Geostatistical regionalization of glacial aquitard thickness in northwestern Germany, based on fuzzy kriging

In many instances hydrogeological parameters obtained by conventional methods for selected localities within an aquifer or an aquitard are not sufficient for adequate regionalization at the scale of the entire layer. Here, we demonstrate an application of the fuzzy kriging method in regionalization of hydrogeological data, in which the set of conventional, crisp values is supplemented by imprecise information subjectively estimated by an expert. It is believed that such an approach eventually may reflect the real-world conditions more closely than a traditional crisp-value approach, because the former does not impose exactness artificially on phenomena which are diffuse by their nature. Spatial interpolation was done for the thickness of one of the major aquitards (till and glaciolacustrine clay) in northwestern Germany. The dataset consists of 329 crisp values from boreholes supplemented by 172 imprecise values defined as fuzzy numbers. It is demonstrated that the reliability of regionalization was higher, compared to regionalization performed with the crisp dataset only. Fuzzy kriging was performed with FUZZEKS (Fuzzy Evaluation and Kriging System) developed at the Ecosystem Research Center at the University of Kiel.     

A variance-ratio test for supporting a variable mean in kriging

This article discusses the issue of whether to use a variable mean and describes a test that can be used to evaluate whether it is justified to add terms to the drift (deterministic part) of a geostatistical model. The basic model could be the intrinsic one, where the deterministic part is a constant, and the alternate model could be any model that includes a constant term in the expression for the drift. Also, differences between constant- and variable-mean models are discussed.     

Foliation fields and 3D cartography in geology: Principles of a method based on potential interpolation

A modeling method that takes into account known points on a geological interface and plane orientation data such as stratification or foliation planes is described and tested. The orientations data do not necessarily belong to one of the interfaces but are assumed to sample the main anisotropy of a geological formation as in current geological situations. The problem is to determine the surfaces which pass through the known points on interfaces and which are compatible with the orientation data. The method is based on the interpolation of a scalar field defined in the space the gradient in which is orthogonal to the orientations, given that some points have the same but unknown scalar value (points of the same interface), and that scalar gradient is known on the other points (foliations). The modeled interfaces are represented as isovalues of the interpolated field. Preliminary two-dimensional tests carried-out with different covariance models demonstrate the validity of the method, which is easily transposable in three dimensions.     

中国地质统计学（空间信息统计学）发展的回顾与前景

讨论了地质统计学（空间信息统计学）发展的若干问题，其内容包括４部分：１．地质统计学的理论及方法；２．关于软件系统的现状；３．关于实际应用；４．地质统计学发展前景的若干看法。     

Improving Sequential Simulation with a Structured Path Guided by Information Content

Multiple-point simulation is a newly developed geostatistical method that aims at combining the strengths of two mainstream geostatistical methods: object-based and pixel-based methods. It maintains the flexibility of pixel-based algorithms in data conditioning, while enhancing its capability of reproducing realistic geological shapes, which is traditionally reserved to object-based algorithms. However, the current snesim program for multiple-point simulation has difficulty in reproducing large-scale structures, which have a significant impact on the flow response. To address this problem, we propose to simulate along a structured path based on an information content measure. This structured path accounts for not only the information from the data, but also some prior structural information provided by geological knowledge. Various case studies show a better reproduction of large-scale structures. This concept of simulating along a structured path guided by information content can be applied to any sequential simulation algorithms, including traditional variogram-based two-point geostatistical algorithms.     

Indicator Simulation Accounting for Multiple-Point Statistics

Geostatistical simulation aims at reproducing the variability of the real underlying phenomena. When nonlinear features or large-range connectivity is present, the traditional variogram-based simulation approaches do not provide good reproduction of those features. Connectivity of high and low values is often critical for grades in a mineral deposit. Multiple-point statistics can help to characterize these features. The use of multiple-point statistics in geostatistical simulation was proposed more than 10 years ago, on the basis of the use of training images to extract the statistics. This paper proposes the use of multiple-point statistics extracted from actual data. A method is developed to simulate continuous variables. The indicator kriging probabilities used in sequential indicator simulation are modified by probabilities extracted from multiple-point configurations. The correction is done under the assumption of conditional independence. The practical implementation of the method is illustrated with data from a porphyry copper mine.     

Temporal stability of soil moisture in an oasis of northwestern China

Temporal stability of soil moisture has been widely used in hydrological monitoring since it emerged. However, the spatial analysis of temporal stability at the landscape scale is often limited because of insufficient sampling numbers. This work made an effort to investigate the spatial variations of temporal stability of soil moisture in an oasis landscape. The specific objectives of the study were to explore the spatial patterns of temporal stability and to determine the controlling factors of temporal stability in the desert oasis. A time series of soil moisture measurements were gathered on 23 occasions at 118 locations over 3 years in a rectangular transect of approximately 100 km². The nonparametric Spearman's rank correlation coefficient, standard deviation of relative difference (SDRD), and mean absolute bias error (MABE) were used to quantify the temporal stability of soil moisture. Results showed that the temporal stability of soil moisture was depth dependent and season dependent. The spatial pattern of soil moisture in a deep soil layer and between two same seasons generally had a high temporal stability. SDRD and MABE were spatially autocorrelated and exhibited strong spatial structures in the geographic space. The concept of temporal stability can be extended to describe the time‐stable areas of soil moisture with geostatistics. There were great differences between SDRD and MABE in describing the temporal stability of soil moisture and in identifying the controlling factors of temporal stability. In this case, MABE was a better alternative to estimate the areal mean soil moisture using representative locations than SDRD. Land use type, soil moisture condition, and soil particle composition were the dominant controls of temporal stability in the oasis. These insights could help to better understand the essence of temporal stability of soil moisture in arid regions.     

云南个旧多金属矿石门坎—保和地区Sn、Sb元素的成矿信息识别与提取

石门坎—保和地区位于云南个旧多金属成矿区西南部,成矿背景复杂,成矿作用具有多期性和多样性。利用研究区1∶1万土壤化探数据,采用泛克里格法和因子分析相结合的方法,提取不同层次的成矿异常信息。结果表明:主因子F_3包含Mo-Au-Sb等元素,反映成矿过程中的岩体和热液相关信息;主因子F_4包含Sn-Bi-W元素,指示中低温热液矿化环境; Sb沿杨家田断裂呈串珠状分布,反映了由北东向构造控制的空间变化特征,与已知矿点对应良好; Sn元素异常在研究区北部呈双峰状环形分布,推测受隐伏岩体或者断层控制。根据元素组合异常F_3和F_4的分布规律,结合地质资料圈定出2个找矿靶区,为进一步找矿工作提供了方向。