Trend surface analysis as a special case of IRF-k kriging     

D. Marcotte  M. David 《Mathematical Geology》1988,20(7):821-824

This short note establishes the equivalence between trend surface analysis with polynomials of orderk and IRF-k (intrinsic random function of orderk) kriging with a nugget effect covariance model.  相似文献   

Estimation of proportions of lithotypes using auxiliary information     

K. B. Patel  H. S Pandalai  A. Subramanyam 《Mathematical Geology》1996,28(6):765-781

The problem of estimating the proportion of lithological (ore) types in volumes of mineral deposits is considered when an auxiliary variable Z(z) is observed along with the lithology L(x) at x. The process {Z(x)} is assumed to be stationary and an assumption on the statistical relationship between {Z(x)} and {L(x)} processes is made. Consequently, the second-order stationarity of {L(x)} is not required. A method using the kriged distribution of the auxiliary variable is proposed. A case study illustrating the procedure is given.  相似文献   

Trend removal in spatially correlated datasets     

Anita Singh  Ashok K. Singh 《Mathematical Geology》1996,28(1):111-132

Typically, datasets originated from mining exploration sites, industrially polluted and hazardous waste sites are correlated spatially over the region under investigation. Ordinary kriging (OK) is a well-established geostatistical tool used for predicting variables, such as precious metal contents, biomass, species counts, and environmental pollutants at unsampled spatial locations based on data collected from the neighboring sampled locations at these sites. One of the assumptions required to perform OK is that the mean of the characteristic of concern is constant for the entire region under consideration (e.g., there is no spatial trend present in the contaminant distribution across the site). This assumption may be violated by dalasets obtained from environmental applications. The occurrence of spatial trend in a dataset collected from a polluted site is an indication of the presence of two or more statistical populations (strata) with significantly different mean concentrations. Use of OK in these situations can result in inaccurate kriging estimates with higher SDs which, in turn, can lead to incorrect decisions regarding all subsequent environmental monitoring and remediation activities. A univariate and a multivariate approach have been described to identify spatial trend that may be present at the site. The trend then is removed by subtracting the respective means from the corresponding populations. The results of OK before and after trend removal are being compared. Using a real dataset, it is shown that standard deviations (SDs) of the kriging estimates obtained after trend removal are uniformly smaller than the corresponding SDs of the estimates obtained without the trend removal.  相似文献   

Quality mapping of the Ryytimaa dolomite in western Finland     

Eevaliisa Laine 《Mathematical Geology》1996,28(4):477-499

The Ryytimaa dolomite formation in western Finland is mined for fertilizing purposes in agriculture. Ordinary kriging, indicator kriging, and indicator principal components simulation were used to map the dolomite quality. The fertilizing properties depend on the relative amounts of MgO and neutralizing CaO in dolomite. Based on the chemical composition the dolomite is divided into six quality classes according to the Finnish legislation. This quality classification is only partially in accordance with the three populations inferred from the distributions of the MgO, CaO, and neutralizing CaO contents. These populations probably represent compositionally different dolomite layers, now forming complicated fold interference structures that are visible on the kriged maps. The mapping of the quality, and thus, selective mining of the dolomite deposit is possible using the quality classification based on the three populations. In contrast, selective mining of the dolomite based on the legislation is difficult—at least with techniques used in this study.  相似文献   

Adding bounds to kriging     

Randal J. Barnes  Kwangho You 《Mathematical Geology》1992,24(2):171-176

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.  相似文献   

Identifying spatial heterogeneity of coal resource quality in a multilayer coal deposit by multivariate geostatistics     

Mohamad Nur Heriawan  Katsuaki Koike   《International Journal of Coal Geology》2008,73(3-4):307-330

