对数泛克立金法在处理化探数据中的应用

本文研究如何用地质统计学方法处理服从对数正态分布的化探数据的问题。经对湖北阳新岩体铜含量数据的大量电算、分析、对比,最后选用了对数泛克立金法。由计算机自动绘出的估值图和漂移、剩余图能很好地反映该区化探趋势和异常,既优于趋势面分析和滑动平均法,也优于泛克立金法,且能获得较稳健的变差图。故此法对化探数据自动成图很有用处。     

Arsenic distribution in the environment: The effects of scale

The distribution of As in a variety of sample materials was studied at different scales, from continental to local, combining published data sets with the aim of delineating the impact and relative importance of geogenic vs. anthropogenic As sources. Geochemical mapping of As with a variety of sample materials demonstrates that variation is high at all scales (local to continental) – from sample densities of 400 sites per km² to 1 site per 5000 km². Different processes govern the As distribution at different scales. A high sample density is needed to reliably detect mineralisation or contamination in soil samples. In both cases the impact on the much larger geochemical background variation is limited to a local scale. Distribution patterns in geochemical maps on the sub-continental to continental scale are dominated by natural variation. Given that the geochemical background is characterised by a high variation at all scales, it appears impossible to establish a reliable single value for “good soil quality” or a “natural background concentration” for As for any sizeable area, e.g., for Europe. For such a differentiation, geochemical maps at a variety of scales are needed.     

Manual hierarchical clustering of regional geochemical data using a Bayesian finite mixture model

Interpretation of regional scale, multivariate geochemical data is aided by a statistical technique called “clustering.” We investigate a particular clustering procedure by applying it to geochemical data collected in the State of Colorado, United States of America. The clustering procedure partitions the field samples for the entire survey area into two clusters. The field samples in each cluster are partitioned again to create two subclusters, and so on. This manual procedure generates a hierarchy of clusters, and the different levels of the hierarchy show geochemical and geological processes occurring at different spatial scales. Although there are many different clustering methods, we use Bayesian finite mixture modeling with two probability distributions, which yields two clusters. The model parameters are estimated with Hamiltonian Monte Carlo sampling of the posterior probability density function, which usually has multiple modes. Each mode has its own set of model parameters; each set is checked to ensure that it is consistent both with the data and with independent geologic knowledge. The set of model parameters that is most consistent with the independent geologic knowledge is selected for detailed interpretation and partitioning of the field samples.     

Application of geostatistics to identify gold-rich areas in the Finisterre-Fervenza region,NW Spain

Three univariate geostatistical methods of estimation are applied to a geochemical data set. The studied methods are: ordinary kriging (cross-validation), factorial kriging, and indicator kriging. These techniques use the probabilistic and spatial behaviour of geochemical variables, giving a tool for identifying potential anomalous areas to locate mineralization. Ordinary kriging is easy to apply and to interpret the results. It has the advantage of using the same experimental grid points for its estimates, and no additional grid points are needed. Factorial kriging decomposes the raw variable into as many components as there are identified structures in the variogram. This, however, is a complex method and its application is more difficult than that of ordinary or indicator kriging. The main advantages of indicator kriging are that data are used by their rank order, being more robust about outlier values, and that the presentation of results is simple. Nevertheless, indicator kriging is incapable of separating anomalous values and the high values from the background, which have a behaviour different to the anomaly. In this work, the results of the application of these 3 kriging methods to a set of mineral exploration data obtained from a geochemical survey carried out in NW Spain are presented. This area is characterised by the presence of Au mineral occurrences. The kriging methods were applied to As, considered as a pathfinder of Au in this area. Numerical treatment of Au is not applicable, because it presents most values equal to the detection limit, and a series of extreme values. The results of the application of ordinary kriging, factorial kriging and indicator kriging to As make possible the location of a series of rich values, sited along a N–S shear zone, considered a structure related to the presence of Au.     

Spatial variability of soil organic matter and nutrients in paddy fields at various scales in southeast China

The present study examines the spatial dependency of soil organic matter and nutrients in paddy fields at three different scales using geostatistics and geographic information system techniques (GIS). The spatial variability of soil organic matter (SOM), total nitrogen (TN) and available phosphorus (AP) has been characterized using a total of 460, 131 and 64 samples that were, respectively, collected from the Hangzhou–Jiaxing–Huzhou (HJH) Plain (10 km), Pinghu county (1,000 m) and a test plot area (100 m) within the Pinghu county, Zhejiang province of the southeast China. Semivariograms showed that the SOM and TN had moderate spatial dependency on the large scale of HJH plain and moderate scale of Pinghu county with long spatial correlation distances. At the moderate scale of Pinghu county and the small scale of a test plot area, the AP data did not show any spatial correlation, but had moderate spatial dependency in HJH plain. Spherical and exponential variogram models were best fitted to all these soil properties. Maps of SOM and TN were generated through interpolation of measured values by ordinary kriging, and AP by lognormal kriging. This study suggests that precision management of SOM and TN is feasible at all scales, and precision management of AP is feasible at large scales.     

