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。     

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...     

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 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...     

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。     

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.     

Modelling Spatial Variability Along Drainage Networks with Geostatistics

Local characteristics of drainage networks such as cross-section geometry and hydraulic roughness coefficient, influence surface water transfers and must be taken into account when assessing the impact of human activities on hydrological risks. However, as these characteristics have not been available till now through remote sensing or hydrological modelling, the only available methods are interpolation or simulation based on scarce data. In this paper we propose a statistical model based on geostatistics that allows us to take account of both the spatial distribution and spatial uncertainties. To do this, we modify the geostatistical framework to suit directed tree supports corresponding to drainage network structures. The stationarity concept is specified assuming conditional independence between parts of the network; variogram fitting and modelling are then modified accordingly. A sequential multi Gaussian simulation procedure going upstream along the network is proposed. We illustrate this approach by studying the width of an 11-km long artificial drainage network in the south of France.     

Geostatistics applied to best-fit interpolation of orientation data

Automatic methods used in geosciences to interpolate between orientation data have often limited applicability and strength, in particular where large ranges of orientations occur. In this paper, we show that geostatistical methods yield rather strong and powerful results when applied to directional data. The procedure involves the calculation of variograms, followed by a kriging interpolation of the data. In order to free from the circular property of directional data, the treatment of initial angular data sets is performed using scalar values provided by the direction cosines of double-angle values. The strength and application of the method are demonstrated by the analysis of theoretical and natural data sets. Natural examples are focused on the calculation and the analysis of cleavage trajectory maps.     

Extending Multivariate Space-Time Geostatistics for Environmental Data Analysis

Environmental studies require multivariate data such as chemical concentrations with space-time coordinates. There are two general conditions related to such data: the existence of correlations among the coregionalized variables and the differences in numbers of data which occur because of insufficient data caused by measurement error or bad weather conditions. This study proposes geostatistical techniques for space-time multivariate modeling that take into consideration these correlations and data absences. These techniques consist of suitable modeling of semivariograms and cross-semivariograms for quantifying correlation structures among multivariables and of extending standardized ordinary cokriging. The tensor product cubic smoothing surface method is used for space-time semivariogram modeling. These methods are applied to the chemical component data of the Ariake Sea, a typical closed sea in southwest Japan. In order to clarify environmental changes in the Ariake Sea, the concentration data of four nutritive salts (NO₂–N, NO₃–N, NH₄–N, and PO₄–P) at 38 stations over 25 years are used as environmental indicators. For each of the kinds of data, there are spaces and times for which there is no data available. The effectiveness of the modeling of space-time semivariograms and the high estimation capability of the extended cokriging are demonstrated by cross-validation. Compared with ordinary kriging for a single variable, multivariate space-time standardized ordinary cokriging can provide a more detailed concentration map of nutritive salts and while elucidating their temporal changes over sparsely spaced data areas. In the space-time models by ordinary kriging, on the other hand, smooth trends are obvious.     

Stationarity Scores on Training Images for Multipoint Geostatistics

This research introduces a novel method to assess the validity of training images used as an input for Multipoint Geostatistics, alternatively called Multiple Point Simulation (MPS). MPS are a family of spatial statistical interpolation algorithms that are used to generate conditional simulations of property fields such as geological facies. They are able to honor absolute “hard” constraints (e.g., borehole data) as well as “soft” constraints (e.g., probability fields derived from seismic data, and rotation and scale). These algorithms require 2D or 3D training images or analogs whose textures represent a spatial arrangement of geological properties that is presumed to be similar to that of a target volume to be modeled. To use the current generation of MPS algorithms, statistically valid training image are required as input. In this context, “statistical validity” includes a requirement of stationarity, so that one can derive from the training image an average template pattern. This research focuses on a practical method to assess stationarity requirements for MPS algorithms, i.e., that statistical density or probability distribution of the quantity shown on the image does not change spatially, and that the image shows repetitive shapes whose orientation and scale are spatially constant. This method employs image-processing techniques based on measures of stationarity of the category distribution, the directional (or orientation) property field and the scale property field of those images. It was successfully tested on a set of two-dimensional images representing geological features and its predictions were compared to actual realizations of MPS algorithms. An extension of the algorithms to 3D images is also proposed. As MPS algorithms are being used increasingly in hydrocarbon reservoir modeling, the methods described should facilitate screening and selection of the input training images.     

地质统计学在东天山化探信息提取中的应用

地球化学场和地球物理场都具有一定的空间结构性和空间自相关性,而揭示这种空间相关性的有力工具是变差函数。利用变差函数对东天山的1∶20万区域地球化学数据Cu和Au进行了结构分析。结果表明：两元素在东西方向有着较好的稳定性和连续性,南北方向有较大的变化性并具有一定的线性漂移,总体呈现带状异常,与东天山EW方向大断裂具有很好的一致性。利用泛克里格法对Cu、Au进行了异常信息的提取和评价,泛克里格法提取的剩余异常不仅能突出高异常区,也较清晰地反映了部分低缓异常带,为研究区域化探异常分布特征提供了丰富的信息。