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1.
Generally, multiple variables are sampled in addition to the one used to quantify the main phenomenon under study. In some
situations, this secondary information is sampled exhaustively for the study area and can be incorporated for helping in estimating
the variable of interest. There are several methodologies available for incorporating densely sampled secondary information.
Collocated cokriging is one of these methodologies and has the advantage to other methodologies, of accounting for spatial
correlation. However, one drawback in its application comes from the difficulty in modeling the coregionalization. Simplified
models of coregionalization were developed specifically for the collocated cokriging case.
This paper presents, through a case study, the incorporation of dense secondary information using collocated cokriging. The
watertable above a coal underground mine is mapped using water-level readings at monitoring piezometers complemented by highly
correlated topographic data. The incorporation of dense secondary information through the utilization of a linear model of
coregionalization and Markov models is comparatively evaluated in various aspects such as mathematical quality, coherence
with the natural phenomena and the ease of utilization and modeling. Simple kriging with local varying means also is evaluated
as it accounts for nonstationarity and is easily implemented. All these methods that incorporate topography as secondary information
for mapping the watertable provided maps more in accordance with the natural phenomena than ordinary kriging using the principal
attribute solely. Among these methods, strictly collocated cokriging using a linear model of coregionalization showed overall
superior performance. 相似文献
2.
Several alternative estimation and interpolation methods for making annual precipitation maps of Asturias are analysed. The
data series in this study corresponds to the year 2003. There exists an evident relationship between precipitation and altitude,
with a high correlation coefficient of 0.70, that reflects the hillside effect; that is, the increase in the amount of precipitation
in more mountainous areas. The direct spatial variability of precipitation and of altitude and the cross variability of precipitation–altitude
are defined by two exponential variogram models: one with a short-range structure (15–30 km) that reflects the control exerted
by the lesser, local mountain ranges over the amount of precipitation; and another with a long-range structure (80 km) that
supposes the influence over precipitation of the major mountainous alignments of the inland areas of the Cantabrian Mountain
Range (Cordillera Cantábrica) situated between 60 and 90 km from the coastline. These variogram models had to be validated for coregionalization by the
Pardo-Igúzquiza and Dowd method so as to be able to make the cokriging map. The geometric estimation methods employed were
triangulation and inverse distance. The geostatistical estimation methods developed were simple kriging, ordinary kriging,
kriging with a trend model (universal kriging), lognormal kriging, and cokriging. In all of these methods, a 3 × 3 km2 grid was selected with a total of 2580 points to estimate, a circular search window of 60 km, and a relatively small number
of samples with the aim of highlighting the local features and variations on isohyet maps. The kriging methods were implemented
using the WinGslib software, incorporating two specific programs, Prog2 and Fichsurf, so as to be able then to make isohyet
maps using the Surfer software. All the methods employed, apart from triangulation, rendered realistic maps with good fits
to the values of the original data (precipitation) of the sample maps. The problem with triangulation lies not in the reliability
of the estimates but in the fact that it gives rise to contrived maps because of the tendency of isohyets to present abundant
triangular facets. The reliability of the methods was based on cross-validation analysis and on evaluation of the different
types of errors, both in their values and in their graphical representations. Substantial differences were not found in the
values of the errors that might discriminate some methods from others in an evident way. Bearing the aforesaid in mind, should
we have to make an evaluation of the different estimation methods in decreasing order of acceptance, this would be: kriging
with a trend model, inverse distance, cokriging, lognormal kriging, ordinary kriging, simple kriging, and triangulation. The
application of other estimation methods such as colocated cokriging, kriging with an external drift, and kriging of variable
local means (residual kriging) is dependent on the availability of a digital model of the terrain with an altitude grid of
the region. 相似文献
3.
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 总被引：10，自引：1，他引：9
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Ordinary kriging (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%。 相似文献
4.
喀斯特地区春季土壤水分空间插值方法对比 总被引：1，自引：0，他引：1
以杨眉河小流域为研究区,通过土壤水分采样,选取辅助变量,采用普通克里金、协同克里金、回归克里金3种地统计学方法对土壤水分数据进行空间插值。结果表明：1）回归克里金对研究区土壤水分估算误差最小,其次为协克里金,普通克里金的误差最大;2）普通克里金生成的土壤水分表面最为平滑,而回归克里金最大程度反映了研究区实际的土壤水分空间变化;3）对于协同克里金,以湿度指数（WI）样点数据作为辅助变量的估算误差小于将WI栅格数据作为辅助变量的估算误差。总之,在可获得有效辅助变量的条件下,回归克里金对研究区土壤水分估算的效果优于协同克里金与普通克里金。 相似文献
5.
