Hierarchical Geostatistical Analysis of an Experimental Stratigraphy

A hierarchical geostatistical analysis is conducted on a high-resolution, multiscale hydraulic conductivity (ln K) map, created by scaling up an experimental stratigraphy. Unlike a previous study which evaluates ln K variograms within individual depositional environments, this study analyzes deposits (or samples) that incorporate multiple depositional environments. Based on conductivity cutoffs selected from a global ln K histogram, an indicator map is created to divide the deposits into 4 categories: sand, silty sand, clayey silt, and clay (Hierarchy-I). Based on facies and facies assemblage types selected using geological criteria, two more indicator maps are created at a higher hierarchy (Hierarchy-II) to divide the deposits into 14 units and 2 units, respectively. For each sample, its experimental ln K variogram is decomposed into 4 auto- and cross-transition component variograms. The decomposition characteristics are then evaluated against the underlying heterogeneity and specific division rule. The analysis reveals that: (1) ln K cutoffs (sand contents of the physical stratigraphy) can be used to distinguish the shifts in dominant deposition mode; (2) sample univariate modes depend on the choice of hierarchical division; (3) sample variograms exhibit smooth-varying correlation structures (exponential-like variograms are observed in samples with a large variance in mean facies length); (4) the decomposition characteristics are sensitive to the division based on conductivity cutoffs, but not sensitive to the division based on depositional environment (For all samples, with appropriate division, the sample variogram is closely approximated by the sum of the cross-transition component variograms.); and (5) at the Hierarchy-II level, the 2-unit division gives similar decomposition characteristics as the 14-unit division. For the select samples, parsimony in hierarchical division is achieved at the facies assemblage scale.     

Estimating the effects of spatial variability of infiltration on the output of a distributed runoff and soil erosion model using Monte Carlo methods

Monte Carlo procedures were used to evaluate the effects of spatial variations in the values of the infiltration parameter on the results of the ANSWERS distributed runoff and erosion model. Simulation results obtained were compared with measured values. Field infiltration measurements indicated spatial correlation at much smaller distances than the size of an element. Therefore, at first only the error of the mean had to be taken into consideration for block infiltration rates. Consequently, not only single hydrographs were produced, but also error bands. Secondly, nine other hypothetical spatial correlation structures were also evaluated using Monte Carlo methods. in particular at low nugget variances, increasing spatial correlation of infiltration resulted in increasing coefficients of variation in model outputs. In general, rainstorms with low rainfall intensities were more difficult to simulate accurately than extreme events with high rainfall intensities. This is explained by the greater influence of the infiltration uncertainties at low rainfall intensities.     

Geostatistical analysis of arsenic concentration in groundwater in Bangladesh using disjunctive kriging

The National Hydrochemical Survey of Bangladesh sampled the water from 3,534 tube wells for arsenic throughout most of Bangladesh. It showed that 27% of the shallow tube wells (less than 150 m deep) and 1% of the deep tube wells (more than 150 m deep) exceeded the Bangladesh standard for arsenic in drinking water (50 µg L^–1). Statistical analyses revealed the main characteristics of the arsenic distribution. Concentrations ranged from less than the detection limit (0.5 µg L^–1), to as much as 1,600 µg L^–1, though with a very skewed distribution, and with spatial dependence extending to some 180 km. Disjunctive kriging was used to estimate concentrations of arsenic in the shallow ground water and to map the probability that the national limit for arsenic in drinking water was exceeded for most of the country (the Chittagong Hill Tracts and the southern coastal region were excluded). A clear regional pattern was identified, with large probabilities in the south of the country and small probabilities in much of the north including the Pleistocene Tracts. Using these probabilities, it was estimated that approximately 35 million people are exposed to arsenic concentrations in groundwater exceeding 50 µg L^–1 and 57 million people are exposed to concentrations exceeding 10 µg L^–1 (the WHO guideline value).     

Assessment of C-band SRTM DEM in a dense equatorial forest zone

A Digital Elevation Model issued from the SRTM mission was assessed on a study area located in a dense equatorial forest setting in French Guiana. The SRTM DEM defined on a 90-m grid was compared to three check sources: (1) airborne laser altimeter data, (2) an accurate heliborne DEM, and (3) spot heights. The paper also includes a comparison with a radargrammetric RADARSAT DEM. The results show that the accuracy of the SRTM DEM is about 10 m (standard deviation of errors). For a given slope aspect, the absolute value and the standard deviation of elevation errors increase almost linearly with the slope value. The slope aspect has a major influence on the sign of the elevation error: elevations are underestimated for slope facing SRTM signal (foreslopes, northwest), and conversely in the opposite direction (backslopes, southeast). Maximum errors are observed along these two directions. To cite this article: B. Bourgine, N. Baghdadi, C. R. Geoscience 337 (2005).     

