Uncertainties in the estimation of earthquake magnitudes in Greece

Instrumental magnitudes in Greece have been reported as: a) Mmagnitudes based on the records of the Wiechert or Mainka seismographs,b) M_LGR magnitudes based on the records of the Wood-Anderson(WA) seismographs (T_o = 0.8 sec, V_effective 1000) or othershort period seismographs calibrated against WA records and,c) M_LSM magnitudes based on strong motion records(accelerograms). Comparison of such magnitudes with momentmagnitudes, M_w, for 329 earthquakes, with epicenters in thebroader Aegean area, performed in this study, showedthat M, M_LGR+0.5 and M_LSM are practically equalto M_w, with a small overall standard error ( = 0.23).Therefore, equivalent moment magnitudes, M_w ^*,estimated from these magnitudes and reported in the catalogues of theGeophysical Laboratory of the University of Thessaloniki are equal tomoment magnitudes for all practical purposes with reasonable uncertainties.It has been further shown that surface wave magnitudes, M_s,for M_s <6.0, can be also transferred into momentmagnitudes, M_w ^*, but the larger uncertaintiesencountered make its use rather problematic.     

地震震级空间分布的非参数分析

描述了应用非参数局部线性回归对震级平均趋势空间结构的研究。如果推测特定区域的地震数据集有空间相关,则需要使用修正版本的广义交叉验证方法计算光滑参数,以获得平均震级估计量。这种方法允许我们将空间依赖考虑进去从而获得更好的光滑参数。而且,应用参数自助法(bootstrap)可以量化由非参数估计方法得出的空间图的变异,也可以计算在特定震中发生的地震观测的震级大于等于给定阈值的概率。这些方法应用于两个不同的地震数据集:伊比利亚半岛西北部历史地震目录和加利福尼亚1998年1月到2008年4月的地震。     

To the problem of earthquake magnitudes determination

Summary Causes of inconsistency in magnitudes determined by broad-band and short-period instruments and by different systems of observations are elucidated. In so doing, both observations of standard stations of USSO of the USSR and those of Soviet frequency selecting seismic stations () are employed. On the basis of large statistic material of the stationare network of USSO, a dependence of spectral constitution ofP waves and frequency-temporal fields constructed for some earthquakes have been revealed as well as a dependence of magnitude values upon an arrival time of maximal particle velocity. It has been shown that the range of measuring (A/T) _max should be enlarged at least to 15 sec. A conclusion is drawn that the most stable magnitude consistent with the Catalogue by Gutenberg is the one determined by medium-period instruments.     

Reoccurrence formulas for the largest earthquake magnitudes based on the modified cumulative frequency-magnitude relationship

A modified formula of the cumulative frequency-magnitude relation has been formulated and tested in a previous paper by the authors of this study. Based on the modified relationship, the following reoccurrence formulas have been obtained.

1. For the ‘T-years period’ larger earthquake magnitude,M _T $$M_T = \frac{1}{{A_3 }}ln\frac{{A_2 }}{{(1/T) + A_1 }}.$$
2. For the value of the maximum earthquake magnitude, which is exceeded with probabilityP inT-years period,M _PT $$M_{PT} = \frac{{ln(A_2 .T)}}{{A_3 }} - \frac{{ln[A_1 .T - ln(1 - P)]}}{{A_3 }}.$$
3. For the probability of occurrence of an earthquake of magnitudeM in aT-years period,P _MT $$P_{MT} = 1 - \exp [ - T[ - A_1 + A_2 \exp ( - A_3 M)]].$$

The above formulas provide estimates of the probability of reoccurrence of the largest earthquake events which are significantly more realistic than those based on the Gutenberg-Richter relationships; at least for numerous tested earthquake samples from the major area of Greece.     

