Spatial and multivariate analysis of geochemical data from metavolcanic rocks in the Ben Nevis area, Ontario

A study of the lithogeochemistry of metavolcanics in the Ben Nevis area of Ontario, Canada has shown that factor analysis methods can distinguish lithogeochemical trends related to different geological processes, most notably, the principal compositional variation related to the volcanic stratigraphy and zones of carbonate alteration associated with the presence of sulphides and gold. Auto- and cross-correlation functions have been estimated for the two-dimensional distribution of various elements in the area. These functions allow computation of spatial factors in which patterns of multivariate relationships are dependent upon the spatial auto- and cross-correlation of the components. Because of the anisotropy of primary compositions of the volcanics, some spatial factor patterns are difficult to interpret. Isotropically distributed variables such as CO ₂ are delineated clearly in spatial factor maps. For anisotropically distributed variables (SiO ₂ ), as the neighborhood becomes smaller, the spacial factor maps becomes better. Interpretation of spatial factors requires computation of the corresponding amplitude vectors from the eigenvalue solution. This vector reflects relative amplitudes by which the variables follow the spatial factors. Instability of some eigenvalue solutions requires that caution be used in interpreting the resulting factor patterns. A measure of the predictive power of the spatial factors can be determined from autocorrelation coefficients and squared multiple correlation coefficients that indicate which variables are significant in any given factor. The spatial factor approach utilizes spatial relationships of variables in conjunction with systematic variation of variables representing geological processes. This approach can yield potential exploration targets based on the spatial continuity of alteration haloes that reflect mineralization.List of symbols c _i Scalar factor that minimizes the discrepancy between andU _i - D Radius of circular neighborhood used for estimating auto- and cross-correlation coefficients - d Distance for which transition matrixU is estimated - d _ij Distance between observed valuesi andj - E Expected value - E _i Row vector of residuals in the standardized model - F(d _ij) Quadratic function of distanced _ij F(d _ij)=a+bd _ij+cd _ij ² - L Diagonal matrix of the eigenvalues ofU - _i Eigenvalue of the matrixU;ith diagonal element ofL - N Number of observations - p Number of variables - Q Total predictive power ofU - R Correlation matrix of the variables - R _0j Variance-covariance signal matrix of the standardized variables at origin;j is the index related tod andD (e.g.,j=1 ford=500 m,D=1000 m) - R _1j Matrix of auto- and cross-correlation coefficients evaluated at a given distance within the neighborhood - R _m ² Multiple correlation coefficient squared for themth variable - S _i Column vectori of the signal values - s _k ² Residual variance for variablek - T _i Amplitude vector corresponding toV _i;ith row ofT=V ^–1 - T Total variation in the system - U Nonsymmetric transition matrix formed by post-multiplyingR ₀₁ ^–1 byR _ij - U _i Componenti of the matrixU, corresponding to theith eigenvectorV _i;U _i= _iV_iT_i - U* _i ComponentU _i multiplied byc _i - U _ij Sum of componentsU _i+U _j - V _i Eigenvector of the matrixU;ith column ofV withUV=VL - w Weighting factor; equal to the ratio of two eigenvalues - X _i Random variable at pointi - x _i Value of random variable at pointi - y _i Residual ofx _i - Z _i Row vectori for the standardized variables - z _i Standardized value of variable     

Numerical classification of geologic patterns characterized by binary variables

An iterative method of adaptive pattern recognition is used to allocate unclassified individuals to an a priori classification. The model is similar in form to a linear discriminant function, but the coefficient vector is determined by iteration. The method can be used with binary data, and with variables whose statistical distributions are not normal; it is therefore a useful technique for geologists.     

Conditional LAS stochastic simulation of regionalized variables in random fields

Ore reserves forecasts are required to aid in investment decisions, mine design and valuation, short and long term production plans and proper and efficient mill design. In random multivariable fields with limited data and high levels of uncertainty, the kriged block estimates produce a smoothing effect resulting in underestimating high values and overestimating low values. The modified conditional simulation (MCS) methodology solves these problems by simulating the random field to preserve its mean and the variance structure. The simulation model is conditioned to reproduce the data at known sample points to minimize the variability between the simulated data and the true field data. In this study, the authors develop the MCS methodology to simulate ore reserve grades using the best linear unbiased estimation (BLUE) and the local average subdivision (LAS) techniques. The MCS methodology is applied to simulate block grades in a section of the Sabi Gold Project in Zimbabwe. The results are compared with the kriged estimates for this section. Analysis of the results shows that the MCS methodology reproduces the known sample grades with minimum estimation error of 0.001 while the estimation error associated with the kriged estimates is 1.104, a 100% efficiency of the MCS method over the kriging technique.     

