Multivariate Intrinsic Random Functions for Cokriging

In multivariate geostatistics, suppose that we relax the usual second-order-stationarity assumptions and assume that the component processes are intrinsic random functions of general orders. In this article, we introduce a generalized cross-covariance function to describe the spatial cross-dependencies in multivariate intrinsic random functions. A nonparametric method is then proposed for its estimation. Based on this class of generalized cross-covariance functions, we give cokriging equations for multivariate intrinsic random functions in the presence of measurement error. A simulation is presented that demonstrates the accuracy of the proposed nonparametric estimation method. Finally, an application is given to a dataset of plutonium and americium concentrations collected from a region of the Nevada Test Site used for atomic-bomb testing.     

水文数据库随机检索实用模型

随机检索是水文数据库重要的检索功能之一，由于检索要求的不确定性给软件开发带来一定的困难。以数据库SQL语言为基础，通过对语言的简化和提示性的模式化操作，建立了一种实用的随机检索模型。     

Stepwise Conditional Transformation for Simulation of Multiple Variables

Most geostatistical studies consider multiple-related variables. These relationships often show complex features such as nonlinearity, heteroscedasticity, and mineralogical or other constraints. These features are not handled by the well-established Gaussian simulation techniques. Earth science variables are rarely Gaussian. Transformation or anamorphosis techniques make each variable univariate Gaussian, but do not enforce bivariate or higher order Gaussianity. The stepwise conditional transformation technique is proposed to transform multiple variables to be univariate Gaussian and multivariate Gaussian with no cross correlation. This makes it remarkably easy to simulate multiple variables with arbitrarily complex relationships: (1) transform the multiple variables, (2) perform independent Gaussian simulation on the transformed variables, and (3) back transform to the original variables. The back transformation enforces reproduction of the original complex features. The methodology and underlying assumptions are explained. Several petroleum and mining examples are used to show features of the transformation and implementation details.     

Markov Chain Random Fields for Estimation of?Categorical Variables

Multi-dimensional Markov chain conditional simulation (or interpolation) models have potential for predicting and simulating categorical variables more accurately from sample data because they can incorporate interclass relationships. This paper introduces a Markov chain random field (MCRF) theory for building one to multi-dimensional Markov chain models for conditional simulation (or interpolation). A MCRF is defined as a single spatial Markov chain that moves (or jumps) in a space, with its conditional probability distribution at each location entirely depending on its nearest known neighbors in different directions. A general solution for conditional probability distribution of a random variable in a MCRF is derived explicitly based on the Bayes’ theorem and conditional independence assumption. One to multi-dimensional Markov chain models for prediction and conditional simulation of categorical variables can be drawn from the general solution and MCRF-based multi-dimensional Markov chain models are nonlinear.     

Markov Chain Random Fields for Estimation of Categorical Variables

Multi-dimensional Markov chain conditional simulation (or interpolation) models have potential for predicting and simulating categorical variables more accurately from sample data because they can incorporate interclass relationships. This paper introduces a Markov chain random field (MCRF) theory for building one to multi-dimensional Markov chain models for conditional simulation (or interpolation). A MCRF is defined as a single spatial Markov chain that moves (or jumps) in a space, with its conditional probability distribution at each location entirely depending on its nearest known neighbors in different directions. A general solution for conditional probability distribution of a random variable in a MCRF is derived explicitly based on the Bayes’ theorem and conditional independence assumption. One to multi-dimensional Markov chain models for prediction and conditional simulation of categorical variables can be drawn from the general solution and MCRF-based multi-dimensional Markov chain models are nonlinear.     

