Adding bounds to kriging

The ordinary kriging interpolation algorithm is extended by the inclusion of explicit lower and upper bounds on the estimate. The associated estimation variance is written as the ordinary kriging variance plus a non-negative correction term.     

Minimum-variance unbiased quadratic estimation of covariances of regionalized variables

The parameters of covariance functions (or variograms) of regionalized variables must be determined before linear unbiased estimation can be applied. This work examines the problem of minimum-variance unbiased quadratic estimation of the parameters of ordinary or generalized covariance functions of regionalized variables. Attention is limited to covariance functions that are linear in the parameters and the normality assumption is invoked when fourth moments of the data need to be calculated. The main contributions of this work are (1) it shows when and in what sense minimum-variance unbiased quadratic estimation can be achieved, and (2) it yields a well-founded, practicable, and easy-to-automate methodology for the estimation of parameters of covariance functions. Results of simulation studies are very encouraging.     

海州湾表层沉积物粒度的空间变异特征

在海州湾海域采集了表层沉积物60个,经实验室分析获得了各采样点不同粒级组分的质量分数,在此基础上运用地统计学方法分析了砂、粉砂和黏粒三组分的空间变异特征,并利用Kriging插值方法绘制了相应的沉积物分布图。结果表明,海州湾表层沉积物中砂和黏粒组分均具有较强的空间自相关性,其空间自相关距离分别达到15 km和28 km,而粉砂则具有中等的空间自相关性,自相关距离在12 km左右;在大于9 km的尺度上,3种粒级沉积物的空间变异性表现出明显的各向异性特征。制图结果表明,研究海域沉积物的总体组成状况是北部偏砂、南部偏黏、中部以粉沙为主。研究结果对连云港航道疏浚、整治及近海水产养殖规划等工作具有一定指导意义。     

Geochemical characterization of heavy metal contaminated area using multivariate factorial kriging

This paper describes a geostatistical method, known as factorial kriging analysis, which is well suited for analyzing multivariate spatial information. The method involves multivariate variogram modeling, principal component analysis, and cokriging. It uses several separate correlation structures, each corresponding to a specific spatial scale, and yields a set of regionalized factors summarizing the main features of the data for each spatial scale. This method is applied to an area of high manganese-ore mining activity in Amapá State, North Brazil. Two scales of spatial variation (0.33 and 2.0 km) are identified and interpreted. The results indicate that, for the short-range structure, manganese, arsenic, iron, and cadmium are associated with human activities due to the mining work, while for the long-range structure, the high aluminum, selenium, copper, and lead concentrations, seem to be related to the natural environment. At each scale, the correlation structure is analyzed, and regionalized factors are estimated by cokriging and then mapped.     

民勤绿洲荒漠带土壤水分的空间分异研究

 通过野外试验和室内分析,对民勤绿洲荒漠带土壤水分的空间分异进行了研究。结果表明,在水平方向上,土壤水分的平均最大值基本出现在绿洲区,最小值出现在绿洲荒漠过渡带。在绿洲区,土壤含水量由表层向下逐渐递增;过渡带土壤含水量呈现出表层和底层低,中间层高的特点;荒漠区土壤含水量呈现出表层和底层高,中层低的特点。土壤水分特性的变异系数最大的是过渡带,最小的是绿洲。土壤水分含量各层最佳拟合模型不尽相同。水分含量的自相关性不强,受随机因素的影响较大。     

Some further clarification on Markov chain random fields and transiograms

The Markov chain random field (MCRF) theory and the transiogram spatial measure were proposed several years ago. Basic sequential simulation algorithms based on simple MCRF models such as the Markov chain sequential simulation algorithm and the Markov chain sequential co-simulation algorithm have been developed and used in a series of application studies. However, misunderstanding of these two ideas and the geostatistical approach built on them arose recently among some researchers in geostatistics. The purpose of this article is to further clarify some issues related to these two ideas, so as to avoid further misunderstanding. For those issues already clarified, trivial, or obviously irrelevant, we do not talk about them here.