地球化学计算中误差传递分析的应用

通过两个实例讨论了地球化学计算中的误差传递问题,对照了四种不同方法的潜力和限制,拓广了蒙特卡洛方法在相关变量分析中的应用,指出其在不同条件下总能用有限机时逼近合理结果,揭示出协方差矩阵法的特殊效益,可相对于独立初始变量展现中间变量的相关关系。     

相关情况下Hasofer_Lind可靠度指标的求解

岩土工程的可靠度计算中, 基本变量之间往往存在着较强的相关性。 阐述了相关情况下 Hasofer-Lind 可靠度指标计算的几种方法: 正交变换法; 改进的验算点一次二阶矩法; Monte-Carlo 模拟法; 优化求解法。 在用优化方法求解可靠度指标 β 时, 利用 Microsoft Excel 中的规划求解器来进行优化求解, 避免了相关变量的独立变换以及求极限状态函数对基本变量的偏导数这两个问题。 实例比较了不同方法的求解结果。     

相关情况下Hasofer—Lind可靠指标的求解

岩土工程的可靠度计算中,基本变量之间往往存在着较强的相关性。阐述了相关情况下Ｈａｓｏｆｅｒ－Ｌｉｎｄ可靠度指标计算的几种方法：正交变换法;改进的验算点一次二阶矩法;Ｍｏｎｔｅ－Ｃａｒｌｏ模拟法;优化求解法。在用优化方法求解右靠度指标β时,利用ＭｉｃｒｏｓｏｆｔＥｘｃｅｌ中的规划求解器来进行优化求解,避免了相关变量的独立变换以及求极限状态函数对基本变量的偏导数这两个问题。实例比较了不同方法的求解结果     

岩石内变量蠕变模型研究

通过一系列砂岩、页岩和辉绿岩室内蠕变试验,获得了不同应力和初始应变状态下岩石蠕变特性。通过误差分析讨论了计算蠕变速率时如何选择时间增量。讨论了复杂加、卸载条件下时间相关蠕变模型的局限性,提出采用不可恢复应变作为内变量来描述复杂条件下岩石蠕变性质,并据此提出了岩石的内变量蠕变模型。试验数据与模型拟合结果对比表明,内变量蠕变模型较好地反映了3种岩石的蠕变行为。此外,还初步讨论了模型在岩石率相关性质研究中的适用性,并利用相关试验数据进行了验证。     

砂岩铀矿的分形特征

铀矿化样品可视为m个变量构成的相空间中的点集 ,用改变子空间尺度的方法求得砂岩铀矿化样品在一维、二维、三维和四维相空间中的分维为 0 .74、1.0 3、1.2 3和 1.5 4。不同矿床和同一矿床的不同矿石类型、不同高程和不同温度范围的矿化样品在不同变量及其组合构成的同维相空间中的分维相同或相近 ,反映它们的空间结构自相似。本文还探讨了相空间维数与分维数、分维数与子空间尺度的关系 ,并评述了分维的地质意义。     

秩特征分析方法在矿产资源预测中的应用

提出了一种新的矿产资源靶区定位预测的统计方法—秩特征分析方法。该方法以地质变量之间秩相关分析为基础,根据地质变量集合中某一地质变量与其余地质变量之间总的秩相关程度来度量该变量的重要性大小,根据每个地质变量在统计单元（万能的资源靶区）上的取值情况计算单元成矿联系度,,再根据单元成矿联系度相对大小评价优选矿产资源靶区。该统计方法可以同时使用定性、定量和半定量三种地质变量,减少了由于数据离散化而造成的地质信息丢失,可以最大限度地利用各种类型地质变量所提供的有用信息。     

结构方程模型在地球化学数据分析中的应用

为了实现通过确定地球化学组合元素来反映成矿异常, 本文在主成分分析模型的基础上, 引入了新的结构方程模型(SEM).与主成分所不同的是, 结构模型综合了经典统计方法中的因子分析和路径分析方法, 以与研究对象具有较好的拟合度为标准来确定最优解, 并通过模型最优解来确定新的成分组合, 因此结构模型所确定的成分变量不一定是具有最大变化性, 而是与研究对象最接近的因子变量, 该因子能够更好地反映研究对象.介绍了结构方程模型方法的原理, 并利用加拿大Nova Scotia省西南部湖泊沉积物地球化学数据建立了与热液型金矿有关的地球化学元素结构方程模型, 研究了结构方程模型所给出的组合变量空间分布规律以及与金矿床的关系.与主成分分析方法所给出的计算结果进行对比发现, 结构模型所计算的与金矿相关的组合变量与矿床的空间相关性较高, 并且对金矿床(矿点)也具有较好的预测性.      

