden of memoryless property. For shape parameter  β> 1, the GE distribution offers increasing hazard function, which is in accordance with the elastic rebound theory of earthquake generation. In the present study, we consider a real, complete, and homogeneous earthquake catalog of 20 events with magnitude above 7.0 (Yadav et al. in Pure Appl Geophys 167:1331–1342, 2010) from northeast India and its adjacent regions (20°–32°N and 87°–100°E) to analyze earthquake inter-occurrence time from the GE distribution. We apply the modified maximum likelihood estimation method to estimate model parameters. We then perform a number of goodness-of-fit tests to evaluate the suitability of the GE model to other competitive models, such as the gamma and Weibull models. It is observed that for the present data set, the GE distribution has a better and more economical representation than the gamma and Weibull distributions. Finally, a few conditional probability curves (hazard curves) are presented to demonstrate the significance of the GE distribution in probabilistic assessment of earthquake hazards.     

On the estimation of earthquake maximum magnitude based on a joint analysis of seismological and geothermal parameters

To improve the reliability of earthquake prediction, it is important to determine those layers in the crust of the earth in which the foci of most strong earthquakes occur. An analysis of regional earthquake catalogues shows that in depressions strong events originate within a specific layer in the middle part of the crust. An investigation of the geothermal regime in the depressions under study shows that the thickness and location of this layer depend on geothermal parameters which correlate with the strongest earthquake magnitude in particular areas. Thus, it seems possible to use geothermal and seismological parameters for estimating the maximum magnitude of earthquakes for at least some areas.     

Precursory swarm and its application for long range earthquake forecasting in Taiwan region

At trenches a few earthquake swarms of low magnitude have been observed before the medium size earthquake swarms. The first swarm was designated as precursory swarm and the second as mainshocks. Seismicity fluctuations before six such mainshocks events of medium size earthquakes of magnitudes ranging from 5.3 to 6.1 occurring in the east belt of Taiwan region have been discussed. A precursory gap between the precursory swarm and mainshock events has been observed. The duration of the gaps increases with magnitudes of the mainshocks suggesting a causal relationship between the two. Regression equations between the largest magnitude in the precursory swarms, the largest mainshock magnitude and the precusory gaps have been given.     

A study of earthquake inter-occurrence times distribution models in Taiwan

Natural Hazards - Statistical studies on earthquake recurrence time probabilities have frequently been applied to seismic hazard analyses. In Taiwan, an instrumental catalog provides a good...     

活动断裂的变形特征及其大地震复发周期的估算

活动断裂是晚更新世10~12万年以来一直在活动, 现在正在活动, 未来一定时期内仍会发生活动的各类断裂。活动断裂控制着大地震的发生,是不同类型地震的发震构造。从活动断裂的变形特征来看,不同性质的活动断裂具有不同的发震构造模型,研究这些问题对认识强震的发震条件,划分潜在的震源区或地震危险区,评估发震构造和发震地点具有重要的意义。基于国内外对不同类型活动断裂的认识,结合近10年来在青藏高原地区对活动断裂的研究,总结了活动断裂的基本变形特征和对大地震复发周期估算的认识。研究表明,东昆仑断裂库塞湖段类似2001年Ms 8.1级大地震的强震复发周期为250～350年,阿尔金断裂康西瓦段类似Ms 7.4大地震的强震复发周期为370～500年,而在青藏高原东缘的龙门山地区,类似2008年5月12日Ms 8.0汶川大地震的强震复发周期为3000～6000年。这些结果可能暗示着走滑断裂大地震的复发周期远短于逆冲断裂大地震的长复发周期,这是值得高度重视和深入研究的新课题。     

玄武岩力学参数的随机性统计与概率分布估计

充分认识岩石力学参数的随机性和合理评估其概率分布特征是客观评价岩石工程稳定性的基础。以白鹤滩大型水电站的斜斑玄武岩和杏仁玄武岩为研究对象,对各约50个试样进行单轴压缩试验获得大量全应力-应变曲线。采用统计分析和假设检验的方法,研究了两种玄武岩的特征强度、变形参数、特征应变和破裂面角度的随机分布特征和最优的概率密度函数形式。分析结果揭示:离散性是玄武岩的固有属性,只有一定数量的多次重复试验才能可靠地评估其基本力学特性;两种玄武岩的特征强度、变形参数、特征应变和破裂面角度的最优概率分布形式并不一致,分别为正态分布、对数正态分布、Weibull分布和Weibull分布。该试验的统计分析结果可为深入认识火成岩的变形破坏规律和工程安全可靠度或失效概率研究提供试验数据支撑。     

Correlating recurrent radon precursors with local earthquake magnitude and crust strain near the Chihshang fault of eastern Taiwan

