Cokriging nonstationary data

Universal cokriging is used to obtain predictions when dealing with multivariate random functions. An important type of nonstationarity is defined in terms of multivariate random functions with increments which are stationary of orderk. The covariance between increments of different variables is modeled by means of the pseudo-cross-covariance function. Criteria are formulated to which the parameters of pseudo-cross-covariance functions must comply so as to ensure positive-definiteness. Cokriging equations and the induced cokriging equations are given. The study is illustrated by an example from soil science.     

3 D inversion of borehole gravity data using cokriging

Borehole gravity has been used in mineral exPloration recently with the advent of slim-hole gravime-ters. It is logical to Perform inversion to utilize the information in the newly acquired data. The i...     

协同克立格法在广西林旺金矿化探数据处理中的应用

协同克立格法,同时兼具化探数据多元性及克立格法表征空间属性的特点。考虑到地质变量两个以上的空间属性,在化探数据处理中运用协同克立格法,可以进一步提高估计精度。运用协同克立格法对广西林旺矿区中金元素成矿进行预测,经相关性分析显示,在矿区中元素的基本组合是Au、Ag、As、Hg,协同克立格插值以Au为主要变量,伴生元素Ag、As、Hg为次要变量。把插值计算后的结果与传统多元统计方法和普通克立格法的计算结果进行比较,结果协同克立格法得到的估值误差较小,预测精度较高,在成矿元素的预测中具有一定程度的优越性。     

基于综合环境因子的协同克里金法分析茎柔鱼资源丰度空间分布

茎柔鱼是我国重要的远洋捕捞对象之一,研究其资源丰度空间分布问题,有助于更好地理解茎柔鱼的生态习性,并提高我国鱿钓渔船的生产效率。本文利用上海海洋大学鱿钓技术组提供的2003-2012年6-9月秘鲁外海茎柔鱼捕捞数据,结合海表面温度（SST）,海表面高度（SSH）,海表面盐度（SSS）和叶绿素浓度（Chl a）进行协同克里金插值预测其资源丰度的空间分布。为了解决协同克里金插值中4个环境因子的权重问题,本文将4个环境因子进行归一化处理,利用主成分分析方法将其整合为单一综合环境因子,以此作为协变量。将综合环境因子与单位捕捞努力量渔获量（CPUE）进行相关性检验后进行协同克里金插值,根据平均误差（ME）,均方根误差（RMSE）和标准化均方根（RMSSE）对插值结果评价,探讨此种方法的可行性。研究结果认为:（1）主成分分析方法获得的6-9月份的综合环境因子均与CPUE具有显著相关性;（2）6-7月份ME分别为0.002 6和0.002 5,预测准确性很高,平均预测结果稍高于实际观测值;而8-9月份的ME分别为-0.007 8和-0.000 2,预测准确性较高,平均预测结果稍低于实际观测值。6月份的RMSE估值精度最高,8月份的估值精度最低。6-7月份的RMSSE值小于1,说明都高估了预测的不确定性,8-9月份的RMSSE值大于1,说明都低估了预测的不确定性,则在6-9月份中的预测精度和准确性上会有一定程度的偏差。从ME、RMSE和RMSSE三者综合来看,6-9月的预测值具有一定的可靠性。     

综合应用测井及地震资料建立复杂断块地质模型

针对滩海油田具有完钻井少,以地震资料为主的特点,采用井震结合的方法进行地质建模。复杂断块油藏具有许多内部断层,充分利用地震解释层位和断层成果建立合理的构造模型。采用“多步建模”的思路,选用序贯高斯同位协同模拟算法建立储层参数模型。以测井资料为硬数据,地震反演数据为软数据,先后建立自然伽玛模型、泥质含量模型和砂泥岩相模型,然后以砂泥岩相模型为约束,建立储层参数模型。经研究表明,综合使用地震解释成果和三维地震数据体,有助于建立准确、合理的构造模型;而采用“多步建模”的思路,利用序贯高斯同位协同模拟算法,并综合测井资料、地震资料建立储层参数模型,有助于从地质的角度对储层参数模拟进行约束,提高储层随机建模精度,保证储层参数模型的准确和可靠性。     

Conditioning Geostatistical Operations to Nonlinear Volume Averages

The all-important process of data integration calls for algorithms that can handle secondary data often defined as nonlinear averages of the primary (hard) data over specific areas or volumes. It is suggested to approximate these nonlinear averages by linear averages of a nonlinear transform of the primary variable. Kriging of such nonlinear transforms, followed by the inverse transform, allows exact reproduction of all original data, both of point support and nonlinear volume averages. In a simulation mode, the previous cokriging provides the mean and variance of a conditional distribution from which to draw a simulated value, which is then backtransformed into a simulated value of the primary variable. The nonlinear averaged data values are then reproduced exactly. The direct sequential simulation algorithm adopted does not call for using any Gaussian distribution.     

Comparison of two techniques for applying disjunctive kriging: The Gaussian anamorphosis model versus the direct statistical inference of the bivariate distributions

Indicator cokriging is an alternative to disjunctive kriging for estimation of spatial distributions. One way to determine which of these techniques is more accurate for estimation of spatial distributions is to apply each to a particular type of data. A procedure is developed for evaluation of disjunctive kriging and indicator cokriging for such an application. Application of this procedure to earthquake ground motion data found disjunctive kriging to be at least as accurate as indicator cokriging for estimation of spatial distributions of peak horizontal acceleration. Indicator cokriging was superior for all other types of earthquake ground motion data.     

A comparison between cokriging and ordinary kriging: Case study with a polymetallic deposit

Cokriging is applied to the estimation of mineral resources in a polymetallic deposit. Several major steps, which should be taken in using cokriging, are highlighted as necessary practical considerations. The case study is related to an ultramafic copper-nickel deposit. Six elements, Cu, Ni, Au, Ag, Pt, and Pd, occurring in the deposit, are partitioned into three subgroups and the elements within each group are simultaneously estimated on the basis of over 4000 drill assays. A comparison was made between ordinary kriging and cokriging methods through cross-validation. The results show that cokriging has significantly improved the estimates of resources by reducing the overall estimation error by over 15% and the variance of error by over 20%.     

A geostatistically based approach to the identification of aquifer transmissivities in Yolo Basin, California

A geostatistically based approach is developed for the identification of aquifer transmissivities in Yolo Basin, California. The approach combines weighted least-squares with universal kriging and cokriging techniques in an overall scheme that (1)considers a prioriknown information on aquifer transmissivity and specific capacities of wells, (2)considers uncertainties in water level and transmissivity data, and (3)estimates the reliability of the generated transmissivity values. Minimization of a global least-squares function that incorporates calibration and plausibility criteria leads to a transmissivity map that shows a good agreement with pumping-test results.