The Effect of Using Cokriging against Ordinary Kriging When Estimating Phosphate Deposits at Elsebaiya Area, Egypt

Application of geostatistical techniques when evaluating mineral deposits could reflect some geological characteristics which help through the stage of planning and production. In the present study, an attempt has been done on two phosphate deposits at Elsebaiya area on both sides of the River Nile namely: Um Tondoba mine at Elsebaiya East area and Western River Nile mine in Elsebaiya West area. Depending on the available data, statistical analysis illustrated differences in the distribution of P2O5 % and ore thickness within the studied areas. Geostatistics used to start with constructing variograms for P2O5 % and thickness for the two phosphate deposits to be used with ordinary kriging models, also constructing cross variograms between P2O5 % and thickness to be used with cokriging models where the difference in the variogram parameters reflected a specific variation for each deposit horizontally and vertically. The ordinary kriging models and cokriging models illustrated different distribution behavior through both the two kriging techniques.

利用Cokriging提高估算土壤盐离子浓度分布的精度——以黄河三角洲为例

估算土壤中化学物质的含量与空间分布是了解多孔介质中水盐运移规律并进而因地制宜地提出盐渍土改良措施的关键。大面积的实地采样分析费时费力且耗资巨大。通过地统计分析,使用有限的采样数据可获得土壤溶质的准确变异。本文探讨和比较了Ordinarykriging(OK)与Cokriging(COK)这两种内插方法。结果显示一半的采样点数据的COK较之全部采样点数据的OK精度更高,相对均方根误差降幅为130.83%;采用同样的协同变量(239个全盐量数据),一半的采样点数据的COK较之全部采样点数据的COK精度更高,相对均方根误差降幅为20.10%。协同变量与主变量的相关度决定了COK的预测精度,当相关系数由77%升高为99%时,相对均方根误差降低了48.30%。

Mapping Soil Electrical Conductivity Using Ordinary Kriging Combined with Back-propagation Network

Accurate mapping of soil salinity and recognition of its influencing factors are essential for sustainable crop production and soil health. Although the influencing factors have been used to improve the mapping accuracy of soil salinity, few studies have considered both aspects of spatial variation caused by the influencing factors and spatial autocorrelations for mapping. The objective of this study was to demonstrate that the ordinary kriging combined with back-propagation network(OK_BP), considering the two aspects of spatial variation, which can benefit the improvement of the mapping accuracy of soil salinity. To test the effectiveness of this approach, 70 sites were sampled at two depths(0–30 and 30–50 cm) in Ningxia Hui Autonomous Region, China. Ordinary kriging(OK), back-propagation network(BP) and regression kriging(RK) were used in comparison analysis; the root mean square error(RMSE), relative improvement(RI) and the decrease in estimation imprecision(DIP) were used to judge the mapping quality. Results showed that OK_BP avoided the both underestimation and overestimation of the higher and lower values of interpolation surfaces. OK_BP revealed more details of the spatial variation responding to influencing factors, and provided more flexibility for incorporating various correlated factors in the mapping. Moreover, OK_BP obtained better results with respect to the reference methods(i.e., OK, BP, and RK) in terms of the lowest RMSE, the highest RI and DIP. Thus, it is concluded that OK_BP is an effective method for mapping soil salinity with a high accuracy.

基于Ordinary Kriging路域土壤重金属含量的空间分布——以国道316线福州至闽清段为例

土壤重金属污染日渐加重,道路交通活动产生的重金属污染导致路域土壤重金属含量上升,构成潜在生态威胁。为探明路域土壤重金属污染范围及其变化趋势,在316国道福州-闽清段外侧100 m×100 m范围内布设5条与道路垂直的采样断面,每条断面依据道路远近布设11个采样点,在距离道路路侧200 m处采集2个对照土壤样品,共采集57个采样点表层的土壤样品,并采用XRF-DP 4050测定土壤中重金属(Cr、Pb、Zn、Mn和Fe)含量。在此基础上,对土壤中不同重金属间进行相关性分析,并用普通克里金进行插值分析路域土壤重金属的空间分布特征。结果表明,测量领域内的土壤中Cr、Pb、Zn含量整体趋势呈现随道路距离增加而递减,其对照区含量较低,含量受道路交通影响;其中Cr呈指数分布,在0 m处含量最高;Pb、Zn呈偏态分布,峰值出现在10~20 m。Fe、Mn在对照区含量较高,其测量领域含量不易受道路交通影响,含量主要与成土母质有关。

Determination of Ash Contents in Coal by Means of Ordinary Kriging Method

The ash contents in coal particles were examined in the paper dependably on particle size and its density. So, the two-dimensional regressive function Z = Z（P, D） was the searched object, where Z is random variable describing ash contents, P---density and D---particle diameter. This dependence was determined based on experimental data concerning the coal of type 31. For this coal, the method of ordinary kriging was applied to calculate the values of random variable Z. This method required the proper selection of so-called variogram function, in which four forms were considered in this paper in purpose to select the best solution. The given results were then evaluated by the mean standard error value and compared with empirical data.

