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

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.     

证据权重法在张家口地区铅锌银富集区定量评价中的应用

文章以张家口铅锌银多金属富集区为例,在前人研究的基础上,运用GIS平台提取了与成矿关系密切的赋矿层位、岩体5km缓冲区、深大断裂3km和次级断裂1km的复合缓冲区及化探、物探异常等证据图层,选用证据权重法模型对研究区进行了成矿远景区分析和评价,取得了较好效果,并讨论了预测过程中信息提取时应注意的问题。     

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.     

Modeling urban expansion by using variable weights logistic cellular automata: a case study of Nanjing,China

Simulation models based on cellular automata (CA) are widely used for understanding and simulating complex urban expansion process. Among these models, logistic CA (LCA) is commonly adopted. However, the performance of LCA models is often limited because the fixed coefficients obtained from binary logistic regression do not reflect the spatiotemporal heterogeneity of transition rules. Therefore, we propose a variable weights LCA (VW-LCA) model with dynamic transition rules. The regression coefficients in this VW-LCA model are based on VW by incorporating a genetic algorithm in a conventional LCA. The VW-LCA model and the conventional LCA model were both used to simulate urban expansion in Nanjing, China. The models were calibrated with data for the period 2000–2007 and validated for the period 2007–2013. The results showed that the VW-LCA model performed better than the LCA model in terms of both visual inspection and key indicators. For example, kappa, accuracy of urban land and figure of merit for the simulation results of 2013 increased by 3.26%, 2.96% and 4.44%, respectively. The VW-LCA model performs relatively better compared with other improved LCA models that are suggested in literature.     

On counting the number of data pairs for semivariogram estimation

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.     

Spatial variability and interpolation of daily precipitation amount

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%.     

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

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.     

因子克立格分析的理论综述及应用展望

   因子克立格分析是研究多元地质统计学的基拙，是由因子克立格法和协区域化分析两部分组成，方法上包括了区域化变量(集)的分解和分解后每一空间分童的估值;本文阐述了因子克立格分析从产生到应用的理论发展、研究成果及应用展望。     

Kriging with imprecise (fuzzy) variograms. II: Application

The geostatistical analysis of soil liner permeability is based on 20 measurements and imprecise prior information on nugget effect, sill, and range of the unknown variogram. Using this information, membership functions for variogram parameters are assessed and the fuzzy variogram is constructed. Both kriging estimates and estimation variances are calculated as fuzzy numbers from the fuzzy variogram and data points. Contour maps are presented, indicating values of the kriged permeability and the estimation variance corresponding to selected membership values called levels.     

Application of spatial filter theory to kriging

Data-processing requirements for remotely sensed, digital images include spatial filtering to suppress image noise, enhance edges/contacts, and improve image clarity. Spatial filter theory demonstrates that the addition of a high-pass filtered image to a low-pass filtered image yields the original digital image. Application of this principle in kriging can be accomplished by using the same covariance matrix to solve for two weighting vectors to yield a result analogous to low- and high-pass filtering. The addition of kriged estimates calculated using both weighting vectors is analogous to summing high-, and low-pass filtered digital images. This modified method of kriging yields estimates associated with less smoothing compared to ordinary kriging. Statistical moments of original sample data are better preserved through estimation by this method.