现代地质统计学的新进展

结合现代地质统计学最新进展,对现代地质统计学的现状进行了研究,着重时时空域中的多元信息地质编译学和时空多元动态模拟进行了探讨,并在最后指出了现代地质统计学今后的发展方向。     

多点地质统计学建模研究进展

从精细油藏描述中地质建模的意义和现状入手,介绍了多点地质统计学建模研究现状及其与传统地质建模方法的差 异。以辽河盆地西部凹陷某蒸汽驱试验区为例,分析了多点地质统计学建模中建模的基础、训练图像的建立、多点地质统计学 建模与传统地质建模相比所具有的优势等内容。指出多点地质统计学在井间预测方面具有明显优于其他传统建模方法的特 点。在文献调研基础上,结合自身工作实践,探讨了多点地质统计学建模目前存在的问题和未来的发展方向。指出未来多点 地质统计学建模的发展方向主要包括多信息综合地质成因分析基础上的训练图像获取、多点地质统计学算法进行改进和完善 和多点地质统计学建模方法应用领域的扩大等。     

Book Review: Geostatistics Rio 2000, Quantitative Geology and Geostatistics: By M. Armstrong,C. Bettini,N. Champigny,A. Galli,and A. Remacre (eds.) Kluwer Academic Publishers,Dordrecht, 2002, 235 p., $94 (U.S.), ISBN 1-4020-0470-2 (hard back)

Mathematical Geosciences -     

Kernel Principal Component Analysis for Efficient,Differentiable Parameterization of Multipoint Geostatistics

This paper describes a novel approach for creating an efficient, general, and differentiable parameterization of large-scale non-Gaussian, non-stationary random fields (represented by multipoint geostatistics) that is capable of reproducing complex geological structures such as channels. Such parameterizations are appropriate for use with gradient-based algorithms applied to, for example, history-matching or uncertainty propagation. It is known that the standard Karhunen–Loeve (K–L) expansion, also called linear principal component analysis or PCA, can be used as a differentiable parameterization of input random fields defining the geological model. The standard K–L model is, however, limited in two respects. It requires an eigen-decomposition of the covariance matrix of the random field, which is prohibitively expensive for large models. In addition, it preserves only the two-point statistics of a random field, which is insufficient for reproducing complex structures. In this work, kernel PCA is applied to address the limitations associated with the standard K–L expansion. Although widely used in machine learning applications, it does not appear to have found any application for geological model parameterization. With kernel PCA, an eigen-decomposition of a small matrix called the kernel matrix is performed instead of the full covariance matrix. The method is much more efficient than the standard K–L procedure. Through use of higher order polynomial kernels, which implicitly define a high-dimensionality feature space, kernel PCA further enables the preservation of high-order statistics of the random field, instead of just two-point statistics as in the K–L method. The kernel PCA eigen-decomposition proceeds using a set of realizations created by geostatistical simulation (honoring two-point or multipoint statistics) rather than the analytical covariance function. We demonstrate that kernel PCA is capable of generating differentiable parameterizations that reproduce the essential features of complex geological structures represented by multipoint geostatistics. The kernel PCA representation is then applied to history match a water flooding problem. This example demonstrates that kernel PCA can be used with gradient-based history matching to provide models that match production history while maintaining multipoint geostatistics consistent with the underlying training image.     

Special Issue: Geostatistics and Machine Learning

Mathematical Geosciences - Recent years have seen a steady growth in the number of papers that apply machine learning methods to problems in the earth sciences. Although they have different...     

Book Review: Geostatistics with Applications in Earth Sciences. By D. D. Sarma. Capital Publishing Company,New Delhi, 2002, 170 p., ISBN 81-85589-04-6

Mathematical Geosciences -     

Geostatistics for Compositional Data: An Overview

Mathematical Geosciences - This paper presents an overview of results for the geostatistical analysis of collocated multivariate data sets, whose variables form a composition, where the components...     

Geostatistics of Dependent and Asymptotically Independent Extremes

Spatial modeling of rare events has obvious applications in the environmental sciences and is crucial when assessing the effects of catastrophic events (such as heatwaves or widespread flooding) on food security and on the sustainability of societal infrastructure. Although classical geostatistics is largely based on Gaussian processes and distributions, these are not appropriate for extremes, for which max-stable and related processes provide more suitable models. This paper provides a brief overview of current work on the statistics of spatial extremes, with an emphasis on the consequences of the assumption of max-stability. Applications to winter minimum temperatures and daily rainfall are described.     

Geostatistics for Power Models of Gaussian Fields

This paper introduces geostatistical approaches (i.e., kriging estimation and simulation) for a group of non-Gaussian random fields that are power algebraic transformations of Gaussian and lognormal random fields. These are power random fields (PRFs) that allow the construction of stochastic polynomial series. They were derived from the exponential random field, which is expressed as Taylor series expansion with PRF terms. The equations developed from computation of moments for conditional random variables allow the correction of Gaussian kriging estimates for the non-Gaussian space. The introduced PRF geostatistics shall provide tools for integration of data that requires simple algebraic transformations, such as regression polynomials that are commonly encountered in the practical applications of estimation. The approach also allows for simulations drawn from skewed distributions.     

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。