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.     

“地震预警”法律概念的构成及延展

“地震预警”法律概念是讨论和规范地震预警相关行为的基础,也是地震预警立法首先要明确的问题。目前,国家层面尚未制定专门的地震预警法律法规,地方已经颁布的管理办法中对“地震预警”法律概念的规定也不完全一致。随着地震预警立法进程的不断推进,“地震预警”法律概念的确定和统一愈发重要和迫切。“地震预警”法律概念应涵括其技术属性和社会属性,秉持完整规范、避免歧义的原则,将时间、空间、机理和影响等要素排列组合而成。为深入理解这一概念,本文还讨论了发布主体、预警客体、技术服务、法律责任等地震预警法律规范的基本内容。     

参数的期望估计及其在形变分析中的应用

利用“参数的期望估计”能准确定位、定量粗差及参数的期望估计不受粗差影响折特殊性质,寻找地壳变形区域和不变形区域,以确定拟稳点,进而进行拟稳变换,分析地菜变,将是一种有效方法。     

Estimation for partially observed Markov processes

Many stochastic process models for environmental data sets assume a process of relatively simple structure which is in some sense partially observed. That is, there is an underlying process (X_n, n 0) or (X_t, t 0) for which the parameters are of interest and physically meaningful, and an observable process (Y_n, n 0) or (Y_t, t 0) which depends on the X process but not otherwise on those parameters. Examples are wide ranging: the Y process may be the X process with missing observations; the Y process may be the X process observed with a noise component; the X process might constitute a random environment for the Y process, as with hidden Markov models; the Y process might be a lower dimensional function or reduction of the X process. In principle, maximum likelihood estimation for the X process parameters can be carried out by some form of the EM algorithm applied to the Y process data. In the paper we review some current methods for exact and approximate maximum likelihood estimation. We illustrate some of the issues by considering how to estimate the parameters of a stochastic Nash cascade model for runoff. In the case of k reservoirs, the outputs of these reservoirs form a k dimensional vector Markov process, of which only the kth coordinate process is observed, usually at a discrete sample of time points.     

成都城市发展对热岛强度影响的主成份回归分析

本文对成都市总人口、建成区面积等11个因子、作了主成份回归L-S估计和M-估计,讨论了成都城市发展对“热岛”强度的主要影响因子。结果表明,城区房屋建筑面积及总人口数是影响城市气候(气温)的主要因子,其次为城市人口总户数、建成面积等。 文中,对回归方程进行了拟合计算,回归效果比较满意(尤其是稳健回归)。     

Comparison of structural and least-squares lines for estimating geologic relations

Two different goals in fitting straight lines to data are to estimate a true linear relation (physical law) and to predict values of the dependent variable with the smallest possible error. Regarding the first goal, a Monte Carlo study indicated that the structural-analysis (SA) method of fitting straight lines to data is superior to the ordinary least-squares (OLS) method for estimating true straight-line relations. Number of data points, slope and intercept of the true relation, and variances of the errors associated with the independent (X) and dependent (Y) variables influence the degree of agreement. For example, differences between the two line-fitting methods decrease as error in X becomes small relative to error in Y. Regarding the second goal—predicting the dependent variable—OLS is better than SA. Again, the difference diminishes as X takes on less error relative to Y. With respect to estimation of slope and intercept and prediction of Y, agreement between Monte Carlo results and large-sample theory was very good for sample sizes of 100, and fair to good for sample sizes of 20. The procedures and error measures are illustrated with two geologic examples.     

大理州2005年初夏干旱成因探析

大理州2005年初夏出现了严重干旱气象事件.从500pHa高空环流特征、500pHa距平场特征、西太平洋副高特征量及北太平洋中低纬海温距平场、OLR距平场对这次干旱的成因进行了分析,分析结果表明：2005年初夏（4月1日～6月10日）降水异常偏少气温明显偏高是发生干旱的主要原因,高空大气环流异常、西太平洋副高持续偏强偏西、冷空气活动偏北是导致干旱的直接原因;孟加拉湾南部4月OLR场呈明显正距平,抑制低值系统的发展和东北移影响云南,是影响2005年大理初夏干旱重要原因;北太平洋中低纬海温特征与大理州初夏干旱有一定的遥相关性.     

