Estimation of covariance matrix from geochemical data with observations below detection limits

Multivariate statistical analyses have been extensively applied to geochemical measurements to analyze and aid interpretation of the data. Estimation of the covariance matrix of multivariate observations is the first task in multivariate analysis. However, geochemical data for the rare elements, especially Ag, Au, and platinum-group elements, usually contain observations the below detection limits. In particular, Instrumental Neutron Activation Analysis (INAA) for the rare elements produces multilevel and possibly extremely high detection limits depending on the sample weight. Traditionally, in applying multivariate analysis to such incomplete data, the observations below detection limits are first substituted, for example, each observation below the detection limit is replaced by a certain percentage of that limit, and then the standard statistical computer packages or techniques are used to obtain the analysis of the data. If a number of samples with observations below detection limits is small, or the detection limits are relatively near zero, the results may be reasonable and most geological interpretations or conclusions are probably valid. In this paper, a new method is proposed to estimate the covariance matrix from a dataset containing observations below multilevel detection limits by using the marginal maximum likelihood estimation (MMLE) method. For each pair of variables, sayY andZ whose observations containing below detection limits, the proposed method consists of three steps: (i) for each variable separately obtaining the marginal MLE for the means and the variances, , , , and forY andZ: (ii) defining new variables by and and lettingA=C+D andB=C–D, and obtaining MLE for variances, and forA andB; (iii) estimating the correlation coefficient _YZ by and the covariance _YZ by . The procedure is illustrated by using a precious metal geochemical data set from the Fox River Sill, Manitoba, Canada.     

A MIXTURE MODEL OF ANNUAL PRECIPITATION IN PERU*

A two component mixed log-normal distribution effectively models annual precipitation totals at two stations in Peru characterized by widely differing interannual patterns of precipitation. Physical evidence supports the division of station records into two subsamples. Years with ENSO events and years without ENSO events identify the components of a mixed probability model. The mixed model produces a superior fit to the two parameter log-normal distribution. Model application provides a reliable means of precipitation prediction and also quantitatively describes the highly variable temporal and spatial pattern of annual precipitation in western Peru.     

基于浪潮组合的台风暴潮强度等级划分

为准确定位风暴的强弱及灾害的大小,文中提出了泊松-二维对数正态分布,并将其用于海岸地区台风暴潮致灾强度的长期预测。选取青岛地区建国以来所出现的主要台风暴潮作为观测资料,以水位和显著波高系列组成样本,进行了台风暴潮重现期的统计推算。提出了判别台风暴潮致灾强度的新标准。实例显示,新标准概念清楚,简单易行,适用于青岛地区台风暴潮的强度确定。基于新模式的风暴潮强度随机分析方法对我国其它海岸地区的防潮减灾具有参考意义。     

Size distribution of urban blocks in the Tokyo Metropolitan Region: estimation by urban block density and road width on the basis of normative plane tessellation

The size distribution of urban blocks is important for the characterisation of urban block patterns and is known to follow several parametric statistical distributions. However, it has not previously been analysed on the basis of a normative plane tessellation and in terms of urban block density and mean road width. In this article, we formulate the size distribution of Voronoi cells using the gamma distribution estimated by urban block density and mean road width. We found that (1) both log-normal and gamma distributions can be good candidates for the size distribution of urban blocks at the scale of a region that consists of regular urban blocks and that has a uniform road width; and (2) the size distribution of urban blocks depends on the balance between pattern and width improvement effects. Based on one study region in Tokyo, if the pattern improvement effect is more prominent than the width improvement effect, the mode of urban block sizes tends to be larger than if it is not. These findings are expected to provide scientific support for urban planning (e.g. land readjustment projects).     

联结(copula)函数在概率地震危险性分析中的应用

介绍了一种成熟的已广泛应用于金融领域的估计不确定性的方法——copula函数方法, 并推广了n重的Frankrsquo;s copulas; 在实际应用中, 本文采用了俞言祥和美国西部由Boore等人给出的两个衰减模型, 针对其中存在的模型不确定性以及它们之间的相互依赖性, 构造出概率意义上联合的copula分布函数, 并将其应用于实例分析. 结果表明, 对比于传统逻辑树中所用的线性结合方法, copula将两者带来的概率分布写成一个联合概率分布, 能够很好地考虑双方不尽相同的意见. 另外, 由于copula函数可采用各种各样的边际分布函数来获得联合概率分布, 且在金融风险投资评估已有大量的应用, 因此在现代地震危险性评估中将有着广泛的前景.      