相关系数及其在矿产资源预测中的应用

定量变量和定性变量之间相关亲疏程度的度量研究一直未被重视。本文提出几种“C—D”相关系数,它们有效地刻划了定量变量与定性变量之间的亲疏程度。另外,针对现有定性变量的相关系数只重定性变量之“形”而忽视其“质”的缺憾,本文提出几种“D”相关系数,以充分挖掘定性变量中所蕴含的有用信息。最后,给出这些相关系数在矿产资源预测中的应用实例。     

结构方程模型及其在地学数据建模中的回顾与展望

结构方程模型是一种建立、估计和检验因果关系的方法。它可以替代多重回归、路径分析、因子分析、协方差分析等方法,清晰分析单项指标对总体的作用和单项指标间的相互关系,是一种主要应用于验证性模型分析的多元统计建模技术。由于能够通过可观测变量来度量潜变量得分以及分析不同子模型下潜变量之间的协同效应等优点,结构方程模型被广泛应用在心理学、行为学、市场学等领域的数据建模分析研究中,提供了从提出概念—设计模型—获取数据—验证模型的成熟应用路径。地学数据的建模技术一直是地学研究的热点之一,其目的是在海量、多元、高维、多时态的地学数据中,提取出有价值的模型结构以及潜变量,研究不同地学变量以及潜变量之间的交互关系,从而支撑环境治理、灾害防治、资源勘察、生态评价等相关应用和研究。随着地学数据规模变化和建模工具的不断发展,地学数据建模的样本逐渐从抽样建模变为全样本建模,建模方式从有地学模型指导下的建模变为无约束/弱约束建模,建模依据从基于变量因果关系建模变为基于变量相关性的建模,模型复杂度从单模型/单过程建模变为多模型/多过程的综合建模。结构方程模型作为一种综合的建模方法,其可以同时包含因子分析、潜变量估计、路径分析等多种多元分析技术,这种多层次、多分支的建模方法融合了知识驱动建模和数据驱动建模的特点。结构方程模型在地学数据建模中主要面临以下三个方面的挑战,一是从主要面向验证性建模分析的方式向探索性建模分析的方式转变;二是从有完整地学模型约束的建模型方式向弱模型/无模型约束的地学数据建模方式转变;三是从无空间属性的统计变量建模向空间统计变量建模的转变。这对模型本身和数据建模的方法都提出了新的要求。针对以上三个问题,文章在回顾结构方程模型的概念和发展历程的基础上,介绍了三个结构方程模型在地学数据建模中的应用案例,一是利用湖泊沉积物地球化学数据在弱约束条件下提取地球化学金矿内生控矿因子的建模案例;二是利用结构方程模型的综合参数优化方法,通过计算后验概率与观察后验概率的匹配约束来弱化、校正证据权模型中证据独立性问题在计算金矿找矿后验概率中的影响;三是利用结构方程模型来研究墨西哥马格达莱纳流域森林保护策略,通过对不同区域的森林区块进行编号,将空间分布数据转变为传统的无空间属性的统计变量,并分析了不同环境策略对森林保护的影响。      

基于哈密顿体系辛几何算法求解空间地基问题

地基应力和位移场的求解是岩土工程中的基本问题之一,以往的求解方法是在一类变量范围内求解,属于拉格朗日体系。利用弹性力学的哈密顿理论,通过适当的变量代换,由力学的控制方程引入对偶变量,直接将方程导入到哈密顿体系,应用分离变量法求解。在哈密顿体系下,利用辛几何的性质,在完备的解空间内将方程的解用本征向量函数展开,讨论零本征值和非零本征值对应的不同本征解及其物理意义。数值算例表明,所得结果同以往结果一致。该方法不同于传统方法,为地基的研究提供了一条新途径和思路。     

Applications of Error Propagation Analyses to Geochemical Calculation

Two examples are given for comparing applications and limitations of four methods which can be used to deal with error propagation in geochemical calculations.The examples indicate that the Monte Carlo method can also be employed to evaluate the effect of covariance.A special function of the method for covariance matrix shown here can reveal the correlations of middle variables relative to the independent primary variables.     

Evaluation and error analysis: Kalman gain regularization versus covariance regularization

Ensemble size is critical to the efficiency and performance of the ensemble Kalman filter, but when the ensemble size is small, the Kalman gain generally cannot be well estimated. To reduce the negative effect of spurious correlations, a regularization process applied on either the covariance or the Kalman gain seems to be necessary. In this paper, we evaluate and compare the estimation errors when two regularization methods including the distance-dependent localization and the bootstrap-based screening are applied on the covariance and on the Kalman gain. The investigations were carried out through two examples: 1D linear problem without dynamics but for which the true Kalman gain can be computed and a 2D highly nonlinear reservoir fluid flow problem. The investigation resulted in three primary conclusions. First, if localizations of two covariance matrices are not consistent, the estimate of the Kalman gain will generally be poor at the observation location. The consistency condition can be difficult to apply for nonlocal observations. Second, the estimate of the Kalman gain that results from covariance regularization is generally subject to greater errors than the estimate of the Kalman gain that results from Kalman gain regularization. Third, in terms of removing spurious correlations in the estimation of spatially correlated variables, the performance of screening Kalman gain is comparable as the performance of localization methods (applied on either covariance or Kalman gain), but screening Kalman gain outperforms the localization methods in terms of generality for application, as the screening method can be used for estimating both spatially correlated and uncorrelated variables, and moreover, no assumption about the prior covariance is required for the screening method.     

