Dynamic data integration for structural modeling: model screening approach using a distance-based model parameterization

This paper proposes a novel history-matching method where reservoir structure is inverted from dynamic fluid flow response. The proposed workflow consists of searching for models that match production history from a large set of prior structural model realizations. This prior set represents the reservoir structural uncertainty because of interpretation uncertainty on seismic sections. To make such a search effective, we introduce a parameter space defined with a “similarity distance” for accommodating this large set of realizations. The inverse solutions are found using a stochastic search method. Realistic reservoir examples are presented to prove the applicability of the proposed method.     

基坑潜水疏干的简化计算在昊华水泥厂中的应用

以流线、流面、汇点的概念为基础,对稳定流双井干扰和直线隔水边界附近涌水量理论公式进行对比分析,提出了二个虚拟界面,其中虚拟界面Ⅰ,运用流线、流面的性质,流线方程等给出证明;虚拟界面Ⅱ则通过半无限条形降落漏斗的分析,应用元流和总流的能量方程得到流量为零,流线为零的平面。在同样条件下,条形无限涌水量是半无限潜含水层涌水量的二倍。应用总流能量方程对三种情况水头损失的分析,解释了这种关系存在的合理性,得出虚拟界面Ⅱ,并以此得出该界面内的最大残余水头计算公式。将基坑降水运用虚拟界面简化为扇形,条形半无限含水层,从而实现单井预测,该方法应用到昊华水泥厂基坑降水中,预测效果理想。     

Multi-Scale Texture Modeling

Patterns of crystallographic preferred orientation are referred to as texture. The specific subject of texture analysis is the experimental determination and interpretation of the statistical distribution of orientations of crystals within a specimen of polycrystalline material, which could be metals or rocks. The objective is to relate an observed pattern of preferred orientation to its generating processes and vice versa. In geosciences, texture of minerals in rocks is used to infer constraints on their tectono-metamorphic history. Since most physical properties of crystals, such as elastic moduli, the coefficients of thermal expansion, or chemical resistance to etching depends on crystal symmetry and orientation, the presence of texture imparts directional properties to the polycrystalline material. A major issue of mathematical texture analysis is the resolution of the inverse problem to determine a reasonable orientation density function on SO(3) from measured pole intensities on , which relates to the inverse of the totally geodesic Radon transform. This communication introduces a wavelet approach into mathematical texture analysis. Wavelets on the two-dimensional sphere and on the rotational group SO(3) are discussed, and an algorithms for a wavelet decomposition on both domains following the ideas of Ta-Hsin Li is given. The relationship of these wavelets on both domains with respect to the totally geodesic Radon transform is investigated. In particular, it is shown that the Radon transform of these wavelets on SO(3) are again wavelets on . A novel algorithm for the inversion of experimental pole intensities to an orientation density function based on this relationship is developed.     

地震综合效应场函数及其在地震预报中的应用──（一）地震综合效应场函数及其计算方法

在系统地分析了目前各种测震学地震预报方法科学思路的基础上,认为测震学地震预报方法基本上可以分为两大类。一类是以已经发生的一些地震作为未来可能发生的地震的“因”,即由于已经发生的地震对区域应力场的影响,导致未来发生较强地震。这一类包括的预报方法较多,如空区、条带、ｂ值、地震迁移、相关地震等等及其由此衍生出来的各种方法。另一类是把已经发生的一些地震作为区域应力场增强的“果”,即已经发生的地震是区域应力场增强过程中的一种反映,而未来地震不一定是已经发生的地震所导致的结果。这一类包括“地震窗口”、小震群活动等方法。针对第一类方法,各种预报方法都是力图从地震三要素中提取未来地震的信息,而具体作法又都是利用地震三要素这个多维空间的某个剖面。为了从地震活动诸要素的多维空间提取综合信息,我们对每个地震加入了破裂面方位,构成了地震第四要素,并依据地震４要素建立了地震综合效应场函数。地震综合效应场函数概括了多种测震学地震预报方法的科学思路和预报经验,从而可以形成测震学的综合预报方法。     

Estimation of covariance matrix from geochemical data with observations below detection limits

