A general form of probability kriging for estimation of the indicator and uniform transforms

Probability kriging is implemented in a general cokriging procedure (c.f. Myers, 1982) for estimatingboth the indicator and uniform transforms. Paired-sum semi-variograms are used to facilitate the modeling of the cross-covariance between the uniform transform and each indicator transform. Estimates of the uniform transform are averaged over all cutoffs, the average used to derive an estimate of the original data. This estimate can be biased with respect to the mean data value, but is unbiased with respect to the data median.     

Models for Support and Information Effects: A Comparative Study

The recoverable reserves in an ore deposit depend on several factors, in particular the size of the selective mining units (support effect) and the misclassifications when sending these units to mill or dump according to their estimated grade (information effect). Both effects imply a loss of selectivity and have to be correctly forecasted. In this work, several models are reviewed and applied to a synthetic ore deposit characterized by a highly skewed grade histogram and a spatial connectivity of high grades. The affine correction, mosaic correction, and discrete Gaussian model are compared when assessing the global recoverable reserves, whereas local estimations are performed by indicator kriging with affine correction, bigaussian disjunctive kriging, and multigaussian conditional expectation. Despite their convenience and simplicity, distribution-free methods like affine correction or indicator kriging have a poorer accuracy than the other methods. In the global framework, the discrete Gaussian model is a better alternative and is based on mild assumptions. Local estimations are not accurate and may be improved by resorting to a more suitable parametric model or to conditional simulations.     

基坑体系可靠度的条件概率计算方法

基坑存在多种失效模式,考虑失效模式之间的相关性,双界限法计算体系失效概率存在计算结果区间范围较大的弊端。利用均匀试验和非参数回归方法建立响应面,在响应面的基础上,对Monte Carlo模拟生成的随机参数进行插值,得到各个失效模式指标,结合Pearson相关系数检验两两失效模式之间的相关性,用条件概率方法计算基坑体系失效概率,提出了基于条件概率考虑多失效模式相关的基坑体系可靠度分析方法。在此基础上,通过1个典型算例进行对比分析,计算结果表明,该方法不仅计算简便,而且结果可靠,其结果可为基坑体系可靠度分析理论提供一条新的途径。     

An indicator kriging model for investigation of seismic hazard

Time domain probabilistic techniques most often are used for assessment of seismic hazard. Such techniques are based on the historic frequency of ground motion. Hazard is expressed as a probability of experiencing a particular level of seismic activity over a given length of time. One of these techniques utilizes frequency of extreme values for assessment of hazard. The major disadvantage of this technique, however, becomes evident when maximum seismic activity for two consecutive years occurs only a few weeks or months apart. In this case, the extreme value approach overestimates seismic hazard. A new approach for hazard assessment is founded on principles of indicator kriging. This technique evaluates seismic hazard as a simple frequency record, which is more realistic for regions of little to moderate seismicity.     

Estimation of potential failure risks in a mine slope using indicator kriging

Indicator kriging has been applied to the study of failure mechanisms in a mine slope in Minas Gerais, Brazil, to estimate potential failure risks in limited areas along this slope. Timbopeba Mine, Vale Company, is an open pit iron mine situated in the Quadrilátero Ferrífero, a very important mining district in Minas Gerais. A slope excavated in quartzite with a maximum height of 200 m at the time of this study, has presented many failure problems involving the sliding of blocks formed by discontinuities. These blocks are of limited size in comparison to the dimensions of the overall slope. They appear along the entire slope, wherever discontinuity orientations have led to the kinematic feasibility of these blocks. Geostatistics permits the estimation of local failure probability distributions associated to these local failures, which would not be possible with traditional statistical models. The geostatistical method employed in this study, indicator kriging, is quite suitable because it is unnecessary to assume a particular global distribution of the phenomena being modeled. The model was used for locating areas with a great tendency for sliding failure, as it considers the local spatial variability of discontinuity orientations. Copyright © 2010 John Wiley & Sons, Ltd.     

基于土壤水分动态随机模型的土壤湿度概率密度函数研究进展

简要回顾和评述了几个典型土壤水分动态随机模型和相应的土壤湿度概率密度函数,并基于这些模型的模拟结果就系统随机波动、气候因素、土壤特性、植被条件、地形特征对稳定状态土壤湿度概率密度函数的影响分别进行了分析和讨论,同时还引用相关的实验结果对这些影响进行佐证.结果表明,土壤湿度概率密度函数对以上因子的响应非常敏感,对揭示土壤水分动态和诠释生态水文现象有很好的指导意义.指出未来土壤湿度概率密度函数的研究方向:开发更加逼近真实情况的随机模型;用土壤湿度概率密度函数的思想量化植被水分胁迫、耦合土壤水分动态与养分动态;对某一地区建立其土壤湿度概率密度函数,并用该函数指导其他相关的生态建设和研究.     

