Gradual Deformation and Iterative Calibration of Gaussian-Related Stochastic Models

This paper describes a new method for gradually deforming realizations of Gaussian-related stochastic models while preserving their spatial variability. This method consists in building a stochastic process whose state space is the ensemble of the realizations of a spatial stochastic model. In particular, a stochastic process, built by combining independent Gaussian random functions, is proposed to perform the gradual deformation of realizations. Then, the gradual deformation algorithm is coupled with an optimization algorithm to calibrate realizations of stochastic models to nonlinear data. The method is applied to calibrate a continuous and a discrete synthetic permeability fields to well-test pressure data. The examples illustrate the efficiency of the proposed method. Furthermore, we present some extensions of this method (multidimensional gradual deformation, gradual deformation with respect to structural parameters, and local gradual deformation) that are useful in practice. Although the method described in this paper is operational only in the Gaussian framework (e.g., lognormal model, truncated Gaussian model, etc.), the idea of gradually deforming realizations through a stochastic process remains general and therefore promising even for calibrating non-Gaussian models.     

The fractal character of photos of slabbed cores

Core photos have been analyzed statistically and found to be fractional Gaussian noise (fGn) in both horizontal and vertical directions. This fractal character, fGn, is the same as that previously found to describe vertical and horizontal well logs. An equation for the two-dimensional spectral density of core photos is presented that generates computer photos very similar to real core photos.     

Conditional simulation of remotely sensed rainfall data using a non-Gaussian v-transformed copula

Quantification of rainfall and its spatial and temporal variability is extremely important for reliable hydrological and meteorological modeling. While rain gauge measurements do not provide reasonable areal representation of rainfall, remotely sensed precipitation estimates offer much higher spatial resolution. However, uncertainties associated with remotely sensed rainfall estimates are not well quantified. This issue is important considering the fact that uncertainties in input rainfall are the main sources of error in hydrologic processes. Using an ensemble of rainfall estimates that resembles multiple realizations of possible true rainfall, one can assess uncertainties associated with remotely sensed rainfall data. In this paper, ensembles are generated by imposing rainfall error fields over remotely sensed rainfall estimates. A non-Gaussian copula-based model is introduced for simulation of rainfall error fields. The v-transformed copula is employed to describe the dependence structure of rainfall error estimates without the influence of the marginal distribution. Simulations using this model can be performed unconditionally or conditioned on ground reference measurements such that rain gauge data are honored at their locations. The presented model is implemented for simulation of rainfall ensembles across the Little Washita watershed, Oklahoma. The results indicate that the model generates rainfall fields with similar spatio-temporal characteristics and stochastic properties to those of observed rainfall data.     

Spatial variation assessment of groundwater quality using multivariate statistical analysis(Case Study: Fasa Plain,Iran)

Groundwater is considered as one of the most important sources for water supply in Iran. The Fasa Plain in Fars Province, Southern Iran is one of the major areas of wheat production using groundwater for irrigation. A large population also uses local groundwater for drinking purposes. Therefore, in this study, this plain was selected to assess the spatial variability of groundwater quality and also to identify main parameters affecting the water quality using multivariate statistical techniques such as Cluster Analysis (CA), Discriminant Analysis (DA), and Principal Component Analysis (PCA). Water quality data was monitored at 22 different wells, for five years (2009-2014) with 10 water quality parameters. By using cluster analysis, the sampling wells were grouped into two clusters with distinct water qualities at different locations. The Lasso Discriminant Analysis (LDA) technique was used to assess the spatial variability of water quality. Based on the results, all of the variables except sodium absorption ratio (SAR) are effective in the LDA model with all variables affording 92.80% correct assignation to discriminate between the clusters from the primary 10 variables. Principal component (PC) analysis and factor analysis reduced the complex data matrix into two main components, accounting for more than 95.93% of the total variance. The first PC contained the parameters of TH, Ca²⁺, and Mg²⁺. Therefore, the first dominant factor was hardness. In the second PC, Cl^-, SAR, and Na⁺ were the dominant parameters, which may indicate salinity. The originally acquired factors illustrate natural (existence of geological formations) and anthropogenic (improper disposal of domestic and agricultural wastes) factors which affect the groundwater quality.     

一种基于沉积模式的多点地质统计学建模方法

地下储层分布是位置的函数,不同位置处的沉积模式具有差异性。在储层预测时,除了挖掘已有资料所提供的结构和统计信息外,还应该引入待估点位置的信息,以反映沉积储层模式随位置变化的非平稳特征。提出了一种基于沉积模式的多点地质统计学方法,通过距离函数将储层特征与沉积位置相关联,采用整体替换、结构化随机路径以及多重网格策略再现沉积模式。基于现代鄱阳湖沉积所建立的合成非平稳性三角洲前缘沉积地层建模表明,新设计的方法较传统的建模方法更好地反映了三角洲相沉积地层非平稳沉积模式,新设计方法有更好的地质适用性。研究丰富了储层三维建模理论和方法,为实际油藏建模提供了新手段。     

沈阳市新城子区土壤重金属元素的空间变异性

利用地质统计学方法,系统地研究了沈阳市新城子区土壤重金属元素的空间分布及空间变异性特征。研究结果显示,土壤中Cd和Pb的含量明显高于全国平均值和辽宁省土壤背景值。变异函数分析结果表明,Hg具有明显的空间自相关性,Cd、Pb和As均具有中等空间自相关的特征。Cd和Pb含量较高,并呈显著的正相关,主要受灌溉、施肥等外在因素的影响。重金属元素空间变异性的研究对当地土壤环境评价和土地质量评估具有一定的指示和引导作用。     

分区绘制等值线的地下水污染质分布

使用ArcGIS 在不同水文地质分区中绘制等值线的方法,对长春市2004 年50 个水质采样点的数据进行空间统计分析,分区绘制了地下水重要组分NH+ 4 和Fe、Mn 的单项评价等值线图,分析了其分布及来源。结果表明,采用按水文地质条件分区绘制等值线的方法比原来由观测数据直接生成等值线的方法更趋合理。     

空间模式的广义自相似性分析与矿产资源评价

尺度不变性(scale invariance)包括自相似性(各向同性)、自仿射性(成层结构)、广义自相似性(各向异性标度不变性),是由各种地质过程和地质事件所产生的地质特征和模式的本质属性．尺度不变性可用分形和多重分形模型来表征．这些尺度特征的定量化可为刻画地质空问模式和模式识别提供有力的工具．例如。热液矿床的群聚现象可以用局部分形特征(局部奇异性)来刻画．通过在特征空问中(如频率空问)识别空问模式的广义自相似性．可以将空间混合模式进行分解或异常的识别．介绍了几种相关的分形模型和方法。包括度量空问模式广义尺度独立性(GSI)的线性模型;基于广义尺度独立性的异常分解S—A方法;度量空问模式的局部奇异性方法;以及如何利用分形特征预测未发现矿床的2种方法．有些方法已应用于许多矿产资源评价实例中．给出了对加拿大Nova Scotia省西南部湖泊沉积物样品中的4种元素As、Pb、Zn和Cu的地球化学数据处理分析结果。证明了局部奇异性分析和S—A异常分解方法对地球化学异常的增强和分离的有效性．研究表明：由S—A方法分解的异常往往具有多重分形的特点,而且普遍具有局部奇异性．研究区内具有明显奇异性的地区(元素含量富集区)是金矿异常区域。它们与金矿成矿作用和已知矿床的赋存密切相关．