The active Chihshang fault in the southern segment of longitudinal valley of eastern Taiwan is part of the suture boundary between the Eurasia plate and the Philippine Sea plate. Radon anomalies in groundwater were recorded prior to three major earthquakes—(1) 2003 M _w = 6.8 Chengkung, (2) 2006 M _w = 6.1 Taitung, and (3) 2008 M _w = 5.4 Antung. The epicenters were located 24, 52, and 13 km, respectively, from the radon-monitoring well (D1) in the Antung hot spring about 3 km southeast of the Chihshang fault. Prior to the three major earthquakes, radon decreased from background levels of 787 ± 42, 762 ± 57, and 700 ± 57 pCi/L to minima of 326 ± 9, 371 ± 9, and 480 ± 43 pCi/L, respectively. Based on the radon volatilization model and the rock dilatancy model, this paper correlates the observed radon minima with local earthquake magnitude and crust strain. The correlation is a useful means of forecasting local disastrous earthquakes in the southern segment of longitudinal valley of eastern Taiwan.     

Integration and magnitude homogenization of the Egyptian earthquake catalogue

The aim of the present work is to compile and update a catalogue of the instrumentally recorded earthquakes in Egypt, with uniform and homogeneous source parameters as required for the analysis of seismicity and seismic hazard assessment. This in turn requires a detailed analysis and comparison of the properties of different available sources, including the distribution of events with time, the magnitude completeness, and the scaling relations between different kinds of magnitude reported by different agencies. The observational data cover the time interval 1900–2004 and an area between 22°–33.5° N and 25°–36° E. The linear regressions between various magnitude types have been evaluated for different magnitude ranges. Using the best linear relationship determined for each available pair of magnitudes, as well as those identified between the magnitudes and the seismic moment, we convert the different magnitude types into moment magnitudes M _W, through a multi-step conversion process. Analysis of the catalogue completeness, based on the M _W thus estimated, allows us to identify two different time intervals with homogeneous properties. The first one (1900–1984) appears to be complete for M _W ≥ 4.5, while the second one (1985–2004) can be considered complete for magnitudes M _W ≥ 3.     

汶川地震触发崩滑地质灾害空间分布及影响因素

通过遥感解译和实地考察,获取了2008年汶川地震触发崩滑的空间分布,利用GIS空间分析和Lo-gistic回归,分析崩滑的空间分布特征及其影响因素,建立了地震触发崩滑与其影响因素之间的回归方程。结果表明,(1)研究区共有5 154个崩滑群,覆盖总面积1 139 km2;(2)崩滑沿北川—映秀发震断层的两侧(断层上盘区占90%),呈北东向宽度不一的条带状分布;(3)Ⅺ和Ⅹ烈度区崩滑面积占区域面积的73.2%,Ⅷ度及以下烈度区崩滑面积比例较小;(4)崩滑发育及空间分布不仅受控于发震断层的活动,断层上下盘效应、地形放大效应等也是其重要影响因素。崩滑与其影响因子的回归方程表明:(1)到北川—映秀发震断层距离因子和到震中距离因子的偏回归系数远大于其他因子的偏回归系数,北川—映秀断层发震活动是控制崩滑空间分布的主导因子;(2)岩性软硬程度对崩滑空间分布的影响不显著;(3)地形坡度、高程、坡度变率、多年累积降雨、人工修路及植被覆盖对崩滑的发育产生影响。地形高程因子对崩滑空间分布的影响大于坡度、坡度变率因子的影响。人工道路、多年降雨及植被覆盖对地震崩滑的影响程度依次降低。     

An application of regional time and magnitude predictable model for long-term earthquake prediction in the vicinity of October 8, 2005 Kashmir Himalaya earthquake

A regional time and magnitude predictable model has been applied to estimate the recurrence intervals for large earthquakes in the vicinity of 8 October 2005 Kashmir Himalaya earthquake (25°–40°N and 65°–85°E), which includes India, Pakistan, Afghanistan, Hindukush, Pamirs, Mangolia and Tien-Shan. This region has been divided into 17 seismogenic sources on the basis of certain seismotectonics and geomorphological criteria. A complete earthquake catalogue (historical and instrumental) of magnitude Ms ≥ 5.5 during the period 1853–2005 has been used in the analysis. According to this model, the magnitude of preceding earthquake governs the time of occurrence and magnitude of future mainshock in the sequence. The interevent time between successive mainshocks with magnitude equal to or greater than a minimum magnitude threshold were considered and used for long-term earthquake prediction in each of seismogenic sources. The interevent times and magnitudes of mainshocks have been used to determine the following predictive relations: logT _t = 0.05 M _min + 0.09 M _p − 0.01 log M ₀ + 01.14; and M _f = 0.21 M _min − 0.01 M _p + 0.03 log M ₀ + 7.21 where, T _t is the interevent time of successive mainshocks, M _min is minimum magnitude threshold considered, M _p is magnitude of preceding mainshock, M _f is magnitude of following mainshock and M ₀ is the seismic moment released per year in each seismogenic source. It was found that the magnitude of following mainshock (M _f) does not depend on the interevent time (T _t), which indicates the ability to predict the time of occurrence of future mainshock. A negative correlation between magnitude of following mainshock (M _f) and preceding mainshock (M _p) indicates that the larger earthquake is followed by smaller one and vice versa. The above equations have been used for the seismic hazard assessment in the considered region. Based on the model applicability in the studied region and taking into account the occurrence time and magnitude of last mainshock in each seismogenic source, the time-dependent conditional probabilities (PC) for the occurrence of next shallow large mainshocks (Ms ≥ 6.5), during next 20 years as well as the expected magnitudes have been estimated.     