This study presents a new geostatistical approach to characterization of the geometry and quality of a multilayer coal deposit using the data of seam thickness as a geometric property and the contents of ash, sodium, total sulphur, and the heating value as quality properties. A coal deposit in East Kalimantan (Borneo), Indonesia, which has a synclinal geological structure, was chosen as the study site. Semivariogram analysis clarified the strong dependence of heating value on ash content in the top and bottom parts of each seam and the existence of a strong correlation with sodium content over the sub-seams in the same location. The correlations between the geometry and quality of the seams were generally weak. A linear coregionalization model was used to derive the spatial correlation coefficients of two variables at each scale component from the single- and cross-semivariogram matrices. Because the data were correlated spatially in the same seam or over different seams, multivariate techniques (ordinary cokriging and factorial cokriging) were mainly used and the resultant spatial estimates were compared to those derived using a univariate technique (ordinary kriging). A factorial cokriging was effective to decompose the spatial correlation structures with different scales. Another important characteristic was that the sodium content shows distinct segregation: the low zones are concentrated near the boundary of the sedimentary basin, while the high zones are concentrated in the central part. The main component of sodium originates from the abundance of saline water. Therefore, it can be inferred that seawater had stronger effects on the coal depositional process in the central basin than in the border part. The geostatistical modeling results suggest that the thicknesses of all the major seams were controlled by the syncline structure, while the coal qualities chiefly were originated from the coal depositional and diagenetic processes.  相似文献   

Geochemical characterization of heavy metal contaminated area using multivariate factorial kriging   总被引：1，自引：0，他引：1  

Joaquim C. B. Queiroz  José R. Sturaro  Augusto C. F. Saraiva  Paulo M. Barbosa Landim 《Environmental Geology》2008,55(1):95-105

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.  相似文献   

On counting the number of data pairs for semivariogram estimation     

Max D. Morris 《Mathematical Geology》1991,23(7):929-943

In planning spatial sampling studies for the purpose of estimating the semivariogram, the number of data pairs separated by a given distance is sometimes used as a comparative index of the precision which can be expected from a given sampling design. Because spatial data are correlated, this index can be unreliable. An alternative index which partially corrects for this correlation, themaximum equivalent uncorrelated pairs, is proposed for comparing spatial designs. The index is developed under the assumption that the underlying stochastic process is Gaussian and is appropriate when the (population) semivariogram is to be estimated by the sample semivariogram.  相似文献   

Spatial variability and interpolation of daily precipitation amount     

E. G. Beek  A. Stein  L. L. F. Janssen 《Stochastic Environmental Research and Risk Assessment (SERRA)》1992,6(3):209-221

Daily precipitation amounts show spatial variation over sub-continential regions. Point measurements, representative for regions of land, have to be interpolated towards unobserved locations. In this study four days in 1984 were selected to investigate the spatial variability of daily precipitation amount in North-western Europe in relation to the meteorological conditions. Data were interpolated using Kriging. Crossvalidation was used to compare interpolated values with measured values. Large differences in the spatial structure of daily precipitation amount are obsered as a result of different meterological conditions. Stratification of the study area into a coastal, a mountainous and an interior stratum proved to be successful, reducing the Mean Squared Error of Prediction with up to 55%.  相似文献   

Generation of runoff series at ungauged locations using empirical orthogonal functions in combination with kriging     

H. Hisdal  O. E. Tveito 《Stochastic Environmental Research and Risk Assessment (SERRA)》1992,6(4):255-269

The method of Empirical Orthogonal Functions (EOF method) is combined with an objective interpolation technique, kriging, to generate runoff series at ungauged locations. In a case study the results are compared to series interpolated by a combination of EOF analysis and regression using catchment characteristics as independent variables. The results are also compared to linear weighting of an existing runoff series, a commonly used method for spatial interpolation. The influence of altitude on the runoff is studied comparing kriging based on 2 and 3 coordinates. The study showed that the capacity of EOF analysis combined with kriging is as good as the traditionally used linear weighting. The results, when altitude is included in the kriging, are improved.  相似文献