Statistical evaluation of tectonomagmatic discrimination diagrams for granitic rocks and proposal of new discriminant-function-based multi-dimensional diagrams for acid rocks

The four tectonic discrimination diagrams of Pearce et al. [Journal of Petrology, v. 25, p. 956–983] for granitic rocks were first evaluated using the literature cited by these authors as well as from our new database. The first diagram (Y?Nb) cannot discriminate volcanic-arc and collision settings. Both Y?Nb and Yb?Ta diagrams have an overlapping field for within-plate and ocean-ridge granitoids. The remaining two diagrams (Y?+?Nb?Rb and Yb?+?Ta?Rb) use a mobile element (Rb) in their y-axis. Although these diagrams successfully discriminate volcanic-arc and within-plate granites, they perform less well for collision tectonics. Besides, felsic or acid rocks are scarce in ocean-ridge settings, which limits the usefulness of these diagrams for this geological environment. Therefore, using an extensive database, we proposed a set of five new discriminant-function-based multi-dimensional diagrams for acid magmas from four tectonic settings (island arc, continental arc, continental rift, and collision). The very similar tectonic settings of island and continental arcs are discriminated for the first time. These diagrams are based on correct statistical treatment of compositional data, because they use natural logarithm transformation of major-element ratios and linear discriminant analysis (LDA). The use of discordant outlier-free samples prior to LDA improved the success rates by about 3–5%. Success rates of these diagrams as inferred from a testing set were between 76% and 88% for island arc, 60% and 92% for continental arc, and 72% and 84% for both continental rift and collision settings. Finally, application of these new diagrams to case studies not compiled in our initial database used for constructing these diagrams provided the following results: a collision setting for the Himalayas at about 30 Ma; an island arc setting for Quaternary acid rocks from geothermal boreholes in El Salvador; an island- or continental-arc setting for northern Italy at 35–52 Ma; a continental-arc setting for the Italy–Austria border at about 30 Ma; either a rift or a collision setting for northern Nigeria at about 164 Ma; a collision setting for central Nigeria at about 144 Ma and for the Cretaceous Masirah ophiolites of Oman; and an island arc setting for the Cretaceous Semail ophiolites of Oman. In spite of the relative mobility of major elements, these applications suggest utility of the new discrimination diagrams for all four tectonic settings.     

常量金标准物质定值中离群值的统计识别

离群值的剔除常用数理统计的方法,如格拉布斯检验法和迪克逊检验法等,但是这些统计方法用于常量金标准物质分析结果的统计检验,都存在着对离群值剔除明显不够的问题.本文建立了以常量金重复分析相对偏差允许限为依据的离群值统计识别方法,包括统计计算待定值样品中金的算术平均值x和相对偏差允许限YG,确定合格的测定结果的数据区间,从而识别出离群值并予以剔除;一次剔除后,按照新的统计量确定下一轮的离群值剔除范围,直到无离群值后,给出金的平均值及其波动范围.以15个人工组合的常量金标准物质为例,模拟金标准物质定值分析,以密码形式分派给不同单位和分析者,共收集10套独立分析结果,采用本法剔除离群值后,所得金算术平均值与金标准参考值更加接近,其相对偏差的质量分数为0.35,达到优秀;而格拉布斯法(或迪克逊法)和中位值法的质量分数分别为0.42和0.40,只能达到良好.应用本文建立的离群值统计识别方法,质量分数等级有了明显提高,增强了数据统计分析的有效性.     

A Practical Procedure for the Measurement of Fragmentation by Blasting by Image Analysis

Summary. The operation of a digital image analysis system in a limestone quarry is described. The calibration of the system, required in order to obtain moderately reliable fragmentation values, is done from muckpile sieving data by tuning the image analysis software settings so that the fragmentation curve obtained matches as close as possible the sieving. The sieving data have also been used to extend the fragment size distribution curves measured to sizes below the system’s optical resolution and to process the results in terms of fragmented rock, discounting the material coming from a loose overburden (natural fines) that is cast together with the fragmented rock. Automatic and manual operation modes of the image analysis are compared. The total fragmentation of a blast is obtained from the analysis of twenty photographs; a criterion for the elimination of outlier photographs has been adopted using a robust statistic. The limitations of the measurement system due to sampling, image processing and fines corrections are discussed and the errors estimated whenever possible. An analysis of consistency of the results based on the known amount of natural fines is made. Blasts with large differences in the amount of fines require a differentiated treatment, as the fine sizes tend to be the more underestimated in the image analysis as they become more abundant; this has been accomplished by means of a variable fines adjustment factor. Despite of the unavoidable errors and the large dispersion always associated with large-scale rock blasting data, the system is sensitive to relative changes in fragmentation.     