考虑活动地块边界带的分区震级经验关系

地方性震级M_L和面波震级M_S是两种常用的震级标度, 二者经常需要依据经验公式进行相互转换． 基于历史地震整体统计的经验公式由于资料有限, 且没有考虑区域地质条件的差异, 在实际使用中所产生的误差较大． 本文整理了40多年来同时包含M_L和M_S的1万2621条历史地震数据, 通过回归分析得到了震级M_L与M_S的经验关系; 并进一步按照震源所处的Ⅱ级活动地块边界带进行了分区回归分析, 得到了27个分区内地震震级M_L与M_S的经验关系． 结果显示, 经过分区转换后的M_L与M_S具有更好的相关性, 且考虑活动地块边界带所获取的地震震级能有效地降低M_L与M_S之间的转换误差．      

地震人员伤亡快速评估

根据2000~2004年发生在中国大陆地区典型成灾性地震,统计实际人员伤亡数据与地震灾害损失快速评估数据的关系。结果表明,评估结果与实际数据之间误差很大。针对这一情况,笔者从建筑物易损性矩阵的地区差异性以及人口数据动态变化的角度,对当前地震人员伤亡快速评估模型进行修正。结果表明,修正后的评估结果更加接近于实际死亡人数。     

The third asymptotic distribution of largest magnitudes in the Balkan earthquake provinces

Summary The third asymptotic distribution of the theory of largest values is applied to sixteen earthquake provinces in the Balkan area. The model which assumes an upper magnitude limit fits the observations better than the first distribution. Graphs and tables provide estimates of return periods of largest magnitudes.Communication presented at the XV General Assembly of the European Seismological Commission in Krakow, 22–28 September, 1976.     

基于JOPENS/MSDP地震定位方法的定位结果分析

按照中国地震局测震台网运行管理细则要求,地震编目中的震级是对地震波形进行WA仿真处理后的震级。本文对湖北数字测震台网2016年1月—2018年12月记录到的M_L≥2.0的68次地震事件,在震级方面分别做了仿真前后的对比分析,并给出其偏差。结果表明：仿真后的震级多数大于仿真前的震级,但震级差均在0.4级以内。本文的研究为湖北地震台网震级测定提供了参考。地震分析预报人员速报时可不采用仿真震级,但对于编目和研究人员可采用仿真震级。     

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.     

A methodology to select seismic coefficients based on upper bound “Newmark” displacements using earthquake records from Turkey

Strong motion records taken during earthquakes in Turkey are used to calculate Newmark displacements in slopes. These displacements are then utilized in developing a novel displacement-based methodology to select the seismic coefficient which is used to calculate pseudostatic safety factor. In the first step of the study, calculated Newmark displacements are evaluated in three different categories which are as follows: using all data, using data for different earthquake magnitude (M) ranges with and without distance constraint and using data for different peak acceleration (a_max) ranges. For all categories, different equations are obtained to assign slope displacements as a function of the ratio of yield acceleration to peak acceleration. The results show that categorization of data is an important issue, because the displacements are earthquake magnitude and peak acceleration dependent. In the second step, equations obtained for different peak acceleration ranges are used to propose charts linking upper bound slope displacements (D), seismic coefficients (k_h) and pseudostatic safety factors (PSF), which are three important parameters of a pseudostatic approach. This enables the k_h values be chosen based on the allowable displacements, instead of the current applications based on judgement and expertise. The results show that k_h values for any allowable displacement should be based on anticipated a_max values, while use of high PSF values results in lower displacements. Extensive comparison with solutions from the literature is also made. The methodology is best suited for earthquake triggered shallow landslides in natural slopes, consisting of materials which do not lose strength during dynamic loading.     

A solution procedure for the earthquake analysis of arch dam-reservoir systems with compressible water

Two processes using the Newmark implicit integration scheme are presented for the analysis of the earthquake response of a three-dimensional model for arch dam-reservoir systems including the effect of compressibility of the water. The solid structure and fluid regions are modelled separately, and the forcing functions at the interface are due to the hydrodynamic pressures from the reservoir acting on the upstream face of the dam wall, and the accelerations from the dam wall acting in turn on the reservoir. For the purposes of an initial investigation, elastic properties are assumed for the material of the dam, whilst in the reservoir radiation damping at the upstream boundary has been included, but bottom absorption has not. The excitation is provided by means of a combisweep which is fashioned so that its continuously varying frequencies pass through the fundamental frequencies of both the arch dam-reservoir system and the reservoir alone. Consequently the response is highly resonant, thus providing a severe test for the numerical procedures. From the numerical results obtained for an example problem it is concluded that both schemes provide an acceptable solution to the problem posed, and the possibility of enhancement to cater for more complex situations is discussed.     