基于Kriging的地形高程插值

将地形高程作为区域化变量,根据普通Kriging法由散乱的高程点进行地形高程插值,并采用Matlab软件开发专门的程序,实现研究区高程插值计算与结果可视化分析。以广州市南沙区10 km2范围内的200个高程点数据为例,分别运用球面模型、指数模型和高斯理论变差函数模型进行10 m×10 m格网插值,借助Matlab可视化分析插值结果及其精度,表明采用指数模型效果最好。

普通Kriging法在空间内插中的运用

用克里格法进行插值不仅能获得预测结果,而且能够获得预测误差.克里格法也是求线性最优、无偏内插的一种方法.该方法优于最近距离插值、距离反平方插值等任何一种线性插值方法.普通克里格法在克里格法中是使用较广泛的一种方法.

普通Kriging法在空间插值中的运用

目的为提高矿产出储量计算的精确性。方法运用普通克里格法解决空间插值问题。针对地质人员采集数据信息的局限性,采用普通克里格插值方法弥补数据量的缺乏。对新疆贝克滩水系沉积物化探数据进行空间分析。结果预测值参数——均值为106.39,峰度为-0.30,最大值为148.76,标准差为27.57,偏度为-1.12,最小值为53.91;交叉验证法参数:指标值为10.86。结论通过交叉检验、QQ检验、预测直方图方法验证表明,采用普通克里格法得到的预测值效果较好。

多波束测深数据的抗差Kriging拟合

针对普通Kriging法处理多波束测深数据受异常值影响的问题,推导变异函数样本值的抗差计算公式来消除异常值对变异函数拟合的干扰。利用实测数据对算法进行实现,验证其在精确估计和检测异常方面的优势。进一步采用该算法对数据进行规则格网的构建,将其与人工剔除异常生成的格网比较,获得一致的效果,证明算法在自动检测异常的同时生成高精度海底地形规则格网的可行性。

基于Kriging方法和GIS技术的地价时空格局研究

为了研究城市内部地价变化的区域规律,以及引起局部地价上涨的原因,采用剔除二阶趋势的普通Kriging方法,结合GIS技术进行栅格运算,对北京市1998-2005年间的土地交易价格数据进行了时空分布格局的研究。研究发现:北京市地价分布与环线具有很好的耦合关系,市中心辐射影响明显,尚没有形成独立的次级中心;城市内部地价增长的主要原因为功能中心的辐射影响,城市规划和升值预期的影响以及基础设施改造和交通条件的改善;在北京市郊区化过程中,地价变化表现出先外围大幅增长后内部大幅增长的规律,表现出资源约束下的城市土地利用模式。

Kriging插值组件的混合编程实现

在.NET技术框架下,提出使用C#语言和R语言混合编程模式实现普通Kriging插值功能组件,并应用该组件完成东北三省气温插值分析。实验效果表明,在.Net技术框架下,使用R和C#混合编程模式开发普通Kriging插值功能的周期短成本低且容易扩展到其他空间统计分析功能实现。

基于普通Kriging法的速度场模型建立

目前,我国已采用CGCS2000国家大地坐标系,根据现有高分辨率的速度场资料建立我国地壳运动速度场模型已很有必要.Kriging插值法不仅能获得预测结果,而且能够获得预测误差.Kriging法也是求线性最优、无偏内插的一种方法.提出了基于普通Kriging法的速度场模型生成算法,并实现了多面函数拟合法和反距离加权法建立速度场模型.通过实验结果验证比较内插精度,证实Kriging法精度最高,且插值精度达到了毫米级.