概率图解法原理及可视化应用研究

概率图解法是一种在二维图形上直观显示品位数据线性特征的数据处理方法,通过对单一品位总体和混合品位总体线性形态的分析,给出了定量的统计分析结果,进而为品位数据集建立合理的地质假设提供依据.品位数据表现为直线形态代表矿床经历一次成矿作用,品位数据曲线出现一个明显的拐点代表该矿床经历了二次成矿作用.目前还没有出现可视化效果好,参数调节灵活,并提供不同参数设定情况下筛分图对比的概率图解法软件.这里在研究概率图解法原理及其在品位数据研究中应用的基础上,利用VB可视化编程技术,完成了概率图筛分软件的研制,为研究矿产普查与勘探中成矿期次和物质来源问题,提供了有价值的信息和依据.     

Resampling methods for evaluating the uncertainty of the nonparametric magnitude distribution estimation in the Probabilistic Seismic Hazard Analysis

The cumulative distribution function (CDF) of magnitude of seismic events is one of the most important probabilistic characteristics in Probabilistic Seismic Hazard Analysis (PSHA). The magnitude distribution of mining induced seismicity is complex. Therefore, it is estimated using kernel nonparametric estimators. Because of its model-free character the nonparametric approach cannot, however, provide confidence interval estimates for CDF using the classical methods of mathematical statistics.To assess errors in the seismic events magnitude estimation, and thereby in the seismic hazard parameters evaluation in the nonparametric approach, we propose the use of the resampling methods. Resampling techniques applied to a one dataset provide many replicas of this sample, which preserve its probabilistic properties. In order to estimate the confidence intervals for the CDF of magnitude, we have developed an algorithm based on the bias corrected and accelerated method (BC_a method). This procedure uses the smoothed bootstrap and second-order bootstrap samples. We refer to this algorithm as the iterated BC_a method. The algorithm performance is illustrated through the analysis of Monte Carlo simulated seismic event catalogues and actual data from an underground copper mine in the Legnica–Głogów Copper District in Poland.The studies show that the iterated BC_a technique provides satisfactory results regardless of the sample size and actual shape of the magnitude distribution.     

利用颗粒流离散元素法研究台湾遽变式滑坡的运动和规程模式

山崩和滑坡的分布在全球非常普遍,往往对民众造成生命与财产极大的损失,仅1992至2001年间,山崩和滑坡造成全球超过9 000人死亡;台湾位于欧亚大陆板块与菲律宾板块的交接处,为当今世界上最活跃的造山带之一,地块极为年轻和不稳定,地震频繁,加上每年夏秋二季的台风侵袭,因此山坡地上极易发生大型遽变式的滑坡事件.台湾近年来最令人瞩目的大型遽变式滑坡事件有草岭的多次滑坡事件(包括1999年集集地震所诱发的滑坡事件)、1999年集集地震所诱发的九份二山崩塌事件和2009年莫拉克台风造成小林村灭村的献肚山滑坡事件[1].     

Structure of earthquake occurrence in space,time and magnitude

Distributions of time between consecutive earthquakes verify an approximately universal scaling law for stationary seismicity. The shape of these distributions is shown to arise as a mixture of one distribution for short‐distance events and an exponential distribution for far‐off events, the distinction from short and long distances being relative to the size of the region studied. The distributions of consecutive distances show a double power law decay and verify an approximate scaling law which guarantees the simultaneous fulfillment of the scaling laws for time. The interplay between space and time can be seen as well by looking at the distribution of distances for a fixed time separation. These results suggest that seismicity can be understood as a series of intertwined independent continuous‐time random walks, with power law‐distributed waiting times and Lévy‐flight jumps. However, a simple model based on these ideas does not capture the invariance of seismicity under renormalization.     