空间软数据及其插值方法研究进展 总被引：7，自引：0，他引：7
由于对地观测技术的迅速发展,空间数据的种类和数量增长迅猛,由空间数据反演得到的各种信息日趋膨胀,这些反演结果中的信息不少以软数据的形式出现。在实际应用中,这些软数据往往与空间插值的目标变量具有一定的相关性,甚至成为控制目标变量空间分布特征的重要因素。然而,由于这些数据通常表示为非数值形式,在计算和处理上存在着一定困难,以致被传统的插值方法所忽视,从而造成信息浪费。近来出现的空间软插值方法是一种利用空间软数据作为辅助信息并以改善插值效果的方法,能够较好的处理并利用软数据所隐含的信息,具有较好的应用发展前景。本文根据空间软数据的特点及其分类,系统综述了空间软插值方法及其应用领域。首先分析了空间数据软硬性质的根本区别,论述了软数据的分类和“硬化”方法,然后介绍空间插值模型中对空间软数据的集成方法和原理,最后对空间软插值方法及其应用研究领域进行了展望。 相似文献
6.
Michael Kuntz 《International journal of geographical information science》2014,28(9):1904-1921
Small-sized housing samples and price predictions at nonobserved locations require geostatistical approaches, particularly the kriging estimator. Nevertheless, geostatistics has thus far received little attention in real estate economics. The article’s objective is to empirically compare the prediction accuracy of univariate kriging variants, namely detrended kriging (DK) and universal kriging (UK), and multivariate extensions, including detrended cokriging (DCK) and universal cokriging (UCK). Both latter methods consider structural and neighborhood characteristics as auxiliary variables. While the price surfaces of DK and UK show nearly identical cross-validated accuracies, the cross-validation-based prediction accuracy of DCK and UCK differ in favor of the latter. If real estate agencies are faced with a univariate sample of property prices, either DK or UK can be used, while in the multivariate case, UCK is recommended, although numerically more complex. 相似文献
7.
The Capanema Mine, an iron ore deposit, is located in the central portion of the Quadrilátero Ferrífero, State of Minas Gerais, southeastern Brazil. Mine development data from approximately 7000 drillholes were used for a comparative study between kriging variance and interpolation variance as uncertainty measurements associated with ordinary kriging estimates. As known, the traditional kriging variance does not depend on local data and, therefore, does not measure the actual dispersion of data. On the other hand, the interpolation variance measures adequately the local dispersion of data used for an ordinary kriging estimate. This paper presents an application of the concept of interpolation variance for measuring uncertainties associated with ordinary kriging estimates of Fe and silica grades. These data were selected for their distinct statistical characteristics with Fe presenting a negatively skewed distribution and, consequently, a low dispersion, and silica a positively skewed distribution and, therefore, a high variability. Comparative studies between the two uncertainty measurements associated with ordinary kriging estimates of Fe and silica proved the superiority of the interpolation variance as a reliable and precise alternative to the kriging variance. 相似文献
8.
A treatise on the use of geostatistics for the characterization of nonrenewable resources 总被引：1，自引：0，他引：1
James R. Carr 《Natural Resources Research》1992,1(1):61-73
Five decades of geostatistical development are reviewed to summarize the state of the art for spatial interpolation vis-à-vis kriging or a form thereof. Although a search of the literature reveals a variety of kriging methods, there are but two infrastructures for geostatistical interpolation: simple cokriging, for estimating a single variable using two variables, and generalized cokriging, for estimating one or more variables using the same number of variables that are estimated. The many forms of kriging are varieties of these two interpolation infrastructures. This notion is emphasized to aid the selection of an appropriate interpolation model for a nonrenewable resource. These models are discussed, and literature for the models and for applicable software is cited. Additionally, all aspects of spatial interpolation are discussed, including the adequacy of spatial sampling, distribution characteristics of spatial samples, semivariograms, search parameters, and selection of interpolation models in conformance with spatial data characteristics. Finally, the relationship between interpolation and raster-based geographic information systems is emphasized. 相似文献
9.