普通Kriging算法的井下煤层面重构

为认清煤层面分布规律,以山西省朔州市西易易顺煤矿4号煤层的钻井样本为例,采用克里金算法进行井下煤层面重构。根据变差函数理论模型,计算模型参数;通过交叉检验选用球状模型,针对区域化变量的特征,选择普通克里金算法,求解各观测点对应高程值的估计值以及克里金估计方差,调用克里金工具箱绘制煤层曲面,进行误差分析和综合评价。结果表明:普通克里金算法求得估计值与实测值之间的标准误差为4.683 920 1,变异系数为0.020 104 95,能够较为准确地预测井下煤层面的分布结构,为煤矿井下开采的安全预测提供有力的理论支撑。

Application of Artificial Neural Network, Kriging, and Inverse Distance Weighting Models for Estimation of Scour Depth around Bridge Pier with Bed Sill

This paper outlines the application of the multi-layer perceptron artificial neural network (ANN), ordinary kriging (OK), and inverse distance weighting (IDW) models in the estimation of local scour depth around bridge piers. As part of this study, bridge piers were installed with bed sills at the bed of an experimental flume. Experimental tests were conducted under different flow conditions and varying distances between bridge pier and bed sill. The ANN, OK and IDW models were applied to the experimental data and it was shown that the artificial neural network model predicts local scour depth more accurately than the kriging and inverse distance weighting models. It was found that the ANN with two hidden layers was the optimum model to predict local scour depth. The results from the sixth test case showed that the ANN with one hidden layer and 17 hidden nodes was the best model to predict local scour depth. Whereas the results from the fifth test case found that the ANN with three hidden layers was the best model to predict local scour depth.

基于星载激光雷达数据的森林地上生物量估算方法比较

近年来,星载激光雷达数据已被广泛用于大尺度森林地上生物量估计,但由于其激光光斑采样点不连续,通常使其需要与辅助数据相结合来估算森林地上生物量的连续分布,且估算方法仍存在许多不确定性。研究以祁连山国家公园为样本,结合星载激光雷达ICESat/GLAS数据、Landsat OLI数据和样地调查数据建立了3种基于非参数化算法(普通克里金插值(Ordinary Kriging,OK),支持向量回归(Support Vector regression,SVR)和随机森林(Random forest,RF))的森林地上生物量估算模型,以森林资源清查数据独立验证各模型估计精度。结果发现:3种模型的均方根误差(RMSE)从低到高依次为SVR(19.053 t·hm^(-2))、RF(21.074 t·hm^(-2))和OK(26.362 t·hm^(-2)),平均相对误差(MRE)从低到高依次为SVR(31.890%)、RF(33.314%)和OK(55.398%),且除OK模型外,SVR与RF模型的总体相对误差(TRE)都在可接受的范围内。进一步对SVR与RF模型生成的森林地上生物量空间分布的准确性进行验证,发现相较RF模型,SVR模型生成的森林地上生物量空间分布与森林资源清查数据更为接近。SVR森林地上生物量估计模型在数量精度和分布精度上都表现更优。结果可为今后基于星载激光雷达数据的森林地上生物量估算提供借鉴。

寒潮背景下舟山群岛气温空间插值方案对比评估

在测站稀疏的海岛地区,如何科学选择插值方案以合理体现气象要素的空间分布特征是精细化监测面临的重要问题。以舟山群岛为例,挑选了有中尺度站观测以来(2014—2021年)影响舟山的8次寒潮过程,对比检验了普通克里格(Ordinary Kriging, OK)、反距离权重(Inverse Distance Weighing, IDW)、ANUSPLIN(以下简称ANU)三种方案的插值效果。针对8次过程的过程最低气温、日最低气温降幅和日平均气温降幅,在53个测站中随机选取11个检验站点,发现ANU的插值误差高于OK和IDW。进一步设计了周边站点密集、周边站点稀疏、检验站点脱离本岛三组插值试验,分析表明,ANU的插值表现与周边站点的密集程度息息相关:当周边站点密集时,ANU的插值误差小于OK和IDW;当周边站点稀疏时,ANU的插值误差明显高于OK和IDW。在周边站点密集分布的情形下,无论检验站点位于舟山本岛还是零散小岛上,ANU均能取得最优插值效果,说明在气温插值中ANU对地形的依赖相对较小,插值精度对插值效果的影响亦较小。