化探数据系统分析的应用效果

化探数据系统分析可以提取与不同成矿单元度水平相应的信息，其中包括矿床主控因素的信息。本文所引的两个例分别表现了层控矿床和岩控矿床地球化学场的不同特点，获得了地球化学异常图上没有的信息。此外，同一元素不同尺度滑动平均异常的套合及同一尺度的不同元素异常的套合都是评价含矿性的重要信息。     

Application of universal kriging to geochemical prospecting data

In the 1:50,000 mineral-resource assessments for regions of different rock types, the application of universal kriging to process geochemical prospecting data, obtained from different sampling media, can provide much useful information for evaluating mineralization potential. The method has succeeded in effectively separating local anomalies from the regional background, objectively extracting useful information, and improving the analysis of the metallogenic and ore-controlling factors, thereby playing an important role in qualitative and quantitative predictions. In 1:50,000 mineral-resource assessment it is advantageous to use universal kriging in the processing of geochemical prospecting data because universal kriging has many advantages compared to other oreassessment methods.     

Towards spatial geochemical modelling: Use of geographically weighted regression for mapping soil organic carbon contents in Ireland

It is challenging to perform spatial geochemical modelling due to the spatial heterogeneity features of geochemical variables. Meanwhile, high quality geochemical maps are needed for better environmental management. Soil organic C (SOC) distribution maps are required for improvements in soil management and for the estimation of C stocks at regional scales. This study investigates the use of a geographically weighted regression (GWR) method for the spatial modelling of SOC in Ireland. A total of 1310 samples of SOC data were extracted from the National Soil Database of Ireland. Environmental factors of rainfall, land cover and soil type were investigated and included as the independent variables to establish the GWR model. The GWR provided comparable and reasonable results with the other chosen methods of ordinary kriging (OK), inverse distance weighted (IDW) and multiple linear regression (MLR). The SOC map produced using the GWR model showed clear spatial patterns influenced by environmental factors and the smoothing effect of spatial interpolation was reduced. This study has demonstrated that GWR provides a promising method for spatial geochemical modelling of SOC and potentially other geochemical parameters.     

中天山乌拉斯台地区矿化异常提取及评价

以多重分形理论为基础,对中天山乌拉斯台地区铜多金属元素的岩屑测量数据,采用C-A法获得铜多金属的异常下限值,将其作为阈值进行指示克里格插值,绘制研究区的铜多金属地球化学异常图。研究显示,基于该方法获得的Cu矿化异常高值区主要集中在华力西早期第三侵入次的石英闪长岩和花岗闪长岩岩体中,受北西向和次级北东向断裂构造控制明显,该异常区可以作为寻找热液型铜多金属矿产的重要远景区。该方法对于地球化学数据空间变异性强烈的地区,较之普通克里格插值法具有更好的地球化学异常识别能力和高值信息重建能力,所得结果的最高累计频率值范围与已知矿化点的空间位置吻合度更高,在地球化学异常信息提取工作中具有推广意义。     

Field examples of variations in fault patterns at different scales

Three field examples are presented which show changes in fault patterns at different scales. Normal faults in Jurassic limestones in Somerset consist of zones of sub-parallel segments at the exposure-scale, but contain complex zones of brecciation at the decimetre-scale. Normal faults in chalk at Flamborough Head consist of a complex network of small faults which accommodate strain between a set of large faults. The different-sized faults at Flamborough Head have different geometries and histories, with the larger faults showing a phase of reverse reactivation. The faulting in the Sydney Basin, Australia, can be explained in terms of the evolution and reactivation of transfer zones between overstepping faults. These transfer zones can cause the deformation to appear to be more complex as the analysis becomes more detailed.
Much recent work on the scaling relationslups of faults assumes that self-similar fault patterns occur over a wide range of scales. The data presented in this paper, however, suggest that there are problems in using the deformation pattern at one scale to infer deformation at other scales. Ideally, any analysis should involve the study of a wide range of scales to overcome these problems.     