利用不同方法估测土壤有机质及其对采样数的敏感性分析 总被引：7，自引：5，他引：2
用随机方法从262个采样点中抽取200个点作为已知有机质含量的数据集,将所有采样点的碱解氮作为辅助数据预测有机质的空间分布。利用有机质信息的普通克立格法的方差解释量和预测精度最低,而回归克立格法因在预测过程中加入了回归残差而使方差解释量最大、预测精度最高。为了分析采样数对不同方法预测精度的影响,从上述已知有机质含量的200个点中分别随机抽取40、80、120、160个点构成4个数据集,分别利用它们的有机质信息和不同方法预测了有机质的空间分布,结果表明:对于每个数据集,4种方法的预测精度顺序均为RGK>COK>RG>OK,线性回归法的预测精度随采样点的增加基本不变,而其它三种方法的预测精度却逐渐提高。 相似文献
10.
11.
Steve W. Lyon Rasmus S⊘rensen Johan Stendahl Jan Seibert 《International journal of geographical information science》2013,27(5):723-740
Interpolation of point measurements using geostatistical techniques such as kriging can be used to estimate values at non-sampled locations in space. Traditional geostatistics are based on the spatial autocorrelation concept that nearby things are more related than distant things. In this study, additional information was used to modify the traditional Euclidean concept of distance into an adjusted distance metric that incorporates similarity in terms of quantifiable landscape characteristics such as topography or land use. This new approach was tested by interpolating soil moisture content, pH and carbon-to-nitrogen (C:N) ratio measured in both the mineral and the organic soil layers at a field site in central Sweden. Semivariograms were created using both the traditional distance metrics and the proposed adjusted distance metrics to carry out ordinary kriging (OK) interpolations between sampling points. In addition, kriging with external drift (KED) was used to interpolate soil properties to evaluate the ability of the adjusted distance metric to incorporate secondary data into interpolations. The new adjusted distance metric typically lowered the nugget associated with the semivariogram, thereby better representing small-scale variability in the measured data compared to semivariograms based on the traditional distance metric. The pattern of the resulting kriging interpolations using KED and OK based on the adjusted distance metric were similar because they represented secondary data and, thus, enhanced small-scale variability compared to traditional distance OK. This created interpolations that agreed better with what is expected for the real-world spatial variation of the measured properties. Based on cross-validation error, OK interpolations using the adjusted distance metric better fit observed data than either OK interpolations using traditional distance or KED. 相似文献
12.
This paper is concerned with the problem of predicting the surface elevation of the Braden breccia pipe at the El Teniente mine in Chile. This mine is one of the world’s largest and most complex porphyry-copper ore systems. As the pipe surface constitutes the limit of the deposit and the mining operation, predicting it accurately is important. The problem is tackled by applying a geostatistical approach based on closed-form non-stationary covariance functions with locally varying anisotropy. This approach relies on the mild assumption of local stationarity and involves a kernel-based experimental local variogram a weighted local least-squares method for the inference of local covariance parameters and a kernel smoothing technique for knitting the local covariance parameters together for kriging purpose. According to the results, this non-stationary geostatistical method outperforms the traditional stationary geostatistical method in terms of prediction and prediction uncertainty accuracies. 相似文献
13.
以像西某铝土矿矿集区为试验区,以SPOT-5、资源二号卫星、QuickBird影像为数据源,提出矿山开采动态遥感监测的技术流程,并对试验区铝土矿开采状况进行动态遥感监测.根据基准年及现状年的监测结果,在基准年至现状年的3年间,试验区铝土矿开采量急剧增加,存在越界和界外开采现象,开采秩序一度比较混乱;现状年与基准年相比,越界和界外已停采面积均大幅增加,开采秩序好转;至现状年大多数铝土矿采场未进行复垦和环境治理.研究结果表:研究中采用的集3S技术于一体的矿业开发与矿山地质环境遥感监测技术方法是有效可行的,对其他矿山开采的动态遥感监测具有一定的借鉴意义;监测结果可为矿山的合理开发及可持续发展提供决策依据. 相似文献
14.
