共查询到20条相似文献，搜索用时 229 毫秒
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Ensemble size is critical to the efficiency and performance of the ensemble Kalman filter, but when the ensemble size is small,
the Kalman gain generally cannot be well estimated. To reduce the negative effect of spurious correlations, a regularization
process applied on either the covariance or the Kalman gain seems to be necessary. In this paper, we evaluate and compare
the estimation errors when two regularization methods including the distance-dependent localization and the bootstrap-based
screening are applied on the covariance and on the Kalman gain. The investigations were carried out through two examples:
1D linear problem without dynamics but for which the true Kalman gain can be computed and a 2D highly nonlinear reservoir
fluid flow problem. The investigation resulted in three primary conclusions. First, if localizations of two covariance matrices
are not consistent, the estimate of the Kalman gain will generally be poor at the observation location. The consistency condition
can be difficult to apply for nonlocal observations. Second, the estimate of the Kalman gain that results from covariance
regularization is generally subject to greater errors than the estimate of the Kalman gain that results from Kalman gain regularization.
Third, in terms of removing spurious correlations in the estimation of spatially correlated variables, the performance of
screening Kalman gain is comparable as the performance of localization methods (applied on either covariance or Kalman gain),
but screening Kalman gain outperforms the localization methods in terms of generality for application, as the screening method
can be used for estimating both spatially correlated and uncorrelated variables, and moreover, no assumption about the prior
covariance is required for the screening method. 相似文献
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Peter K. Kitanidis 《Mathematical Geology》1985,17(2):195-208
The parameters of covariance functions (or variograms) of regionalized variables must be determined before linear unbiased estimation can be applied. This work examines the problem of minimum-variance unbiased quadratic estimation of the parameters of ordinary or generalized covariance functions of regionalized variables. Attention is limited to covariance functions that are linear in the parameters and the normality assumption is invoked when fourth moments of the data need to be calculated. The main contributions of this work are (1) it shows when and in what sense minimum-variance unbiased quadratic estimation can be achieved, and (2) it yields a well-founded, practicable, and easy-to-automate methodology for the estimation of parameters of covariance functions. Results of simulation studies are very encouraging. 相似文献
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Optimal Spatial Sampling Design in a Multivariate Framework 总被引：2，自引：0，他引：2
M. C. Bueso J. M. Angulo J. Cruz-Sanjulián J. L. García-Aróstegui 《Mathematical Geology》1999,31(5):507-525
The problem of spatial sampling design for estimating a multivariate random field from information obtained by sampling related variables is considered. A formulation assigning different degrees of importance to the variables and locations involved is introduced. Adopting an entropy-based approach, an objective function is defined as a linear combination in terms of the amount of information on the variables and/or the locations of interest contained in the data. In the multivariate Gaussian case, the objective function is obtained as a geometric mean of conditional covariance matrices. The effect of varying the degrees of importance for the variables and/or the locations of interest is illustrated in some numerical examples. 相似文献
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Dean S. Oliver 《Mathematical Geology》1995,27(8):939-960
The square-root method provides a simple and computationally inexpensive way to generate multidimensional Gaussian random fields. It is applied by factoring the multidimensional covariance operator analytically, then sampling the factorization at discrete points to compute an array of weighted averages that can be convolved with an array of random normal deviates to generate a correlated random field. In many respects this is similar to the LUdecomposition method and to the one-dimensional method of moving averages. However it has been assumed that the method of moving averages could not be used in higher dimensions, whereas direct application of the matrix decomposition approach is too expensive to be practical on large grids.