Stochastic simulation of categorical variables using a classification algorithm and simulated annealing

An important step of reservoir characterization is the stochastic modeling of the geometry of lithofacies which control large-scale heterogeneities of petrophysical properties. Although multiple realizations are necessary to appreciate the uncertainty in the spatial distribution of facies, a common short cut consists of retaining the first realization drawn. This paper presents an alternative to this potentially hazardous selection: (1) a categorical map is generated by allocating a single facies to each grid node according to the local probabilities of occurrence of the facies, and (2) the map then is post-processed using a steepest descent-type algorithm so as to improve reproduction of spatial continuity and transition probabilities between facies. The procedure is illustrated using a synthetic dataset. A waterflood simulation shows that retaining a single realization would yield, in average, larger errors in production forecasts (water cuts and recovered oil) than the single postprocessed facies map.     

Stochastic simulation of spatially correlated geo-processes

In this study, developments in the theory of stochastic simulation are discussed. The unifying element is the notion of Radon projection in Euclidean spaces. This notion provides a natural way of reconstructing the real process from a corresponding process observable on a reduced dimensionality space, where analysis is theoretically easier and computationally tractable. Within this framework, the concept of space transformation is defined and several of its properties, which are of significant importance within the context of spatially correlated processes, are explored. The turning bands operator is shown to follow from this. This strengthens considerably the theoretical background of the geostatistical method of simulation, and some new results are obtained in both the space and frequency domains. The inverse problem is solved generally and the applicability of the method is extended to anisotropic as well as integrated processes. Some ill-posed problems of the inverse operator are discussed. Effects of the measurement error and impulses at origin are examined. Important features of the simulated process as described by geomechanical laws, the morphology of the deposit, etc., may be incorporated in the analysis. The simulation may become a model-dependent procedure and this, in turn, may provide numerical solutions to spatial-temporal geologic models. Because the spatial simlation may be technically reduced to unidimensional simulations, various techniques of generating one-dimensional realizations are reviewed. To link theory and practice, an example is computed in detail.     

Spatial orthogonality of the principal components computed from coregionalized variables

Within the frame of the linear model of coregionalization, this paper sets up equations relating the variogram matrix of the principal components extracted from the variance-covariance matrix to the diagonal variogram matrices of the regionalized factors. The spatial orthogonality of the principal components is investigated in three situations: the intrinsic correlation, two basic structures with independent nugget components, three basic structures with independent nugget components and uncorrelated subsets of variables. Two examples point out that the correlation between the principal components may be nonnegligible at short distances, especially if the correlation structure changes according to the spatial scale considered. For one of the two case studies, an orthogonal varimax rotation of the first principal components is found to greatly reduce the spatial correlation between some of them.     

水文随机模拟进展

综述了近20年来水文随机模拟的新进展,包括三方面:①随机水文模型改进和创新;②水文随机模拟应用研究新进展;③水文随机模拟认识新进展。并指出了今后的研究重点:①对水文过程的重要物理特性和统计特性作深入的分析;②加强非参数模型和非线性模型的研究;③加强流域系统随机模型的研究;④加强建立模型时如何综合利用多种信息的研究;⑤加强模型的各种检验和合理分析。     

Scaling variables and interpretation of eigenvalues in principal component analysis of geologic data

The dominant feature distinguishing one method of principal components analysis from another is the manner in which the original data are transformed prior to the other computations. The only other distinguishing feature of any importance is whether the eigenvectors of the inner product-moment of the transformed data matrix are taken directly as the Q-mode scores or scaled by the square roots of their associated eigenvalues and called the R-mode loadings. If the eigenvectors are extracted from the product-moment correlation matrix, the variables, in effect, were transformed by column standardization (zero means and unit variances), and the sum of the p-largest eigenvalues divided by the sum of all the eigenvalues indicates the degree to which a model containing pcomponents will account for the total variance in the original data. However, if the data were transformed in any manner other than column standardization, the eigenvalues cannot be used in this manner, but can only be used to determine the degree to which the model will account for the transformed data. Regardless of the type of principal components analysis that is performed—even whether it is Ror Q-mode—the goodness-of-fit of the model to the original data is given better by the eigenvalues of the correlation matrix than by those of the matrix that was actually factored.     

基于HYDRUS模拟的ABCD模型变量及参数物理基础研究

以ABCD模型为代表的概念性水文模型是量化水文循环过程的主要手段之一,但是很少有研究检验ABCD模型变量和参数的物理基础及其与传统土壤水力参数的关系。以鄂尔多斯盆地台格庙矿区作为研究区,首先使用HYDRUS-1D软件构建站点尺度土壤-植物-大气连续体模型模拟获取非冻结期“真实的”实际蒸散量,其作为目标函数对ABCD模型进行校正,然后对比ABCD模型模拟的土壤水储量和土壤水渗漏量与SPAC模型模拟的结果,通过开展大量情景模拟探究ABCD模型中关键参数a和b与传统土壤水力参数之间的关系。结果表明：在站点尺度,ABCD模型可以用于模拟非冻结期月时间尺度的实际蒸散量和土壤水渗漏量;ABCD模型中参数a与饱和含水率、残余含水率和曲线形状参数具有较强的线性相关性,与饱和渗透系数呈对数关系;参数b与饱和含水率和曲线形状参数n具有较强的线性相关性,与饱和渗透系数和曲线形状参数α呈对数关系。研究结果可以提高对概念性水文模型变量和参数物理基础的认识,拓展水文模型在水文地质中的应用。     