Optimization and Evaluation of Multiple Hydraulically Fractured Parameters in Random Naturally Fractured Model Blocks: An Experimental Investigation

Researchers have recently realized that the non-tectonic natural fractures are developed in shale formations and significant for the exploitation of shale gas. Studies have shown that the tectonic fractures in naturally fractured reservoirs have influences on the maximization of stimulated reservoir volume (SRV) during hydraulic fracturing. However, the effect of the non-tectonic randomly natural fractures on the fracturing network propagation is not well understood. Laboratory experiments are proposed to study the evolution of fracturing network in naturally fractured formations with specimens that contain non-tectonic random fractures. The influences of the dominating factors were studied and analyzed, with an emphasis on natural fracture density, stress ratio, and injection rate. The response surface methodology was employed to perform the multiple-factor analysis and optimization in the maximization of the SRV. A sensitivity study reveals a number of interesting observations resulting from these parameters on the fracturing network evaluation. It is suggested from the geometry morphology of fracturing network that high natural fracture density and injection rate tend to maximize the fracturing network. The influence of stress contrast on fracturing network is nonlinear; an optimal value exists resulting in the best hydraulic fracturing effectiveness.     

Scale Effect on Principal Component Analysis for Vector Random Functions

Principal component analysis (PCA) is commonly applied without looking at the spatial support (size and shape, of the samples and the field), and the cross-covariance structure of the explored attributes. This paper shows that PCA can depend on such spatial features. If the spatial random functions for attributes correspond to largely dissimilar variograms and cross-variograms, the scale effect will increase as well. On the other hand, under conditions of proportional shape of the variograms and cross-variograms (i.e., intrinsic coregionalization), no scale effect may occur. The theoretical analysis leads to eigenvalue and eigenvector functions of the size of the domain and sample supports. We termed this analysis growing scale PCA, where spatial (or time) scale refers to the size and shape of the domain and samples. An example of silt, sand, and clay attributes for a second-order stationary vector random function shows the correlation matrix asymptotically approaches constants at two or three times the largest range of the spherical variogram used in the nested model. This is contrary to the common belief that the correlation structure between attributes become constant at the range value. Results of growing scale PCA illustrate the rotation of the orthogonal space of the eigenvectors as the size of the domain grows. PCA results are strongly controlled by the multivariate matrix variogram model. This approach is useful for exploratory data analysis of spatially autocorrelated vector random functions.     

Variogram Matrix Functions for Vector Random Fields with Second-Order Increments

The variogram matrix function is an important measure for the dependence of a vector random field with second-order increments, and is a useful tool for linear predication or cokriging. This paper proposes an efficient approach to construct variogram matrix functions, based on three ingredients: a univariate variogram, a conditionally negative definite matrix, and a Bernstein function, and derives three classes of variogram matrix functions for vector elliptically contoured random fields. Moreover, various dependence structures among components can be derived through appropriate mixture procedures demonstrated in this paper. We also obtain covariance matrix functions for second-order vector random fields through the Schoenberg–Lévy kernels.     

Interference of Multiple Strip Footings on Sand Using Small Scale Model Tests

By using small scale model tests, the interference effect on the vertical load-deformation behavior of a number of equally spaced strip footings, placed on the surface of dry sand, was investigated. At any stage, all the footings were assumed to (i) carry exactly equal magnitude of load, and (ii) settle to the same extent. No tilt of the footing was permitted. The effect of clear spacing (s) among footings on the results was explored. A new experimental setup was proposed in which only one footing needs to be employed rather than a number of footings. The bearing capacity increases continuously with decrease in spacing among the footings. The interference effect becomes further prominent with increase in soil friction angle. In contrast to an increase in the bearing capacity, with decrease in spacing of footings, an increase in the footing settlement associated with the ultimate state of shear failure was observed. The present experimental observations were similar to those predicted by the available theory, based on the method of characteristics. As compared to the theory, the present experimental data, however, indicates much greater effect of interference especially for larger spacing among footings.     