Any mine planning requires careful prediction of both the head grade andtonnage ofmineralization. There are various methods of interpolation that attempt to provide reasonable estimatesat unsampled locations. All of these give realizations that are unduly smooth and extremevalues that occur in reality are not reflected in these estimates. Such methods, therefore,provide limited scope for accurate risk assessment. An alternative approach that is rapidlygaining popularity is the method of conditional simulation. This approach attempts to reproduceboth the grade distributions of the sample data as well as its spatial variability. In this paper,a case study is presented on a platinum mineralization to demonstrate and compare sequentialGaussian and sequential conditional simulation techniques and to quantify and discuss therelevant sensitivities. 相似文献
15.
Samanta Biswajit Bandopadhyay Sukumar Ganguli Rajive Dutta Sridhar 《Natural Resources Research》2004,13(3):189-200
In this paper, sparse data problem in neural network and geostatistical modeling for ore-grade estimation was addressed in the Nome offshore placer gold deposit. The problem of sparse data arises because of the random data division into training, validation, and test subsets during ore-grade modeling. In this regard, the possibility of generating statistically dissimilar data subsets by random data division was also explored through a simulation exercise. A combined approach of data segmentation and application of a Kohonen network then was used to solve the data division problem. Two neural networks and five kriging models were applied for grade modeling. The neural network was trained using an early stopping method. Performance evaluation of the models was carried out on the test data set. The study results indicated that all the models that were investigated in this study performed almost equally. It was also revealed that by using the secondary variable watertable depth the neural network and the kriging models slightly improved their prediction precision. Further, the overall R
2 of the models was poor as a result of high nugget (noisy) component in ore-grade variation. 相似文献
16.
DELIANG CHEN LEBING GONG CHONG-YU XU SVEN HALLDIN 《Geografiska Annaler: Series A, Physical Geography》2007,89(4):249-261
A baseline climatology is required in evaluating climate variability and changes on regional and local scales. Gridded climate normals, i.e. averages over a 30‐year period, are of special interest since they can be readily used for validation of climate models. This study is aimed at creating an updated gridded dataset for Swedish monthly temperature normals over the period 1971–2000, based on standard 2‐m air temperature records at 510 stations in mainland Sweden. Spatial trends of the normal temperatures were modelled as functions of latitude, longitude and elevation by multiple linear regression. The study shows that the temperature normals are strongly correlated with latitude throughout the year and especially in cold months, while elevation was a more important factor in June and July. Longitude played a minor role and was only significant in April and May. Regression equations linking temperature to latitude, longitude and elevation were set up for each month. Monthly temperature normals were detrended by subtracting spatial trends given by the regressions. Ordinary kriging was then applied to both original data (simple method) and de‐trended data (composite method) to model the spatial variability and to perform spatial gridding. The multiple regressions showed that between 82% (summer) and 96% (winter) of the variance in monthly temperature normals could be explained by latitude and elevation. Unexplained variances, i.e. the residuals, were modelled with ordinary kriging with exponential semivariograms. The composite grid estimates were calculated by adding the multiple linear trends back to the interpolated residuals at each grid point. Kriged original temperature normals provided a performance benchmark. The cross–validation shows that the interpolation errors of the normals are significantly reduced if the composite method rather than the simple one was used. A gridded monthly dataset with 30‐arcsecond spacing was created using the established trends, the kriging model and a digital topographic dataset. 相似文献
17.
Radial Basis Function Network for Ore Grade Estimation 总被引：1，自引：0，他引：1
Biswajit Samanta 《Natural Resources Research》2010,19(2):91-102
This paper highlights the performance of a radial basis function (RBF) network for ore grade estimation in an offshore placer
gold deposit. Several pertinent issues including RBF model construction, data division for model training, calibration and
validation, and efficacy of the RBF network over the kriging and the multilayer perceptron models have been addressed in this
study. For the construction of the RBF model, an orthogonal least-square algorithm (OLS) was used. The efficacy of this algorithm
was testified against the random selection algorithm. It was found that OLS algorithm performed substantially better than
the random selection algorithm. The model was trained using training data set, calibrated using calibration data set, and
finally validated on the validation data set. However, for accurate performance measurement of the model, these three data
sets should have similar statistical properties. To achieve the statistical similarity properties, an approach utilizing data
segmentation and genetic algorithm was applied. A comparative evaluation of the RBF model against the kriging and the multilayer
perceptron was then performed. It was seen that the RBF model produced estimates with the R
2 (coefficient of determination) value of 0.39 as against of 0.19 for the kriging and of 0.18 for the multilayer perceptron. 相似文献
18.