In this paper, I show that it is possible to calculate the square root of many two- and three dimensional covariance operators analytically so that the method of moving averages can be applied directly to the problem of multidimensional simulation. A few numerical examples of nonconditional simulation on a 256×256 grid that show the simplicity of the method are included. The method is fast and can be applied easily to nested and anisotropic variograms. 相似文献
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Amilcar Soares 《Mathematical Geology》1992,24(2):149-160
A method is proposed for the characterization of the disjoint shapes of a multi-phase set. The method uses a global structural function and provides estimates of the complete mosaic of phases, honoring the individual volume proportions inferred from the experimental samples. The estimates of shapes can be improved by local conditioning to the covariance of each phase and to geometrical characteristics such as spatial orientation of the different strata. The mapping of uncertainty zones for individual phases is one advantage of using a geostatistical approach to characterize the morphology of qualitative (non-numerical) variables. 相似文献
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The aim of this short article is to stress the importance of using only positive-definite functions as models for covariance functions and variograms.The two examples presented show that a negative variance can easily be obtained when a nonadmissible function is chosen for the variogram model. 相似文献
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Combining sensitivities and prior information for covariance localization in the ensemble Kalman filter for petroleum reservoir applications 总被引：1，自引：0，他引：1
Sampling errors can severely degrade the reliability of estimates of conditional means and uncertainty quantification obtained
by the application of the ensemble Kalman filter (EnKF) for data assimilation. A standard recommendation for reducing the
spurious correlations and loss of variance due to sampling errors is to use covariance localization. In distance-based localization,
the prior (forecast) covariance matrix at each data assimilation step is replaced with the Schur product of a correlation
matrix with compact support and the forecast covariance matrix. The most important decision to be made in this localization
procedure is the choice of the critical length(s) used to generate this correlation matrix. Here, we give a simple argument
that the appropriate choice of critical length(s) should be based both on the underlying principal correlation length(s) of
the geological model and the range of the sensitivity matrices. Based on this result, we implement a procedure for covariance
localization and demonstrate with a set of distinctive reservoir history-matching examples that this procedure yields improved
results over the standard EnKF implementation and over covariance localization with other choices of critical length. 相似文献
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Multivariable spatial prediction 总被引：1，自引：0，他引：1
For spatial prediction, it has been usual to predict one variable at a time, with the predictor using data from the same type of variable (kriging) or using additional data from auxiliary variables (cokriging). Optimal predictors can be expressed in terms of covariance functions or variograms. In earth science applications, it is often desirable to predict the joint spatial abundance of variables. A review of cokriging shows that a new cross-variogram allows optimal prediction without any symmetry condition on the covariance function. A bivariate model shows that cokriging with previously used cross-variograms can result in inferior prediction. The simultaneous spatial prediction of several variables, based on the new cross-variogram, is then developed. Multivariable spatial prediction yields the mean-squared prediction error matrix, and so allows the construction of multivariate prediction regions. Relationships between cross-variograms, between single-variable and multivariable spatial prediction, and between generalized least squares estimation and spatial prediction are also given. 相似文献
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Thomas Le Blévec Olivier Dubrule Cédric M. John Gary J. Hampson 《Mathematical Geosciences》2018,50(6):609-637
A Pluri-Gaussian method is developed for facies variables in three dimensions to model vertical cyclicity related to facies ordering and rhythmicity. Cyclicity is generally characterised by shallowing-upward or deepening-upward sequences and rhythmicity by the repetition of facies at constant intervals along sequences. Both of these aspects are commonly observed in shallow-marine carbonate successions, especially in the vertical direction. A grid-free spectral simulation approach is developed, with a separable covariance allowing a dampened hole-effect to capture rhythmicity in the vertical direction and a different covariance in the lateral plane along strata, as in space-time models. In addition, facies ordering is created by using a spatial shift between two latent Gaussian functions in the Pluri-Gaussian approach. Rapid conditioning to data is performed via Gibbs sampling and kriging using the screening properties of separable covariances. The resulting facies transiograms can show complex patterns of cyclicity and rhythmicity. Finally, a three dimensional case study of shallow-marine carbonate deposits at outcrop shows the applicability of the modelling method. 相似文献
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In this paper, we describe two methods of discrimination based on MSE ratio and regression, respectively, and an algorithm of orthogonally stepwise discrimination. The method is not limited by the assumption that the sample covariance matrix is not ill-conditioned or singular, and by any assumption about the distribution of each population as well. So, it has wide range of application to various problems, particularly, to the problem of discrimination with both quantitative and qualitative variables. After variables are selected in the procedure of stepwise discrimination, they need not be rejected. Several examples have been calculated by using the method, and the results are quite satisfying. 相似文献
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Positive definiteness is not enough 总被引：2，自引：0，他引：2
M. Armstrong 《Mathematical Geology》1992,24(1):135-143
Geostatisticians know that the mathematical functions chosen to represent spatial covariances and variograms must have the appropriate type of positive definiteness, but they may not realize that there are restrictions on the types of covariances and variograms that are compatible with particular distributions. This paper gives some examples showing that (1) the spherical model is not compatible with the multivariate lognormal distribution if the coefficient of variation is 2.0 or more (even in 1-D), and (2) the Gaussian covariance and several other models are not compatible with indicator random functions. As these examples concern quite different types of random functions, it is clear that there is a general problem of compatibility between spatial covariance models (or variograms) and a specified multivariate distribution. The problem arises with all distributions except the multivariate normal, and not just the two cited here. The need for a general theorem giving the necessary and sufficient conditions for a covariance or a variogram to be compatible with a particular distribution is stressed. 相似文献