桩间土拱效应离心模型试验及数值模拟研究

抗滑桩的设计理念是采用非连续结构,利用土体自身强度形成的拱效应来达到支挡的目的。通过离心模型试验,对抗滑桩加固滑坡形成土拱效应的现象进行研究,再现了桩间土拱形成的现象及其破坏模式。根据试验现象提出两种典型的土拱破坏模式,即拱顶发生破坏和拱脚发生破坏,并提出改善拱脚受力,防止土拱拱脚发生破坏的工程措施。基于离心模型试验,采用二维颗粒流方法对桩间水平土拱的应力分布和破坏过程进行数值模拟分析,提出土拱破坏的判别标准为抗滑桩所承担的荷载发生急剧变化,此时土拱传递荷载的功能部分失效,并研究了桩间土拱承载力与桩间净距的关系。随着桩间净距的增大,土拱承载力变化的趋势并非线性的减小,当桩间净距增大到一定程度后,土拱承载力会急剧减小,由此可合理确定桩间距的范围。     

新型螺旋成孔根植注浆竹节管桩抗压性状数值模拟研究

新型螺旋成孔根植注浆竹节管桩是一种新的组合桩型,具有承载力高、技术含量高和安全性能好等特点。为了更好地了解新型组合桩的抗压承载机制,应用ABAQUS软件进行抗压数值模拟。通过将模拟结果与现场试验结果对比,验证了数值模型的可靠性。分析模拟结果,发现桩身竹节处存在2～3倍桩径的应力影响范围,并且存在1.6～1.8倍桩径的空壳区,竹节极限承载力从上到下排列线性增长（除第1节和最后一节）。结果还表明,竹节间距、水泥土厚度、桩侧土弹性模量以及桩端土弹性模量都对组合桩极限承载力有影响,而水泥土弹性模量的影响则可忽略。以往相似工法的极限承载力公式都不能很好地诠释本桩型的受力特性,因此,结合理论分析与抗压受力机制,提出考虑侧阻竹节影响系数的单桩极限承载力公式,与现场试验结果对比,较为接近。     

Finite-element method in modeling geologic transport processes

Deterministic mathematical modeling of complex geologic transport processes may require the use of odd boundary shapes, time dependency, and two or three dimensions. Under these circumstances the governing transport equations must be solved by numerical methods. For a number of transport phenomena a general form of the convective-dispersion equation can be employed. The solution of this equation for complicated problems can be solved readily by the finite-element method. Using quadrilateral isoparametric elements or triangular elements and a computational algorithm based on Galerkin's procedure, solutions to unsteady heat flux from a dike and seawater intrusion in an aquifer have been obtained. These examples illustrate that the finite-element numerical procedure is well suited for solving boundary-value problems resulting from modeling of complex physical phenomena.     

非饱和土入渗的数值模拟

入渗引起土中孔隙水压力的变化,是影响非饱和土性状的最重要的原因之一。因此,正确地分析和模拟非饱和土入渗过程具有重要意义。通过对一维和二维降雨入渗问题的研究,展示了湿润锋面、地下水位面及孔隙水压力分布随时间的变化,使得对入渗问题的认识更加直观和清楚。     

水流模拟智能化问题的探讨

对水流模拟的发展历史进行了总结,指出阻碍水流模拟发展的主要问题,提出克服这些瓶颈问题的方法是将智能科学与水利科学交叉融合,实现水流的智能模拟。据此,介绍了水流智能模型理论,结合遗传算法、模糊逻辑、元胞自动机、混沌分析理论、人工神经网络、专家系统、数据挖掘等智能理论和技术,对水流智能模拟的实现途径作了探讨,并指出建造一个优秀的水流模拟智能系统的关键是联合运用各种智能方法,认为智能化是当前水流模拟发展的新方向,水流智能模型将是水利科学的一种新的研究途径,并将在研究水流问题上具有广阔的应用前景。     

粗粒土的离心模型试验与数值模拟

岩土工程数值计算中粗粒土常采用邓肯-张本构模型,为了验证该模型在轴向加载、卸载、侧向加载等复杂应力路径条件下的适用性,进行了粗粒土的三轴试验获取其力学特性及本构模型参数;根据相似性原理制作了堆石坝的离心模型试样,并采用与三轴试验同样级配与粒径的粗粒土进行复杂应力路径的堆石坝离心模型试验,试验中通过改变离心加速度模拟加载、卸载,利用上游蓄水模拟坝体的侧向加载;采用ABAQUS对离心模型试验进行三维数值模拟,并研究了模型箱侧壁摩擦系数与土体的初始应力对数值结果的影响。通过比较离心模型试验与数值模拟成果,表明土体的初始弹性模量对计算结果影响较大,初始应力应选择自重作用下的应力场;邓肯-张本构模型能较好地描述堆石坝的加载应力路径,而模拟卸载应力路径有一定的差异,需要改进邓肯-张本构模型中卸载模量的确定方法。