In most modern coal mines, there are many coal quality parameters that are measured on samples taken from boreholes. These data are used to generate spatial models of the coal quality parameters, typically using inverse distance as an interpolation method. At the same time, downhole geophysical logging of numerous additional boreholes is used to measure various physical properties but no coal quality samples are taken. The work presented in this paper uses two of the most important coal quality variables—ash and volatile matter—and assesses the efficacy of using a number of geostatistical interpolation methods to improve the accuracy of the interpolated models, including the use of auxiliary variables from geophysical logs. A multivariate spatial statistical analysis of ash, volatile matter and several auxiliary variables is used to establish a co-regionalization model that relates all of the variables as manifestations of an underlying geological characteristic. A case study of a coal mine in Queensland, Australia, is used to compare the interpolation methods of inverse distance to ordinary kriging, universal kriging, co-kriging, regression kriging and kriging with an external drift. The relative merits of these six methods are compared using the mean error and the root mean square error as measures of bias and accuracy. The study demonstrates that there is significant opportunity to improve the estimations of coal quality when using kriging with an external drift. The results show that when using the depth of a sample as an external drift variable there is a significant improvement in the accuracy of estimation for volatile matter, and when using wireline density logs as the drift variable there is improvement in the estimation of the in situ ash. The economic benefit of these findings is that cheaper proxies for coal quality parameters can significantly increase data density and the quality of estimations.
相似文献19.
Francky Fouedjio 《Natural Resources Research》2016,25(3):283-296
This article addresses the problem of the prediction of the breccia pipe elevation named Braden at the El Teniente mine in Chile. This mine is one of the world’s largest known porphyry-copper ore bodies. Knowing the exact location of the pipe surface is important, as it constitutes the internal limit of the deposit. The problem is tackled by applying a non-stationary geostatistical method based on space deformation, which involves transforming the study domain into a new domain where a standard stationary geostatistical approach is more appropriate. Data from the study domain is mapped into the deformed domain, and classical stationary geostatistical techniques for prediction can then be applied. The predicted results are then mapped back into the original domain. According to the results, this non-stationary geostatistical method outperforms the conventional stationary one in terms of prediction accuracy and conveys a more informative uncertainty model of the predictions. 相似文献
20.
Regular spacing of drainage outlets from linear fault blocks 总被引：3，自引：0，他引：3
Peter J. Talling Michael D. Stewart Colin P. Stark Sanjeev Gupta & Stephen J. Vincent 《Basin Research》1997,9(4):275-302
Outlets of river basins located on fault blocks often show a regular spacing. This regularity is most pronounced for fault blocks with linear ridge crests and a constant half-width, measured perpendicular to the ridge crest. The ratio of the half-width of the fault block and the outlet spacing is used in this study to characterize the average shape (or spacing ratio) of 31 sets of drainage basins. These fault-block spacing ratios are compared with similar data from small-scale flume experiments and large-scale mountain belts. Fault-block spacing ratios are much more variable than those measured for mountain belts. Differences between fault-block spacing ratios are attributed to variability in factors influencing the initial spacing of channel heads and subsequent rates of channel incision during the early stages of channel network growth (e.g. initial slope and uplift rate, precipitation, runoff efficiency and substrate erodibility). Widening or narrowing of fault blocks during ongoing faulting will also make spacing ratios more variable. It is enigmatic that some of these factors do not produce similar variability in mountain belt spacing ratios. Flume experiments in which drainage networks were grown on static topography show a strong correlation between spacing ratios and surface gradient. Spacing ratios on fault blocks are unaffected by variations in present-day gradients. Drainage basins on the Wheeler Ridge anticline in central California, which have formed on surfaces progressively uplifted by thrust faulting during the last 14 kyr, demonstrate that outlet spacing is likely to be determined during the early stages of drainage growth. This dependency on initial conditions may explain the lack of correlation between spacing ratios of fault blocks and slopes measured at the present day. Spacing ratios determine the location of sediment supply points to adjacent areas of deposition, and hence strongly influence the spatial scale of lateral facies variations in the proximal parts of sedimentary basins. Spacing ratios may be used to estimate this length scale in ancient sedimentary basins if the width of adjacent topography is known. Spacing ratio variability makes these estimates much less precise for fault blocks than for mountain belts. 相似文献