Minimum-variance unbiased quadratic estimation of covariances of regionalized variables

The parameters of covariance functions (or variograms) of regionalized variables must be determined before linear unbiased estimation can be applied. This work examines the problem of minimum-variance unbiased quadratic estimation of the parameters of ordinary or generalized covariance functions of regionalized variables. Attention is limited to covariance functions that are linear in the parameters and the normality assumption is invoked when fourth moments of the data need to be calculated. The main contributions of this work are (1) it shows when and in what sense minimum-variance unbiased quadratic estimation can be achieved, and (2) it yields a well-founded, practicable, and easy-to-automate methodology for the estimation of parameters of covariance functions. Results of simulation studies are very encouraging.     

河道洪水实时预报的半自适应模型研究

提出和讨论了基于马斯京根流量演算河道洪水实时预报的半自适应滤波模型.在该模型中量测误差系列的协方差矩阵可以通过信息更新系列实时估计出来,只有模型误差系列的协方差矩阵需要预先给出.提出了一个处理区间入流较为合理、方便的方法.通过验证和应用说明了该模型的合理性.     

Optimal Spatial Sampling Design in a Multivariate Framework

The problem of spatial sampling design for estimating a multivariate random field from information obtained by sampling related variables is considered. A formulation assigning different degrees of importance to the variables and locations involved is introduced. Adopting an entropy-based approach, an objective function is defined as a linear combination in terms of the amount of information on the variables and/or the locations of interest contained in the data. In the multivariate Gaussian case, the objective function is obtained as a geometric mean of conditional covariance matrices. The effect of varying the degrees of importance for the variables and/or the locations of interest is illustrated in some numerical examples.     

Moving averages for Gaussian simulation in two and three dimensions

The square-root method provides a simple and computationally inexpensive way to generate multidimensional Gaussian random fields. It is applied by factoring the multidimensional covariance operator analytically, then sampling the factorization at discrete points to compute an array of weighted averages that can be convolved with an array of random normal deviates to generate a correlated random field. In many respects this is similar to the LUdecomposition method and to the one-dimensional method of moving averages. However it has been assumed that the method of moving averages could not be used in higher dimensions, whereas direct application of the matrix decomposition approach is too expensive to be practical on large grids. In this paper, I show that it is possible to calculate the square root of many two- and three dimensional covariance operators analytically so that the method of moving averages can be applied directly to the problem of multidimensional simulation. A few numerical examples of nonconditional simulation on a 256×256 grid that show the simplicity of the method are included. The method is fast and can be applied easily to nested and anisotropic variograms.     

Geostatistical estimation of multi-phase structures

A method is proposed for the characterization of the disjoint shapes of a multi-phase set. The method uses a global structural function and provides estimates of the complete mosaic of phases, honoring the individual volume proportions inferred from the experimental samples. The estimates of shapes can be improved by local conditioning to the covariance of each phase and to geometrical characteristics such as spatial orientation of the different strata. The mapping of uncertainty zones for individual phases is one advantage of using a geostatistical approach to characterize the morphology of qualitative (non-numerical) variables.     

Variogram models must be positive-definite

The aim of this short article is to stress the importance of using only positive-definite functions as models for covariance functions and variograms.The two examples presented show that a negative variance can easily be obtained when a nonadmissible function is chosen for the variogram model.     

Combining sensitivities and prior information for covariance localization in the ensemble Kalman filter for petroleum reservoir applications

Sampling errors can severely degrade the reliability of estimates of conditional means and uncertainty quantification obtained by the application of the ensemble Kalman filter (EnKF) for data assimilation. A standard recommendation for reducing the spurious correlations and loss of variance due to sampling errors is to use covariance localization. In distance-based localization, the prior (forecast) covariance matrix at each data assimilation step is replaced with the Schur product of a correlation matrix with compact support and the forecast covariance matrix. The most important decision to be made in this localization procedure is the choice of the critical length(s) used to generate this correlation matrix. Here, we give a simple argument that the appropriate choice of critical length(s) should be based both on the underlying principal correlation length(s) of the geological model and the range of the sensitivity matrices. Based on this result, we implement a procedure for covariance localization and demonstrate with a set of distinctive reservoir history-matching examples that this procedure yields improved results over the standard EnKF implementation and over covariance localization with other choices of critical length.