A Simple Approach to Account for Radial Flow and Boundary Conditions When Kriging Hydraulic Head Fields for Confined Aquifers

The estimation and mapping of realistic hydraulic head fields, hence of flow paths, is a major goal of many hydrogeological studies. The most widely used method to obtain reliable head fields is the inverse approach. This approach relies on the numerical approximation of the flow equation and requires specifying boundary conditions and the transmissivity of each grid element. Boundary conditions are often unknown or poorly known, yet they impose a strong signature on the head fields obtained by inverse analysis. A simpler alternative to the inverse approach is the direct kriging of the head field using the measurements obtained at observation wells. The kriging must be modified to incorporate the available information. Use of the dual kriging formalism enables simultaneously estimating the head field, the aquifer mean transmissivity, and the regional hydraulic gradient from head data in steady or transient state conditions. In transient state conditions, an estimate of the storage coefficient can be obtained. We test the approach on simple analytical cases, on synthetic cases with solutions obtained numerically using a finite element flow simulator, and on a real aquifer. For homogeneous aquifers, infinite or bounded, the kriging estimate retrieves the exact solution of the head field, the exact hydrogeological parameters and the flow net. With heterogeneous aquifers, kriging accurately estimates the head field with prediction errors of the same magnitude as typical head measurement errors. The transmissivities are also accurately estimated by kriging. Moreover, if inversion is required, the kriged head along boundaries can be used as realistic boundary conditions for flow simulation.     

An Empirical Comparison of Kriging Methods for Nonlinear Spatial Point Prediction

Spatial prediction is a problem common to many disciplines. A simple application is the mapping of an attribute recorded at a set of points. Frequently a nonlinear functional of the observed variable is of interest, and this calls for nonlinear approaches to prediction. Nonlinear kriging methods, developed in recent years, endeavour to do so and additionally provide estimates of the distribution of the target quantity conditional on the observations. There are few empirical studies that validate the various forms of nonlinear kriging. This study compares linear and nonlinear kriging methods with respect to precision and their success in modelling prediction uncertainty. The methods were applied to a data set giving measurements of the topsoil concentrations of cobalt and copper at more than 3000 locations in the Border Region of Scotland. The data stem from a survey undertaken to identify places where these trace elements are deficient for livestock. The comparison was carried out by dividing the data set into calibration and validation sets. No clear differences between the precision of ordinary, lognormal, disjunctive, indicator, and model-based kriging were found, neither for linear nor for nonlinear target quantities. Linear kriging, supplemented with the assumption of normally distributed prediction errors, failed to model the conditional distribution of the marginally skewed data, whereas the nonlinear methods modelled the conditional distributions almost equally well. In our study the plug-in methods did not fare any worse than model-based kriging, which takes parameter uncertainty into account.     

内蒙古凉城县草几坝一带土壤化探的数学地质分析

数学地质可用不同的分析方法和图件综合显示多元地球化学数据中的核心信息,对矿床地质特征进行合理的地质解释.凉城草几坝一带1:2.5万土壤化探测量显示出本地区矿化异常是一个以Au为主,伴随有As、Cu、Ag等元素的多元素组合异常.本文应用数学地质分析方法对凉城草几坝一带的南伙房1:2.5万土壤化探数据进行了分析,得出该区异常主要是由一系列北东向构造破碎带所形成的矿化异常.南伙房和坝底地区的土壤化探数据聚类分析表明,8种微量元素可以分为4类,Cu、Ag、Au、As为一类,Pb、Zn为一类,Bi和Sb各为一类.第一类是反映石英脉或蚀变岩型矿化的指示元素组合,第二类反映了中低温的矿化元素组合.南伙房土壤化探元素主因子F1可能代表了石英脉-蚀变岩金矿化.对南伙房440个样品分别计算F1因子得分,得分大于1的有33个,F1因子得分异常等值线图与南伙房工作区Au、As、Cu异常等值线图异常分布情况大致相吻合,因此,Au、As的异常区域及F1因子得分＞1的样品所在的区域重叠处应该是以Au为主的找矿重点区域.     

低密度地球化学填图在热带雨林区的适用性探索：以印度尼西亚苏门答腊岛巴东明古鲁地区为例

不同尺度地球化学填图能否获得稳定的和可追索的地球化学模式,能否真实反映元素含量背景,是检验填图方法是否可行的重要依据。笔者选择印度尼西亚苏门答腊岛巴东—明古鲁地区热带雨林区为研究对象,对比该区1:100 万（1 个样/100 km2）和1:25 万（1 个样/4 km2）两种不同比例尺的地球化学采样所获得的地球化学数据和异常分布模式,发现二者获得的元素含量背景值和中位数非常接近,所圈定的地球化学省在形态和变化趋势上非常类似,浓集中心的位置几乎完全重合,证明低密度地球化学填图也能获得稳定的和可追溯的地球化学模式,认为该方法在热带雨林区也是适用的。低密度地球化学填图圈出的地球化学省基本涵盖了研究区大的矿床和花岗岩体,真实的反映了研究区元素的分布情况,在这些地球化学省内开展更大比例尺的地球化学填图工作,能进一步圈定局部异常直接找矿,降低企业勘查投资风险。     

