A Combined Three-Dimensional Geological-Geostatistical-Numerical Model of Underground Excavations in Rock

Summary. This paper exploits geological and borehole geotechnical data obtained in the exploratory phase of a tunneling project to investigate in a first place if the kriging interpolation scheme may effectively reproduce the spatial variability of rock mass quality (Rock Mass Rating, RMR) in the vicinity of tunnels. For this purpose a quick solver in Fortran has been developed that performs variography analysis of 3D spatial data, fast kriging estimations of RMR between borehole sampling locations at the centroids of the elements of the numerical model, and model validation. For the purpose of an integrated underground excavation design, a step further is made by incorporating into the 3D mechanical numerical model of the rock mass, the three-dimensional (3D) solid geological model, thus coupling the geology with the ground (geotechnical) model (i.e. each element of the numerical model is assigned a geological material). The mechanical properties of each finite difference cell (or Representative Elementary Volume) of the ground model were then prescribed according to its geological type, the spatial heterogeneity of the rock mass expressed quantitatively with the kriging model, and the upscaling calculations of the mechanical properties of the intact rocks determined in the laboratory, based on the size-effect (strength dependence on size) and Damage Theory. Furthermore, a preliminary numerical simulation of the advance of unsupported tunnels in the model of the heterogeneous rock mass was performed for illustration purposes.     

Hybrid Estimation of Semivariogram Parameters

Two widely used methods of semivariogram estimation are weighted least squares estimation and maximum likelihood estimation. The former have certain computational advantages, whereas the latter are more statistically efficient. We introduce and study a “hybrid” semivariogram estimation procedure that combines weighted least squares estimation of the range parameter with maximum likelihood estimation of the sill (and nugget) assuming known range, in such a way that the sill-to-range ratio in an exponential semivariogram is estimated consistently under an infill asymptotic regime. We show empirically that such a procedure is nearly as efficient computationally, and more efficient statistically for some parameters, than weighted least squares estimation of all of the semivariogram’s parameters. Furthermore, we demonstrate that standard plug-in (or empirical) spatial predictors and prediction error variances, obtained by replacing the unknown semivariogram parameters with estimates in expressions for the ordinary kriging predictor and kriging variance, respectively, perform better when hybrid estimates are plugged in than when weighted least squares estimates are plugged in. In view of these results and the simplicity of computing the hybrid estimates from weighted least squares estimates, we suggest that software that currently estimates the semivariogram by weighted least squares methods be amended to include hybrid estimation as an option.     

Spatial Analysis Techniques as Successful Mineral-Potential Mapping Tools for Orogenic Gold Deposits in the Northern Fennoscandian Shield,Finland

Geoscientific Information Systems (GIS) provide tools to quantitatively analyze and integrate spatially referenced information from geological, geophysical, and geochemical surveys for decision-making processes. Excellent coverage of well-documented, precise and good quality data enables testing of variable exploration models in an efficient and cost effective way with GIS tools. Digital geoscientific data from the Geological Survey of Finland (GTK) are being used widely as spatial evidence in exploration targeting, that is ranking areas based on their exploration importance. In the last few years, spatial analysis techniques including weights-of-evidence, logistic regression, and fuzzy logic, have been increasingly used in GTK’s mineral exploration and geological mapping projects. Special emphasis has been put into the exploration for gold because of the excellent data coverage within the prospective volcanic belts and because of the increased activity in gold exploration in Finland during recent years. In this paper, we describe some successful case histories of using the weights-of-evidence method for the Au-potential mapping. These projects have shown that, by using spatial modeling techniques, exploration targets can be generated by quantitatively analyzing extensive amounts of data from various sources and to rank these target areas based on their exploration potential.     