基于嵌入离散裂缝的页岩气藏视渗透率模型

页岩储层具有不同类型的储集空间,但综合考虑不同储集空间,对页岩储层渗透率进行评价的模型未见报道.基于嵌入离散裂缝模型,建立的页岩气藏视渗透率模型包括4个步骤:（1）构建天然裂缝、有机质和无机质的空间分布模型;（2）筛选不同类型储集空间的渗透率计算方法;（3）基于嵌入离散裂缝模型,结合空间分布模型和渗透率计算方法,建立数值模拟模型;（4）在模型的入口和出口端施加压差,求得一定压差下通过该岩心的气体流量,采用达西定律得到该页岩气藏的视渗透率.其计算结果与文献报道的渗透率实验值吻合较好.通过对不同因素的探讨,结果表明,天然裂缝对页岩气藏视渗透率的贡献大于无机质和有机质孔隙.因此,计算页岩视渗透率时有必要对天然裂缝、有机质和无机质孔隙进行综合考虑.      

碎石土滑坡稳定性一元多重属性回归模型分析

为了能在地质勘查和试验的基础上对碎石土滑坡稳定性进行评价,构建了一元多重属性回归模型。基于官家滑坡的14个工程地质剖面的实测资料,选取滑体重量、滑面倾角、滑面长度、水力坡度、浸水面积、内聚力、内摩擦角7个影响因素,采用模型对影响因素和稳定性系数进行回归分析和影响因素显著性研究,得到计算稳定性系数的回归方程,并利用新昌下山滑坡进行模型准确性验证。研究结果表明：根据模型建立的线性回归方程回归性显著,能够用模型对滑坡进行稳定性计算分析;通过模型得出对稳定性系数有显著性影响的因素,综合滑坡实际地质状况确定地下水对稳定性有显著的影响,有助于开展滑坡灾害预警预报工作和采取有效的工程治理措施;新昌下山滑坡介于稳定与较不稳定状态之间,在降雨量比较大的时段应加强监测。     

Multivariate Spatial Modeling for Geostatistical Data Using Convolved Covariance Functions

Soil pollution data collection typically studies multivariate measurements at sampling locations, e.g., lead, zinc, copper or cadmium levels. With increased collection of such multivariate geostatistical spatial data, there arises the need for flexible explanatory stochastic models. Here, we propose a general constructive approach for building suitable models based upon convolution of covariance functions. We begin with a general theorem which asserts that, under weak conditions, cross convolution of covariance functions provides a valid cross covariance function. We also obtain a result on dependence induced by such convolution. Since, in general, convolution does not provide closed-form integration, we discuss efficient computation. We then suggest introducing such specification through a Gaussian process to model multivariate spatial random effects within a hierarchical model. We note that modeling spatial random effects in this way is parsimonious relative to say, the linear model of coregionalization. Through a limited simulation, we informally demonstrate that performance for these two specifications appears to be indistinguishable, encouraging the parsimonious choice. Finally, we use the convolved covariance model to analyze a trivariate pollution dataset from California.     

基于Excel平台土壤含水量多元回归预测模型

土壤含水量是表述土壤干湿程度,反映旱情最直接的重要指标。土壤含水量预测能够反映未来某一时段农牧业旱情发展趋势,为开展旱情预警、各级领导和政府部门指挥抗旱减灾提供决策性依据。以降水、蒸发、风速等实测信息源为影响因子,以Excel为技术平台,创建了土壤含水量多元回归预测模型。该预测模型创建方法简单易行,便于改造和移植,有进一步推广价值。     

抗滑桩锚固段岩体的破坏模式及其有限元分析

基于抗滑桩设计计算以及嵌岩抗滑桩在西南地区广泛应用的现状,作者结合岩石强度理论和有限单元法为基础,着重分析了桩体锚固段岩体的受力特点和变形破坏模式,指出桩间距对岩体屈服变形和破坏模式存在一定的影响,其结论对嵌岩抗滑桩的设计有一定的参考价值.     