大中型水库坝前年最高水位统计变化特性分析

根据全国１６０座大中型水库的实际观测资料,对坝前年最高水位的变化特性进行了较系统的分析研究。结果表明：年最高水位为独立随机变量,概率分布多为负偏,可由三参数对数正态表征。参数由概率权重矩法估计。     

华东高海拔地区夏季气溶胶数浓度及谱分布特征

利用2014年7月黄山光明顶观测获得的气溶胶数浓度、气溶胶数谱数据,对黄山夏季气溶胶数浓度及谱分布特征进行分析,并在此基础上对气溶胶数谱进行了对数正态分布拟合。研究结果表明:黄山夏季气溶胶平均数浓度约为3 518.27 cm~(-3),主要集中在爱根核模态;气溶胶平均数浓度日变化呈双峰分布,峰值浓度的出现伴随着小粒子的增多。气溶胶数浓度与相对湿度和风速成负相关,高浓度的气溶胶多出现在较弱的东南风时;积聚模态气溶胶数浓度受风向影响显著。不同气团背景下气溶胶数谱差异集中在小于100 nm和500~1 000 nm粒径范围。爱根核模态气溶胶在高湿的西南气团影响下数浓度最低、谱较窄,而高温、低湿的东南气团对应的气溶胶数浓度最高、谱最宽,北方气团对应的气溶胶数浓度和谱宽居中;500~1 000 nm粒径范围气溶胶数谱分布特征与之相反。不同背景的气溶胶数谱和体积谱均可采用爱根模态、积聚模态1和积聚模态2三个模态进行对数正态分布拟合,但不同气团背景下的各模态谱型参数差异较大。     

Particle size distribution of cataclastic fault materials from Southern California: A 3-D study

The particle size distributions of fault gouge from the San Andreas, the San Gabriel, and the Lopez Canyon faults in Southern California were measured using sieving and Coulter-Counter techniques over a range of particle sizes from 2 m to 16 mm. The distributions were found to be power law (fractal) for the smaller fragments and log-normal by mass for sizes near and above the peak size. The apparent fractal dimensionD of the smaller particles in gouge samples from the San Andreas fault, the San Gabriel fault and the Lopez Canyon gouge were 2.4–3.6, 2.6–2.9 and 2.4–3.0, respectively. The averageD for the Lopez Canyon gouge was 2.7±0.2, which is in agreement with earlier studies of this gouge using planar 2-D sections. The fractal dimension of the finer fragments from all three faults is observed to be correlated with the peak fragment size, with finer gouges tending to have a largerD. A computer automaton is used to show that this observation may be explained as resulting from a fragmentation process which has a grinding limit at which particle reduction stops.     

浙江海岛植被乔木层种-多度格局及其气候因素分析

采用数理统计方法对浙江海岛植被乔木层种-多度的格局进行研究,并将参数估计法和遗传算法应用于Preston对数正态模型在浙江海岛植被乔木层种-多度格局拟合中,并分析浙江海岛植被（乔木）及其与气候因子的相关关系。结果表明：（1）浙江海岛植被乔木层种-多度格局符合对数正态分布特征,对数正态分布模型在浙江海岛植被乔木层种-多度分布中的适用性与在热带雨林等非海岛群落种-多度格局的适用性一致;（2）浙江海岛植被与毗邻区域的植被同处于相似相近的气候因子下,具有亚热带气候的主要特征,包含了从温带至亚热带地区的针阔混交林、常绿阔叶和落叶阔叶的众多属、种,可作为亚热带气候下植被重要组成部分开展系统生态学研究。     

永吉县一拉溪-冯家屯地区1∶50 000水系沉积物测量异常下限处理方法

本文结合“吉林省吉林中部地区构造岩浆岩带金、铜多金属矿产资源调查”项目中“永吉县一拉溪-冯家屯地区1∶50000水系沉积物测量”所取得的数据,采用目前比较常用的全区统一异常下限的传统方法(简称传统法),根据地球化学特点及地质背景,将该区划分成若干小区。各小区分别采用不同的异常下限的衬值计算法(简称分区衬值法),对Au、As、Sb、Mo进行研究。研究对比发现:传统法采用统一的异常下限,会减弱甚至漏掉一些重要矿化异常信息,本次采用分区衬值法则能较好地显示低背景区的异常信息,克服高背景区异常面积过大,不集中等缺点,取得较好效果,达到更好地发现异常目的。