Geostatistical incorporation of spatial coordinates into supervised classification of hyperspectral data

 This paper presents a methodology to incorporate both hyperspectral properties and spatial coordinates of pixels in maximum likelihood classification. Indicator kriging of ground data is used to estimate, for each pixel, the prior probabilities of occurrence of classes which are then combined with spectral-based probabilities within a Bayesian framework. In the case study (mapping of in-stream habitats), accounting for spatial coordinates increases the overall producer's accuracy from 85.8% to 93.8%, while the Kappa statistic rises from 0.74 to 0.88. Best results are obtained using only indicator kriging-based probabilities, with a stunning overall accuracy of 97.2%. Significant improvements are observed for environmentally important units, such as pools (Kappa: 0.17 to 0.74) and eddy drop zones (Kappa: 0.65 to 0.87). The lack of benefit of using hyperspectral information in the present study can be explained by the dense network of ground observations and the high spatial continuity of field classification which might be spurious. Received: 12 April 2001 / Accepted: 7 September 2001     

相关稳健估计及其在测量数据

在对现有的基于等价权的稳健估计的弊端进行分析的基础上,直接从方差膨胀模型出发,建立起一套基于调整观测量方差-协方差阵的相关稳健估计方法,并通过算例证明其估计思想、模型的正确性和可行性.     

Application of GIS Processing Techniques for Producing Mineral Prospectivity Maps—A Case Study: Mesothermal Au in the Swayze Greenstone Belt,Ontario, Canada

A Geographic Information System (GIS) is used to prepare and process digital geoscience data in a variety of ways for producing gold prospectivity maps of the Swayze greenstone belt, Ontario, Canada. Data used to produce these maps include geologic, geochemical, geophysical, and remotely sensed (Landsat). A number of modeling methods are used and are grouped into data-driven (weights of evidence, logistic regression) and knowledge-driven (index and Boolean overlay) methods. The weights of evidence (WofE) technique compares the spatial association of known gold prospects with various indicators (evidence maps) of gold mineralization, to derive a set of weights used to produce the final gold prospectivity map. Logistic regression derives statistical information from evidence maps over each known gold prospect and the coefficients derived from regression analysis are used to weight each evidence map. The gold prospectivity map produced from the index overlay process uses a weighting scheme that is derived from input by the geologist, whereas the Boolean method uses equally weighted binary evidence maps.The resultant gold prospectivity maps are somewhat different in this study as the data comprising the evidence maps were processed purposely differently for each modeling method. Several areas of high gold potential, some of which are coincident with known gold prospects, are evident on the gold prospectivity maps produced using all modeling methods. The majority of these occur in mafic rocks within high strain zones, which is typical of many Archean greenstone belts.     

一种气候预测综合决策的方法——递归正权综合决策法

根据气候预测的特点，提供了以误差平方和为风险函数，以正权综合为模式的多途径气候预测决策方案。不仅从理论上论证了几种正权方法的优性，还提供了递归技巧，进一步提高了正权综合的预测精度。对1997年汛期降水预测所做的综合决策表明，该方法具有较好的综合决策能力。     

松潘地区岩金统计成矿予测中泛克立格法的应用

川西北地区是国内重要的岩金普查靶区。本文对松潘地区的地质特征,泛克立格法原理,及在本区的应用情况作了介绍,对主要计算步骤,给出基本结果,对计算获得的有意义异常区,进行地质解释,并将此方法与趋势面分析进行对比。     

Efficient updating of kriging estimates and variances

This short note presents a method for efficiently updating ordinary kriging estimates and variances when one or more additional samples are incorporated into the kriging system. First, the foundation linear algebra result is presented. Then the update equations are derived. Finally, an illustrative application of updating is briefly discussed.     

Estimation of regionalized compositions: A comparison of three methods

A regionalized composition is a random vector function whose components are positive and sum to a constant at every point of the sampling region. Consequently, the components of a regionalized composition are necessarily spatially correlated. This spatial dependence—induced by the constant sum constraint—is a spurious spatial correlation and may lead to misinterpretations of statistical analyses. Furthermore, the cross-covariance matrices of the regionalized composition are singular, as is the coefficient matrix of the cokriging system of equations. Three methods of performing estimation or prediction of a regionalized composition at unsampled points are discussed: (1) the direct approach of estimating each variable separately; (2) the basis method, which is applicable only when a random function is available that can he regarded as the size of the regionalized composition under study; (3) the logratio approach, using the additive-log-ratio transformation proposed by J. Aitchison, which allows statistical analysis of compositional data. We present a brief theoretical review of these three methods and compare them using compositional data from the Lyons West Oil Field in Kansas (USA). It is shown that, although there are no important numerical differences, the direct approach leads to invalid results, whereas the basis method and the additive-log-ratio approach are comparable.