天山山区降水量的空间分布及其估算方法

利用天山山区及周边31个国家基本站1998～2008年期间的逐月降水资料结合TRMM卫星月平均降水资料,使用卫星结合雨量计的降水估算方法,得到天山山区逐月降水空间分布,并运用交叉检验方法对降水估算精度评估,Nash-Sutcliffe效率系数在0.5以上,相关系数高达0.9以上。结果表明,TRMM卫星对西北山区的降水活动有一定的探测能力,能够较好的反映天山山区降水时空变化特征,为山区降水数据稀缺条件下的降水空间分布估算提供方法,为相关的水文、气象等研究提供数据支持。     

The 1946 magnitude 6.1 earthquake in the Valais: site-effects as contributor to the damage

The January 25, 1946 earthquake in the central Valais region in southwest Switzerland was the strongest for the last 150 years. It reached an epicentral intensity Io of VIII in the area of Sierre. The Swiss Earthquake Catalogue (ECOS 2002) assigns a moment magnitude of Mw = 6.1 to the event. Assessment of recordings from European stations resulted in a moment magnitude of 5.8 (Bernardi et al. 2005). The earthquake caused moderate to high damage within a circle of about a 25 kilometer radius. Slight damage occurred up to a distance of 200 kilometers from the epicenter. The goal of this study was to reconstruct the damage field and consider its possible site-effects. We used an approach combining historical research with seismo-/geological investigation including a large number of experiments measuring the fundamental frequency of resonance and the shear-wave velocities of the sedimentary layers, using the characteristics of ambient vibration. This kind of research is relevant, since a huge alpine valley characterizes the Valais region, showing ground conditions that make site-effects likely for earthquakes. While we searched for damage in an unlimited area, our investigation of site-effects was limited to the Rhone valley and to Sion and Sierre in the central Valais region in particular.     

Problems in the application of the SSHAC probability method for assessing earthquake hazards at Swiss nuclear power plants

From 2000 to 2004 a large scale probabilistic seismic hazard analysis (PEGASOS) was created and performed as a research project, sponsored by the Swiss NPP utilities to improve the assessment methodology for seismic risk in support of the plant-specific seismic PRAs. The project followed the methodology of the SSHAC [Senior Seismic Hazard Analysis Committee (SSHAC), 1997. Recommendations for Probabilistic Seismic Hazard Analysis: Guidance on Uncertainty and Use of Experts. NU-REG/CR-6372] procedures at its most elaborate way—level 4. Before practical implementation was to occur, a detailed review was performed including validation tests and analysis of uncertainty propagation. This paper presents the main results of the review. The review revealed that current PSHA (Probabilistic Seismic Hazard Analysis) methodology as based on logic trees, in conjunction with the SSHAC procedures, potentially leads to a significant overestimation of the seismic hazard in areas with low seismic activity due to the inherent possibilities of unconstrained accumulation of uncertainties. The preliminary results of the project did not pass any of our logical geological–scientific benchmark tests used in our attempts to perform a validation process of the PEGASOS analysis method. Some of the problems encountered are of generic nature and shall be studied carefully before making the decision of whether or not the Swiss nuclear power industry will adopt the recommended use of SSHAC-procedures as a basis for the evaluation of the seismic hazard for individual nuclear power plant seismic PRA without correction.     

岩体稳定性评价的模糊概率方法

岩体稳定性受多种不确定性因素的影响,不仅具有随机性,也具有模糊性,属于模糊概率的范畴,利用经典的模糊综合评判方法进行研究将会导致不合理的结果。在模糊概率理论的基础上,建立了一类新的岩体稳定性综合评价方法——模糊概率方法,并提出了模糊权重的概念,从而避免了权重取值带来的不确定性。结合所选取的5个影响岩体稳定性的因素,建立了这5个影响因素的隶属函数与模糊权重;利用该方法对某一地下岩体工程进行分析,并与其他方法评价的结果进行比较,表明了其方法的合理性与可靠性。     

Comparing the spatial patterns of earthquake disaster probability and individual risk perception: a case study of Yongkang Township in Tainan,Taiwan

Natural Hazards - During major earthquake disasters, a lack of preparedness on the part of both officials and citizens can result in serious injuries and fatalities. Indeed, due to the unequal...     

南北地震带大地电流分布与地震活动关系探讨

利用中国南北地震带38个固定地电场台站观测数据,研究该区大地电流场流线和电流矢量的分布特点,分析了大地电流矢量场的涡度和散度,并联系动力学机制讨论了大地电流与南北地震带的关系,探讨地震活动与电流涡度时变的对应性。这是首次应用空间密度较高的地电场台站开展这方面的研究工作。结果表明:(1)大地电流线走向和汇聚特点与构造地块的运动特点具有某种一致性,在构造边界上大地电流矢量存在汇集及分异的现象;(2)大地电流汇聚和发散等现象与断裂构造相关,一般表现为流线沿断裂带走向汇集或发散,在断裂交错地区表现出较复杂的形态;(3)大地电流场涡度分布特点可作为大构造块体运移的电性指示,涡度随时间变化可能为某种地震前兆。