Early diagenesis of nurtrients （C, N, P and Si） stored in sediments of two reservoirs in southwestern China

Damming is a common anthropogenic intervention along the course of rivers, which is defined as ＂artificial-lake effect＂, both in China and across the world. Today as many as 48000 dams and/or reservoirs are in operation in the Changjiang River （Yangtze River） drainage area, and more are being constructed. While damming is well known to affect riverbome nutrient loads, and thus the riverine ecosystems owing to removal of carbon fixation, and removal of particles in reservoir sediments, there is limited information on the detailed early diagenesis of sediments in reservoirs including the regeneration processes of nutrients deposited in sediments and exchange flux across the sediment-water interface, which is important for mass balance of riverbome nutrients. In the present study, two large-size reservoirs, Wujiangdu Reservoir （WJDR） and Dongfeng Reservoir （DFR）, located on the main steam of the Wujiang River and with uniformity hydrography and discrepancy biogeochemical activity （e. g. primary production）, were selected for a comparative study on the detailed processes of nutrient regeneration. Water, pore water and sediment were sampled from these two reservoirs and dissolved organic carbon （DOC）, NH4^＋, NO3^-, PO4^3-, dissolved silica （DSi） in the overlying water and pore water, and total organic matter in sediments were determined. The results of correlation analysis suggested that in these two reservoirs, processes of nutrient regeneration near the sediment-water interface were significantly different. As a result of rapid decomposition of algae-derived ＂labile＂ organic matter in upper sediments, nutrient regeneration processes and upward fluxes in WJDR are dramatically stronger than those of DFR. NH4^＋ upward flux from sediment in WJDR was about 17 times higher than that in DFR. PO4^3- flux in WJDR is about 13 times above that in DFR. DOC flux in WJDR is larger that in DFR by 5 times, and DSi by 1 time.     

Reservoir description using dynamic parameterisation selection with a combined stochastic and gradient search

There is a correspondence between flow in a reservoir and large scale permeability trends. This correspondence can be derived by constraining reservoir models using observed production data. One of the challenges in deriving the permeability distribution of a field using production data involves determination of the scale of resolution of the permeability. The Adaptive Multiscale Estimation (AME) seeks to overcome the problems related to choosing the resolution of the permeability field by a dynamic parameterisation selection. The standard AME uses a gradient algorithm in solving several optimisation problems with increasing permeability resolution. This paper presents a hybrid algorithm which combines a gradient search and a stochastic algorithm to improve the robustness of the dynamic parameterisation selection. At low dimension, we use the stochastic algorithm to generate several optimised models. We use information from all these produced models to find new optimal refinements, and start out new optimisations with several unequally suggested parameterisations. At higher dimensions we change to a gradient-type optimiser, where the initial solution is chosen from the ensemble of models suggested by the stochastic algorithm. The selection is based on a predefined criterion. We demonstrate the robustness of the hybrid algorithm on sample synthetic cases, which most of them were considered insolvable using the standard AME algorithm.     

Methylmercury and human biomarkers： Questioning the evidence

Methylmercury （MeHg） is a powerful neurotoxicant in humans. In terms of biomarkers of MeHg exposure, hair and blood have long been used in epidemiological studies as the biomarkers of choice. In fact, total hair mercury （Hg） content as well as organic blood Hg concentrations reflects exposure to organic Hg from food consumption. Extensive studies, establishing a constant and linear relation between MeHg intake versus Hg levels in hair and blood, were conducted by governmental officials to establish guidelines on safe levels of MeHg exposure, which were translated into threshold daily fish consumption rates （usually expressed as μg MeHg per kg bodyweight）. Nowadays, in most epidemiologic studies blood or hair mercury （Hg） level is commonly used as a valid proxy to estimate human exposure to methylmercury （MeHg） through fish consumption without relating this signal to actual fish consumption patterns among populations. Human variability in mercury toxicokinetics was identified and measurement error has been pointed out to be a substantial contributor to observed variability, particularly where dietary information is retrospective and self-reported. However, experimental evidence indicates that significant variability among individuals may exist in the biokinetics of mercury. Also recent findings from previous population-based studies through COMERN initiative also revealed that MeHg metabolic processes might greatly vary across populations. In fact, it is unlikely that the magnitude of the difference measured between observed and expected levels of mercury, given the reported intake, can be entirely explained by laboratory measurement errors or reporting bias.