Neural networks for quick earthquake damage estimation

This paper proposes the use of neural networks to predict damage due to earthquakes from the indices of recorded ground motion. Since the relationship between ground motion indices and resulting damage is difficult to express in mathematical form, neural networks are conveniently applied for this problem. Simulated earthquake ground motions are used to have a well-distributed data set and the ductility factor from non-linear analysis of two single-degree-of-freedom structural models is used to represent the damage. A sensitivity analysis procedure is described to identify qualitatively the input parameters that have a greater influence on the damage. The result of the trained neural network is then verified by using several recorded earthquake ground motions. It is found that some instability in the prediction can occur. Instability occurs when input values exceed the range of the training data. The neural network model using PGA and SI as input give the best performance in the recall tests using actual earthquake ground motion, demonstrating the usefulness of neural network models for the quick estimation of damage through earthquake intensity monitoring.     

A simple statistical estimation procedure for Monte Carlo Inversion in geophysics

Summary This paper examines the use of Monte Carlo Inversion (MCI) as an effective means for inverting ((geo)physical) data. Press, following Keilis-Borok and Yanovskaya, has used it successfully as an independent method for density modelling. However, to-date, no statistical basis for the interpretation of the results determined by it in geophysical applications has been developed. Since its future success and credibility will rest heavily on the development of such a basis, we give a simple statistical estimation procedure which defines in a natural way the procedure which must be used when applying, and interpreting the results obtained from, MCI. In addition, it is shown that MCI complements, rather than competes with, the work of Backus and Gilbert.     

基于数值模拟的设定地震场地谱时程拟合方法

本文将确定性数值模拟方法与地震动预测方程相结合,提出了一种重大水电工程场址设定地震的地震动时程生成方法。该方法基于场址设定地震,首先采用地震动预测方程确定场址的场地相关反应谱;其次建立包含震源和场址的场地模型,通过确定性数值模拟方法生成场址地震动时程;最后对生成的场址地震动时程进行调整,使其反应谱与设计谱相一致,用于工程抗震分析。这一方法生成的地震动时程既考虑了震源机制、传播路径以及局部场地效应等物理背景,又与场地相关的设计地震反应谱保持一致,为重大工程抗震分析与评价提供了一种新的思路。     

A novel model and estimation method for the individual random component of earthquake ground-motion relations

In this paper, I introduce a novel approach to modelling the individual random component (also called the intra-event uncertainty) of a ground-motion relation (GMR), as well as a novel approach to estimating the corresponding parameters. In essence, I contend that the individual random component is reproduced adequately by a simple stochastic mechanism of random impulses acting in the horizontal plane, with random directions. The random number of impulses was Poisson distributed. The parameters of the model were estimated according to a proposal by Raschke J Seismol 17(4):1157–1182, (2013a), with the sample of random difference ξ?=?ln(Y ₁ )-ln(Y ₂ ), in which Y ₁ and Y ₂ are the horizontal components of local ground-motion intensity. Any GMR element was eliminated by subtraction, except the individual random components. In the estimation procedure, the distribution of difference ξ was approximated by combining a large Monte Carlo simulated sample and Kernel smoothing. The estimated model satisfactorily fitted the difference ξ of the sample of peak ground accelerations, and the variance of the individual random components was considerably smaller than that of conventional GMRs. In addition, the dependence of variance on the epicentre distance was considered; however, a dependence of variance on the magnitude was not detected. Finally, the influence of the novel model and the corresponding approximations on PSHA was researched. The applied approximations of distribution of the individual random component were satisfactory for the researched example of PSHA.     

Statistical tools for maximum possible earthquake magnitude estimation

Several procedures for the statistical estimation of the region-characteristic maximum possible earthquake magnitude, m _max, are currently available. This paper aims to introduce and compare the 12 existing procedures. For each of the procedures given, there are notes on its origin, assumptions made in its derivation, condition for validity, weak and strong points, etc. The applicability of each particular procedure is determined by the assumptions of the model and/or the available information on seismicity of the area.