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Jorn F. M. Van Doren Paul M. J. Van den Hof Okko H. Bosgra Jan Dirk Jansen 《Computational Geosciences》2013,17(5):773-788
Reservoir simulation models are frequently used to make decisions on well locations, recovery optimization strategies, etc. The success of these applications is, among other aspects, determined by the controllability and observability properties of the reservoir model. In this paper, it is shown how the controllability and observability of two-phase flow reservoir models can be analyzed and quantified with aid of generalized empirical Gramians. The empirical controllability Gramian can be interpreted as a spatial covariance of the states (pressures or saturations) in the reservoir resulting from input perturbations in the wells. The empirical observability Gramian can be interpreted as a spatial covariance of the measured bottom-hole pressures or well bore flow rates resulting from state perturbations. Based on examples in the form of simple homogeneous and heterogeneous reservoir models, we conclude that the position of the wells and of the front between reservoir fluids, and to a lesser extent the position and shape of permeability heterogeneities that impact the front, are the most important factors that determine the local controllability and observability properties of the reservoir. 相似文献
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顺层边坡稳定性及可靠度的随机有限元分析法 总被引：2，自引：1，他引：1
阐述了基于摄动法的随机有限元基本原理,采用以均值为中心的2阶摄动随机有限元,运用局部平均的空间离散方法,对顺层边坡的应力场进行了2阶统计均值、协方差和方差的分析,并结合顺层边坡沿软弱夹层滑动的破坏特征,推导了基于Mohr-Coulomb准则的顺层边坡整体稳定的安全系数和可靠度的计算表达式。结合典型顺层岩质路堑边坡工程实例,采用摄动随机有限元法进行了边坡稳定性和可靠度的分析计算。结果表明,文中介绍的摄动随机有限元法可以考虑多种随机变量对边坡系统的影响,可同时采用安全系数和可靠度作为边坡稳定性的评价指标,判定结果更为准确和全面。 相似文献
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A spectral algorithm is proposed to simulate an isotropic Gaussian random field on a sphere equipped with a geodesic metric. This algorithm supposes that the angular power spectrum of the covariance function is explicitly known. Direct analytic calculations are performed for exponential and linear covariance functions. In addition, three families of covariance functions are presented where the calculation of the angular power spectrum is simplified (shot-noise random fields, Yadrenko covariance functions and solutions of certain stochastic partial differential equations). Numerous illustrative examples are given.
相似文献18.
Correspondence cluster analysis, developed in this paper, regroups the main advantages of correspondence analysis and cluster analysis. The output of the method, correspondence cluster dendrograms, shows clearly the relationships between variables, between samples, and between variables and samples, on a single diagram. The technique has been applied successfully to distinguish geochemical anomalies from background, to recognize types of anomalies, to study the geochemical characteristics of deposits, etc. Several practical examples presented in this paper show that the method can be used to classify elements and samples into meaningful groups, and that the geochemical character of each sample group can be interpreted in terms of the corresponding element group. The results are consistent with the geological situations at hand, and are usually more elucidating than other classification methods. 相似文献
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Peter I. Brooker 《Mathematical Geology》1985,17(1):81-90
Journel (1974) developed the turning-bands method which allows a three-dimensional data set with specified covariance to be obtained by the simulation of several one-dimensional realizations which have an intermediate covariance. The relationship between the threedimensional and one-dimensional covariance is straightforward and allows the one-dimensional covariance to be obtained immediately. In theory a dense uniform distribution of lines in three-dimensional space is required along which the one-dimensional realizations are generated; in practice most workers have been content to use the fifteen axes of the regular icosahedron. Many mining problems may be treated in two dimensions, and in this paper a turning-bands approach is developed to generate two-dimensional data sets with a specified covariance. By working in two dimensions, the area on which the data is simulated may be divided as finely as desired by the lines on which the one-dimensional realizations are first generated. The relationship between the two-dimensional and one-dimensional covariance is derived as a nontrivial integral equation. This is solved analytically for the onedimensional covariance. The method is applied to the generation of a two-dimensional data set with spherical covariance. 相似文献
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In large multi-element regional surveys statistically derived threshold levels of the form that define, for example, the top 2% of the data for each element as worthy of further investigation have led to the generation of inordinately large lists of geochemical samples for detailed study. This problem is compounded when a number of geological and secondary environments exists of sufficiently different character that separate thresholds should be estimated for each. Additionally, single-element thresholds for multi-element surveys can, in certain circumstances, lead to obviously out-of-character individuals not being recognized.Numerical approaches to the problem of anomaly recognition have commonly used a principal-component or regression analysis procedure as their basis. These, as indeed do all such approaches, have a common drawback in that the outliers being sought can distort the analysis being used to detect them. In addition, regression models have the further problem that there may be outliers in both the response and explanatory variables.A relatively simple approach would be to prepare a multivariate cumulative probability plot where each multi-element geochemical sample is represented as a single value. The resulting diagram would be interpreted much as a univariate probability plot where the presence of more than one straight-line segment is taken as evidence of multiple populations, and outliers as individuals or small groups are separated from the remaining data by gaps on the plot.Such a diagram may be prepared by plotting the rank-ordered values of the generalized or Mahalanobis distance, a multivariate distance measure, versus values of the chi-square statistic. This procedure is based on the covariance matrix of the data, a measure that underlies both principal-component and regression model approaches. In order to work effectively a statistically robust starting covariance matrix is essential.The procedure is described in detail with two examples, one a synthetic bivariate data set containing known outliers, and the other a small, well studied stream sediment data set from Norway extensively used in methodological comparison studies. The result of the procedure is to identify statistical outliers, which are candidates for interpretation as true geochemical anomalies, and to isolate a multi-element subset that is representative of the geochemical background. 相似文献