不同采样点数量下土壤有机质含量空间预测方法对比

运用普通克里格、泛克里格、协同克里格和回归克里格4种方法,结合由DEM获取的高程因子以及土壤全氮和阳离子交换量（CEC）,预测了黑龙江省海伦市耕地有机质含量的空间分布。不同样点数量下海伦市土壤有机质含量的空间变异结构分析表明,样点数量多并不一定能够识别土壤有机质含量的结构性连续组分,最优化的布置采样点位置可能比单纯增加...     

岩石抗剪强度参数的理论概率分布形态研究

岩石抗剪强度参数的概率分布形态是岩石工程可靠度分析和设计的基础。在考虑完整岩石压缩强度为服从正态分布随机变量的条件下,针对Mohr-Coulomb和Drucker-Prager屈服准则的线性系数形式,基于随机变量函数分布理论推导出岩石抗剪强度参数内摩擦角 和黏聚力 的概率密度函数。 和 概率密度函数显示：不仅岩石压缩强度和抗剪强度参数概率分布具有非一致性,而且根据不同屈服准则计算得出的岩石抗剪强度参数概率分布也具有非一致性。在进一步分析屈服准则系数具有不同变异系数和相关系数时的抗剪强度参数概率密度函数特征的基础上,提出根据概率分布的偏度和峰度确定一般情况下抗剪强度参数概率分布形态的方法,从理论上解决岩石压缩强度与抗剪强度参数分布的协调性问题。最后,对大理岩常规三轴压缩试验得出的抗剪强度参数进行大样本统计分析,验证了其概率密度函数理论推导的正确性以及概率分布形态确定方法的合理性。该研究为实际岩石强度概率分析时选择抗剪强度参数合理概率分布形式提供了理论指导。     

基于围岩力学参数概率分布模型的变形敏感性灰关联分析

为了给布伦口-公格尔水电站地下洞室某标段围岩稳定性分析的参数选取提供可靠的理论依据,综合考虑岩体参数的空间变异性,针对常规敏感性分析方法所存在的不足,运用三维离散元计算程序,提出了基于围岩力学参数概率分布模型的变形敏感性灰关联分析方法。该方法以岩体密度?、弹性模量E、泊松比?、黏聚力c、内摩擦角φ及节理内摩擦角φj等6个围岩力学参数作为因素序列,拱顶下沉量作为目标序列,分析影响因素在整个定义区间内的变化对围岩拱顶下沉的敏感程度。结果表明：密度是最敏感因素,其次是弹性模量、黏聚力和泊松比,而内摩擦角以及节理内摩擦角敏感性最小。最后,将常规灰关联敏感性分析与该方法计算结果进行对比,结果表明：除密度、内摩擦角和节理内摩擦角一致外,其余参数敏感性均与结论不一致。因此,文中方法在考虑实际参数概率分布的基础上能够更加准确、合理地对参数进行综合评价。     

基于Bootstrap方法的岩土体参数联合分布模型识别

小样本容量岩土体参数最优联合概率分布模型的识别是一个富有挑战性的问题。基于Bootstrap提出了小样本容量岩土体参数最优边缘分布函数和最优Copula函数识别方法。简要介绍了岩土体参数联合概率分布函数构造的Copula方法,采用AIC准则识别最优的边缘分布函数和Copula函数。将识别结果表示为不同备选边缘分布函数和Copula函数为最优边缘分布和最优Copula的权重系数集合,以基桩荷载-位移双曲线参数试验数据为例证明了所提方法的有效性。结果表明：基于小样本容量岩土体参数试验数据估计的样本均值、标准差和相关系数具有较大的离散性,这种离散性进一步导致了统计量AIC值存在较大变异性。提出的基于Bootstrap的最优边缘分布函数和最优Copula函数识别方法不仅可以有效地考虑统计量AIC值的变异性,而且能够综合地反映不同备选边缘分布函数和Copula函数为最优边缘分布和最优Copula函数的概率,为小样本容量岩土体参数最优边缘分布函数和最优Copula函数的识别提供了一条有效的途径。     

Types, abundances and distribution of kimberlite indicator minerals in alluvial sediments, Wawa–Kinniwabi Lake area, Northeastern Ontario: implications for the presence of diamond-bearing kimberlite

In response to the discovery of diamonds within modern alluvium in the glaciated area of Wawa, Ontario, Canada, the Ontario Geological Survey undertook a regional program of surficial mapping and modern alluvial sediment sampling to assess the potential of the area for diamond-bearing kimberlite. Five varieties of kimberlite-derived indicator minerals were recovered and the composition of three varieties was evaluated, resulting in the identification of G10 Cr-pyrope garnet, inclusion field chromite and Mg-ilmenite. The distribution of indicator minerals was examined in the context of the glacial and bedrock geology. Glacial dispersal from non-kimberlitic marker units is restricted (commonly less than 200 m) and many kimberlite indicator minerals were recovered from samples collected close to cross-cutting NE–SW and NW–SE faults and a strong NE–SW trend in the bedrock associated with the Kapuskasing Structural Zone. From this, several potential exploration targets for diamond-bearing kimberlite are defined.