科尔沁沙地土壤碳储量插值计算对比及其影响因素分析

准确估算土壤碳储量对碳中和的实现与气候变化应对有着重要意义。本研究以地处我国北方半干旱农牧交错带东端的科尔沁沙地为研究区域,基于310个位点0-100 cm深土壤的有机碳数据,用不同插值方法[反距离权重法(IDW)、普通克里金法(OK)和回归克里金法(RK)]对土壤有机碳密度(SOCS)进行空间插值并计算区域土壤有机碳储量,使用平均误差(ME)、平均标准化误差(MSE)和均方根误差(RMSE)对插值结果进行评价,结合实测SOCS验证土壤碳储量计算的最优插值方法。结果表明:1)在半干旱沙地SOCS估算中,最终进入回归预测模型的环境变量按影响程度从大到小依次有年积温、降水量、砂土含量和海拔,SOCS与海拔、年积温、降水量和砂土含量存在显著负相关关系;2)不同插值方法计算的区域土壤有机碳储量具有显著差异(P<0.05),基于RK、IDW和OK计算得土壤有机碳储量分别为150.34、158.03和140.11 Tg。与实测值相比,OK低估了土壤有机碳储量,IDW高估了土壤有机碳储量,这种差异凸显了插值方法在区域尺度土壤有机碳储量估算中的重要性;3)基于RK插值的结果最优(ME=0.208,MSE=1.211,RMSE=1.973,R^(2)=0.3706),相比于OK和IDW的插值精度分别提高了6.0%和22.4%。本研究表明在半干旱沙地RK插值仍然适用并且可以提高插值精度,能更加准确地估算土壤有机碳储量。

空间插值在测氡探测隐蔽火源中的应用比较

为了选择适用于局部观测尺度下测氡探测隐蔽火源的最优空间插值方法,本文以北岩煤矿火区样本数据为研究对象,基于Arc GIS地统计分析模块,通过交叉检验定量筛选出4种插值方法下误差最小的插值模型,定性比较了不同模型的空间分布特征,确定了最优插值方法并进行了钻孔验证。结果表明,4种方法中误差最小的插值模型分别为反距离权重法选择模型幂指数p=1,径向基函数法为薄板样条函数模型,泛克里金法与普通克里金法均为高斯函数模型;综合空间分布图内插、外推表面分布特征及钻孔验证结果,插值方法排序为普通克里金法(高斯函数)>泛克里金法(高斯函数)>径向基函数法(薄板样条函数)>反距离权重法(p=1),优先选择普通克里金法(高斯函数)进行插值来获取煤自燃火区地表氡分布差异信息。

Hybrid response surface method for system reliability analysis of pilereinforced slopes

To consider the complex soil-structure interaction in a pile-slope system,it is necessary to analyze the performance of pile-slope systems based on a three-dimensional(3D)numerical model.Reliability analysis of a pile-slope system based on 3D numerical modeling is very challenging because it is computationally expensive and the performance function of the pile failure mode is only defined in the safe domain of soil stability.In this paper,an efficient hybrid response surface method is suggested to study the system reliability of pile-reinforced slopes,where the support vector machine and the Kriging model are used to approximate performance functions of soil failure and pile failure,respectively.The versatility of the suggested method is illustrated in detail with an example.For the example examined in this paper,it is found that the pile failure can significantly contribute to system failure,and the reinforcement ratio can effectively reduce the probability of pile failure.There exists a critical reinforcement ratio beyond which the system failure probability is not sensitive to the reinforcement ratio.The pile spacing affects both the probabilities of soil failure and pile failure of the pile-reinforced slope.There exists an optimal location and an optimal length for the stabilizing piles.

黄淮海平原不同土地利用方式下土壤呼吸空间变异预测

[目的]探究土壤呼吸的空间变异特征及协同克里金法预测土壤呼吸准确性,从而为精准预测陆地不同生态系统土壤碳收支研究提供数据参考。[方法]选取黄淮海平原北部典型耕地、草地和林地作为研究样区,基于表征土壤理化性质的辅助指标用协同克里金法对土壤呼吸进行了预测,以评估其与普通克里金法预测的精准度。[结果]土壤呼吸在不同土地利用方式的研究样区均呈现中等程度变异,变异系数分别为33%(耕地),24%(草地)和31%(林地)。土壤呼吸空间相关距离由大到小依次是林地(15.12 m)、耕地(3.83 m)和草地(2.47 m)。基于相关分析和协同克里金法模拟确定土壤呼吸空间变异最优辅助指标,在耕地为碳磷比(C/P)、氮磷比(N/P)和土壤pH值;草地和林地除共有辅助指标土壤水分(SM)和土壤温度(ST5)外,土壤pH值和气温(TEMP)依次为其二者特有的辅助指标。土壤呼吸空间变异预测表明协同克里金均比普通克里金法插值精度高,其在草地提升最为明显,平均绝对误差(MAE)、平均相对误差(MRE)、均方根误差(RMSE)和平均标准误差(MSE)分别提高10.14%,9.82%,9.10%,10.87%,在林地中各误差精度提高介于4.78%(MAE)~12.09%(MRE),在耕地中预测精度提升最小,协同克里金法比普通克里金法预测精度仅平均提高3.27%。[结论]土壤呼吸的影响因子作为辅助变量的协同克里金法可以更准确地预测林地、耕地和草地土壤呼吸的空间变异特征。