各向异性扩散在电磁测深曲线平滑中的应用

电磁类地球物理方法由于极易受到各类噪声的干扰,使得估计的视电阻率曲线或相位曲线发生畸变,严重地影响了反演解译精度,如何对这类观测曲线进行合理有效地平滑,是目前数据处理中的重点,也是难点.本文把各向异性扩散（anisotropic diffusion AD）引入到曲线平滑中,提出了各向异性扩散的曲线平滑方法,以平滑点梯度值的降函数作为扩散速度,在梯度较大的位置予以较小的扩散速度以保护特征,在梯度较小的位置予以较大的扩散速度平滑噪声引起的扰动.同时为了减小“飞点”(outliers)对平滑的干扰,采用局部单调扩散进行预处理.实验结果显示,本文提出的平滑方法有效地平滑了噪声与“飞点”的干扰,恢复了曲线的基本形态,有效地保持了曲线基本特征.     

FINDING CAUSES OF OUTLIERS IN MULTIVARIATE ENVIRONMENTAL DATA

Multivariate outliers in environmental data sets are often caused by atypical measurement error in a singlevariable.From a quality assurance perspective it is important to identify these variables efficiently so thatcorrective actions may be performed.We demonstrate a procedure for using two multivariate tests toidentify which variable‘caused’each outlier.The procedure is tested with simulated data sets that havethe same correlation structure as selected water chemistry variables from a survey of lakes in the WesternUnited States.The success rates are evaluated for three of the variables for sample sizes of 50 and 100,significance levels of 0.01 and 0.05 and various amounts of mean shift.The procedure works best forhighly correlated variables.     

利用粒子滤波进行动态精密单点定位观测异常影响控制

采用粒子滤波控制观测异常影响,提高动态精密单点定位精度。粒子滤波是一种非高斯噪声分布的动态滤波,通过重点概率密度进行随机采样以获取高精度状态参数;根据观测噪声概率密度、状态噪声概率密度以及重点概率密度等因素确定粒子权值,降低受污染粒子对定位结果的影响;采用Kalman滤波进行重点采样,减缓粒子退化;采用单差无电离层固定模糊度,减少状态参数维数,进而减少粒子的选取个数。实测数据结果表明,粒子滤波有效控制了观测异常影响,提高了动态精密单点定位的精度。     

最小二乘支持向量机在海洋测深异常值探测中的应用

提出了利用最小二乘支持向量机(LS-SVM)构造海底趋势面,利用该趋势面对海洋测深异常值进行剔除的方法,并与趋势面滤波进行了分析和比较,用定理证明趋势面滤波只是LS-SVM取特定参数时的解。实测算例表明,通过调整LS-SVM的参数,使其构造的趋势面更合理,从而有效地剔除测深异常值。     

粗差数学期望平移模型的理论研究

现有文献对数学期望平移模型的理论分析仅考虑了观测值统计独立的特殊情况。基于观测值统计相关的一般情况,导出了数学期望平移参数估值(▽S_i)的简明表达式。在此基础上,采用统计预测理论对▽S_i进行了直观的理论解释,扩展了统计学文献中的有关结论。借助于实例,分析了▽S_i与最小二乘残差的本质区别。     

统计检验抗差估计新方法研究

20世纪60年代数学家重新从广泛的意义上提出非最小二乘估计问题,并已在抗差估计中取得重要的进展。从1980年起,抗差估计理论开始被引入测量领域,并出现了许多方案。本文依据统计检验,结合IGG1区间划分的部分思想,提出了一种全新的定权思路,给出了一个简要数学模型。利用MATLAB编程,将本文提出的方法与经典的IGG1方法进行了比较,对它的抗差效果进行了总结分析,通过一个经典算例,表明新方法具有准确定位粗差的优点。