地统计学方法进展研究

地统计学近年来成为空间分析的重要工具，其应用领域广泛分布在自然科学的众多领域。系统地论述了地统计学理论方法的进展，给出地统计学的总体理论框架，它包括局部估值、不确定性预测、随机模拟及多点地统计学四部分。并指出所有这些方法的理论基础是随机变量理论，其核心是利用变异函数获得研究对象的空间分布规律。同时，分别介绍了每个部分的具体方法，特别提到了新发展的多点地统计学方法。最后对地统计学的软件应用加以总结，指出将GIS与地统计学相结合是一种必然的趋势。     

析取克立格法及其应用的研究

非线性现象普遍存在于许多自然科学的研究之中,线性地质统计仅限于有效数据的线性组合;而某些非线性方法不容易处理,如条件期望的前提条件苛刻,计算复杂耗费大;析取克立格法(DK)介于两者中,利用二元概率分布函数进行估计,更有效、准确且易实现。并能很好地估计Z(x)的任意函数,解决可回采储量估计等现实问题。介绍了DK方法的基本理论和方法及其应用,并给出了计算实例。     

一种新的储量估算法—杨赤中滤波与推估法及其应用

杨赤中滤波与推估法是一种对矿床地质变量统计的新方法。为使这一新理论用于勘探网规则或不规则情况下及在矿体小而勘探抽样点比较少,产状复杂的铀矿体的储量估算,我们用此法对2个矿床的5个矿体进行了储量估算,取得了较满意的效果。实践证明,杨赤中滤波与推估法与传统的块段法比较,具有公式简明、使用方便、易掌握、计算速度快、结果准确,花费少、经济效益好等优点。本文主要介绍了此种方法实际应用的步骤,应用的体会以及效果的初步评价。     

Theoretical Estimation of the Critical Sampling Size for Homogeneous Ore Bodies with Small Nugget Effect

The aim of this work is to investigate whether it is possible to determine a critical sampling grid density for a given ore body, above which further improvement in the accuracy of the estimated ore reserves would be small or negligible. The methodology employed is based on the theory of information. First, it is proven that the range of influence, when appears in the variogram function, is a measure of the maximum variability frequency observed in the ore body. Then, a simple application of the well-known sampling theorem shows that, under certain assumptions, it is possible to define a critical sampling density as mentioned before. An approximate rule of thumb can then be stated: that critical sampling grid size is half the range of influence observed in the variogram.     

变差函数和神经网络结合的遥感影像分类方法研究

提出利用地统计学变差函数对遥感影像纹理信息进行提取，将变差函数得到的纹理信息与光谱信息相结合，运用神经网络进行分类的遥感影像分类方法。将该分类方法应用于试验区，并与最大似然法的分类结果进行对比分析，结果表明，该方法具有较高的分类精度。     

Spatial distribution of heavy metals in soils: a case study of Changxing,China

Six hundred and sixty-five soil samples were taken from Changxing County in Zhejiang Province, China, to characterize the spatial variability of Hg Cd, Pb, Cu, As and Cr. The geostatistics and geographic information system (GIS) techniques were applied, and the ordinary kriging and lognormal kriging were used to map the spatial patterns of the six heavy metals. Hg, Pb, Cu and As were fitted to the spherical model with a range of 85.75, 82.32, 86.10, and 23.17 km, respectively. Cr was fitted to the exponential model with a range of 6.27 km, and Cd was fitted to the linear model with a range of 37.66 km. Both Pb and Cu had strong spatial dependence due to the effects of natural factors including parent material, topography and soil type. Hg, Cd, Cr and As had, however, moderate spatial dependence, indicating an involvement of human factors. Meanwhile, based on the comparison between the original data and the guide values of the six metals, the disjunctive kriging technique was used to quantify their pollution risks. The results showed that only Cd and Hg exhibited pollution risks in the study area. The pollution source evaluated was closely corresponded with the real discharge of industrial production and the application of organomercury pesticides. The results of this study provide insight into risk assessment of environmental pollution and decision making for agricultural production and industrial adjustment of building materials.