Multivariate statistical analyses have been extensively applied to geochemical measurements to analyze and aid interpretation of the data. Estimation of the covariance matrix of multivariate observations is the first task in multivariate analysis. However, geochemical data for the rare elements, especially Ag, Au, and platinum-group elements, usually contain observations the below detection limits. In particular, Instrumental Neutron Activation Analysis (INAA) for the rare elements produces multilevel and possibly extremely high detection limits depending on the sample weight. Traditionally, in applying multivariate analysis to such incomplete data, the observations below detection limits are first substituted, for example, each observation below the detection limit is replaced by a certain percentage of that limit, and then the standard statistical computer packages or techniques are used to obtain the analysis of the data. If a number of samples with observations below detection limits is small, or the detection limits are relatively near zero, the results may be reasonable and most geological interpretations or conclusions are probably valid. In this paper, a new method is proposed to estimate the covariance matrix from a dataset containing observations below multilevel detection limits by using the marginal maximum likelihood estimation (MMLE) method. For each pair of variables, sayY andZ whose observations containing below detection limits, the proposed method consists of three steps: (i) for each variable separately obtaining the marginal MLE for the means and the variances, , , , and forY andZ: (ii) defining new variables by and and lettingA=C+D andB=C–D, and obtaining MLE for variances, and forA andB; (iii) estimating the correlation coefficient _YZ by and the covariance _YZ by . The procedure is illustrated by using a precious metal geochemical data set from the Fox River Sill, Manitoba, Canada.     

Estimation for partially observed Markov processes

Many stochastic process models for environmental data sets assume a process of relatively simple structure which is in some sense partially observed. That is, there is an underlying process (X_n, n 0) or (X_t, t 0) for which the parameters are of interest and physically meaningful, and an observable process (Y_n, n 0) or (Y_t, t 0) which depends on the X process but not otherwise on those parameters. Examples are wide ranging: the Y process may be the X process with missing observations; the Y process may be the X process observed with a noise component; the X process might constitute a random environment for the Y process, as with hidden Markov models; the Y process might be a lower dimensional function or reduction of the X process. In principle, maximum likelihood estimation for the X process parameters can be carried out by some form of the EM algorithm applied to the Y process data. In the paper we review some current methods for exact and approximate maximum likelihood estimation. We illustrate some of the issues by considering how to estimate the parameters of a stochastic Nash cascade model for runoff. In the case of k reservoirs, the outputs of these reservoirs form a k dimensional vector Markov process, of which only the kth coordinate process is observed, usually at a discrete sample of time points.     

Application of X-ray computed tomography for analyzing cleat spacing and cleat aperture in coal samples

New techniques to determine distributions of cleat aperture, cleat orientation and cleat spacing from CT scans have been developed. For cleat orientation and spacing distributions, two different coal blocks were scanned. The CT scans have been analyzed for the three orthogonal directions. Histograms of the cleat orientations are bimodal, expressing the typical cleat texture of face and butt cleats and bedding perpendicular relaxation fractures. Deviations up to 20° from the peak values in the cleat orientation distributions were used as input for automated image analysis of cleat spacing. Distributions of the cleat spacing measurements are related to the face and butt cleat directions. The term “relevant cleat length” is introduced as a measure to extract the amount of cleat length involved with the cleat spacing measurements. The ratio ranges from 0.03 to 0.38 and expresses the difference in cleat texture in both samples. Cleat spacing versus relevant cleat length shows sample specific patterns for face cleat, butt cleat and bedding. To describe cleat aperture quantitatively, peak height and missing attenuation have been used. The image of a cleat was seen as a convolution of a rectangular fracture profile with a Gaussian point spread function.     

Correlations in aftershock and seismicity patterns

Correlations in space and time play a fundamental role in earthquake processes. One direct manifestation of the effects of correlations is the occurrence of aftershocks due to the stress transfer in the vicinity of a main shock. Less obvious and more speculative changes in correlations may occur in the background seismicity before large earthquakes. Using statistical physics it is possible to introduce a measure of spatial correlations through a correlation length. This quantity characterizes how local fluctuations can influence the occurrence of earthquakes over distances comparable with the correlation length. In this work, the physical basis of spatial correlations of earthquakes is discussed in the context of critical phenomena and the percolation problem. The method of two-point correlation function is applied to the seismicity of California. Well defined variations in time of the correlation length are found for aftershock sequences and background seismicity. The scaling properties of our obtained distributions are analyzed with respect to changes in several scaling parameters such as lower magnitude cutoff of earthquakes, the maximum time interval between earthquakes, and the spatial size of the area considered. This scaling behavior can be described in a unified manner by utilizing the multifractal fit. Utilizing the percolation approach the time evolution of clusters of earthquakes is studied with the correlation length defined in terms of the radius of gyration of clusters. This method is applied to the seismicity of California.     

Modèles géostatistiques de concentrations ou de débits le long des cours d'eau

Estimating concentrations or flow rates along a stream network requires specific models. Two classes of models, recently proposed in the literature, are generalized, to the intrinsic case in particular. We present a global construction by ‘streams’, i.e. on the whole set of paths between sources and outlet. Combining stationary or intrinsic one-dimensional random functions leads to stationary or intrinsic models on segments, with discontinuities at the forks. A construction from outlet to sources, leads to stationary or intrinsic models on each stream, without any discontinuity at the forks. The linear variogram is found as a particular case. The extension to the linear model of coregionalization is immediate, allowing a multivariate modelling of concentrations. To cite this article: C. de Fouquet, C. Bernard-Michel, C. R. Geoscience 338 (2006).