Antimony in the environment: Lessons from geochemical mapping

The distribution of Sb in a variety of sample materials, including soils, plants and surface water, was studied at different scales, from continental to local, combining published data sets with the aim of delineating the impact and relative importance of geogenic vs. anthropogenic Sb sources. Geochemical mapping demonstrates that variation is high at all scales – from the detailed scale with sample densities of many sites per km² to the continental-scale with densities of 1 site per 5000 km². Different processes govern the Sb distribution at different scales. A high sample density of several samples per km² is needed to reliably detect mineralisation or contamination in soil samples. Median concentrations are so low for Sb in most sample materials (below 1 mg/kg in rocks and soils, below 0.1 mg/kg in plants, below 0.1 μg/L in surface water) that contamination is easier to detect than for many other elements. Distribution patterns on the sub-continental to continental-scale are, however, still dominated by natural variation. Given that the geochemical background is characterised by a high variation at all scales, it appears impossible to establish a reliable single value for “good soil quality” or a “natural background concentration” for Sb for any sizeable area, e.g., for Europe. For such a differentiation, geochemical maps at a variety of scales are needed.     

Estimating Regional Hydraulic Conductivity Fields—A Comparative Study of Geostatistical Methods

Geostatistical estimations of the hydraulic conductivity field (K) in the Carrizo aquifer, Texas, are performed over three regional domains of increasing extent: 1) the domain corresponding to a three-dimensional groundwater flow model previously built (model domain); 2) the area corresponding to the 10 counties encompassing the model domain (County domain), and; 3) the full extension of the Carrizo aquifer within Texas (Texas domain). Two different approaches are used: 1) an indirect approach where transmissivity (T) is estimated first and K is retrieved through division of the T estimate by the screen length of the wells, and; 2) a direct approach where K data are kriged directly. Due to preferential well screen emplacement, and scarcity of sampling in the deeper portions of the formation (> 1 km), the available data set is biased toward high values of hydraulic conductivities. Kriging combined with linear regression, simple kriging with varying local means, kriging with an external drift, and cokriging allow the incorporation of specific capacity as secondary information. Prediction performances (assessed through cross-validation) differ according to the chosen approach, the considered variable (log-transformed or back-transformed), and the scale of interest. For the indirect approach, kriging of log T with varying local means yields the best estimates for both log-transformed and back-transformed variables in the model domain. For larger regional scales (County and Texas domains), cokriging performs generally better than other kriging procedures when estimating both (log T)^∗ and T^∗. Among procedures using the direct approach, the best prediction performances are obtained using kriging of log K with an external drift. Overall, geostatistical estimation of the hydraulic conductivity field at regional scales is rendered difficult by both preferential well location and preferential emplacement of well screens in the most productive portions of the aquifer. Such bias creates unrealistic hydraulic conductivity values, in particular, in sparsely sampled areas.     

Comparison of approaches to spatial estimation in a bivariate context

The problem of estimating a regionalized variable in the presence of other secondary variables is encountered in spatial investigations. Given a context in which the secondary variable is known everywhere (or can be estimated with great precision), different estimation methods are compared: regression, regression with residual simple kriging, kriging, simple kriging with a mean obtained by regression, kriging with an external drift, and cokriging. The study focuses on 19 pairs of regionalized variables from five different datasets representing different domains (geochemical, environmental, geotechnical). The methods are compared by cross-validation using the mean absolute error as criterion. For correlations between the principal and secondary variable under 0.4, similar results are obtained using kriging and cokriging, and these methods are superior slightly to the other approaches in terms of minimizing estimation error. For correlations greater than 0.4, cokriging generally performs better than other methods, with a reduction in mean absolute errors that can reach 46% when there is a high degree of correlation between the variables. Kriging with an external drift or kriging the residuals of a regression (SKR) are almost as precise as cokriging.     

Scale Matching with Factorial Kriging for Improved Porosity Estimation from Seismic Data

When seismic data and porosity well logs contain information at different spatial scales, it is important to do a scale-matching of the datasets. Combining different data types with scale mismatch can lead to suboptimal results. A good correlation between seismic velocity and rock properties provides a basis for integrating seismic data in the estimation of petrophysical properties. Three-dimensional seismic data provides an unique exhaustive coverage of the interwell reservoir region not available from well data. However, because of the limitations of measurement frequency bandwidth and view angles, the seismic image can not capture the true seismic velocity at all spatial scales present in the earth. The small-scale spatial structure of heterogeneities may be absent in the measured seismic data. In order to take best advantage of the seismic data, factorial kriging is applied to separate the small and large-scale structures of both porosity and seismic data. Then the spatial structures in seismic data which are poorly correlated with porosity are filtered out prior to integrating seismic data into porosity estimation.     

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.