综合利用小水库群简易优化调度

提出一种以弃水量最小为目标函数的水库群简易优化调度方法──动态空库系数法。任一时刻某水库的空库系数反映该水库在该时刻的蓄水能力和供水能力。本法用时段初各水库空库系数的大小决定水库群的蓄放水次序,在满足约束条件下,时段末保持各水库的空库系数相等,由此尽可能地拦蓄径流,使弃水量最小。     

Locating the Multiple Failure Surfaces for Slope Stability Using Monte Carlo Technique

Owing to the complicated slope stratigraphy (e.g., multiple soil layers and multiple benches or gradients in side slopes), multiple failure surfaces for slope stability have been recognized in geotechnical discipline. This paper aims to develop a systematic and probabilistic approach to locate the multiple failure surfaces combining the traditional limit equilibrium method with Monte Carlo Simulation. Each of the multiple failure surfaces is selected from a large pool of failure surfaces and the correlation coefficient between two failure surfaces in factor of safety (FS) is adopted to characterize the extent to which two failure surfaces are correlated. After eliminating those highly correlated failure surfaces, the multiple failure surfaces can be gradually identified. The number of failure samples and the number of exclusive failure samples corresponding to each of multiple failure surfaces are determined within the proposed methodology. These data are reanalyzed to find the critical failure surface with the maximum failure probability, the critical failure surface with maximum simplified risk, and those failure surfaces dominating the risk of slope failure. The proposed approach is illustrated through two examples excerpted from the literature and validated against the results from the commercial software package and literature. The comparative study manifests that the critical failure surface with the minimum FS does not always coincide with that with the maximum failure probability and with the maximum simplified risk. In addition to FS, the failure surfaces should be received much attention. The proposed methodology provides an effective tool in decision making for slope stabilization and rehabilitation process.     

T -distributed Random Fields: A Parametric Model for Heavy-tailedWell-log Data1

Histograms of observations from spatial phenomena are often found to be more heavy-tailed than Gaussian distributions, which makes the Gaussian random field model unsuited. A T-distributed random field model with heavy-tailed marginal probability density functions is defined. The model is a generalization of the familiar Student-T distribution, and it may be given a Bayesian interpretation. The increased variability appears cross-realizations, contrary to in-realizations, since all realizations are Gaussian-like with varying variance between realizations. The T-distributed random field model is analytically tractable and the conditional model is developed, which provides algorithms for conditional simulation and prediction, so-called T-kriging. The model compares favourably with most previously defined random field models. The Gaussian random field model appears as a special, limiting case of the T-distributed random field model. The model is particularly useful whenever multiple, sparsely sampled realizations of the random field are available, and is clearly favourable to the Gaussian model in this case. The properties of the T-distributed random field model is demonstrated on well log observations from the Gullfaks field in the North Sea. The predictions correspond to traditional kriging predictions, while the associated prediction variances are more representative, as they are layer specific and include uncertainty caused by using variance estimates.     

考虑土体结构性的弹塑性硬化模型

在对人工制备结构性土样等应力比压缩试验结果分析基础上,确定出结构性土体初始屈服面形状和土体初始屈服后塑性应变增量的方向,推导出结构性土体屈服函数的表达式;硬化参数采用塑性功的函数,根据三轴排水剪切试验结果确定出土体的硬化规律。由此构建能反映土体结构性的弹塑性硬化本构模型,并用试验进行了验证。本文提出一种基于试验的建模方法,不依赖经典塑性力学理论的正交流动规则,并建立可考虑土体结构性影响的本构模型,对土体结构性研究具有借鉴意义。     

概念性水文模型多目标参数自动优选方法研究

以三水源新安江模型为例，研究探讨了概念性水文模型多目标参数自动优选方法。目标函数综合考虑了水量平衡、确定性系数、洪峰和枯水流量过程。通过对目标函数的不同组合方式，分别率定模型参数和分析比较结果。研究表明，多目标参数自动优选方法综合考虑了水文过程的各种要素，优于传统的单目标优选结果，具有较高的模拟预报精度。