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Multivariable variogram and its application to the linear model of coregionalization 总被引：1，自引：0，他引：1
In this article, we present the multivariable variogram, which is defined in a way similar to that of the traditional variogram, by the expected value of a distance, squared, in a space withp dimensions. Combined with the linear model of coregionalization, this tool provides a way for finding the elementary variograms that characterize the different spatial scales contained in a set of data withp variables. In the case in which the number of elementary components is less than or equal to the number of variables, it is possible, by means of nonlinear regression of variograms and cross-variograms, to estimate the coregionalization parameters directly in order to obtain the elementary variables themselves, either by cokriging or by direct matrix inversion. This new tool greatly simplifies the procedure proposed by Matheron (1982) and Wackernagel (1985). The search for the elementary variograms is carried out using only one variogram (multivariable), as opposed to thep(p + 1)/2 required by the Matheron approach. Direct estimation of the linear coregionalization model parameters involves the creation of semipositive definite coregionalization matrices of rank 1. 相似文献
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The results of various methods typically used by governments to assess the environmental impact of potential pollutants do not give comparable results. It is argued that the cause is not the assessment techniques themselves but rather the paradigm of ecology from which they spring. 相似文献
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Summary
The feasibility and safety of a mining project or the choice among alternative mining methods could depend on the joint densities
and orientations within the rock mass. The accurate determination of the orientation of all joints is technically difficult
and often economically unrealistic. This study presents a new approach in classifying joints found in exploration boreholes
as joint sets, whose statistical distribution is determined from a few hundred oriented joints in boreholes. Each non-oriented
joint is classified as belonging to a set based on its “a posteriori” probability of membership in a Bayesian framework. The
theoretical rate of success of the classification can be computed for each possible borehole orientation and plotted on a
stereonet to determine the optimal orientation of new boreholes. The performance and limitations of this approach are investigated.
An application example at the Mont Porphyre's large scale block-caving project at Gaspé Mines, Quebec, Canada, is studied. 相似文献
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Generalized cross-validation for covariance model selection 总被引：4，自引：0，他引：4
Denis Marcotte 《Mathematical Geology》1995,27(5):659-672
A weighted cross-validation technique known in the spline literature as generalized cross-validation (GCV), is proposed for covariance model selection and parameter estimation. Weights for prediction errors are selected to give more importance to a cluster of points than isolated points. Clustered points are estimated better by their neighbors and are more sensitive to model parameters. This rational weighting scheme also provides a simplifying significantly the computation of the cross-validation mean square error of prediction. With small- to medium-size datasets, GCV is performed in a global neighborhood. Optimization of usual isotropic models requires only a small number of matrix inversions. A small dataset and a simulation are used to compare performances of GCV to ordinary cross-validation (OCV) and least-squares filling (LS). 相似文献
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A calibration method to solve the groundwater inverse problem under steady- and transient-state conditions is presented. The method compares kriged and numerical head field gradients to modify hydraulic conductivity without the use of non-linear optimization techniques. The process is repeated iteratively until a close match with piezometric data is reached. The approach includes a damping factor to avoid divergence and oscillation of the solution in areas of low hydraulic gradient and a weighting factor to account for temporal head variation in transient simulations. The efficiency of the method in terms of computing time and calibration results is demonstrated with a synthetic field. It is shown that the proposed method provides parameter fields that reproduce both hydraulic conductivity and piezometric data in few forward model solutions. Stochastic numerical experiments are conducted to evaluate the sensitivity of the method to the damping function and to the head field estimation errors. 相似文献
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Corentin Faucher Antoine Saucier Denis Marcotte 《Stochastic Environmental Research and Risk Assessment (SERRA)》2014,28(8):2027-2050
This paper presents a new stochastic simulation method that improves on our unilateral patchwork simulation method (Faucher et al., Stoch Environ Res Risk Assess, 27:253–273, 2012) by eliminating anisotropy biases. As in our unilateral method, images are built by assembling patterns together while controlling the local-mean histogram. The patterns, which are square image-pieces, are picked in a reference image. The reference image is used as a data bank holding the statistical informations about the random field to simulate. In contrast with the unilateral method, the path followed by our new simulation is random and guided by local errors. The new method, called corrective pattern-matching simulation, proceeds iteratively by making local corrections to the simulated image. For several types of images, it is shown that our simulations respect conditioning data and reproduce faithfully the reference image visual appearance. It is shown that the control of the local-mean histogram allows to control one-point statistics and multi-point statistics. 相似文献
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Hassan?RezaeeEmail author Denis?Marcotte 《Stochastic Environmental Research and Risk Assessment (SERRA)》2017,31(7):1727-1745
A new approach is described to allow conditioning to both hard data (HD) and soft data for a patch- and distance-based multiple-point geostatistical simulation. The multinomial logistic regression is used to quantify the link between HD and soft data. The soft data is converted by the logistic regression classifier into as many probability fields as there are categories. The local category proportions are used and compared to the average category probabilities within the patch. The conditioning to HD is obtained using alternative training images and by imposing large relative weights to HD. The conditioning to soft data is obtained by measuring the probability–proportion patch distance. Both 2D and 3D cases are considered. Synthetic cases show that a stationary TI can generate non-stationary realizations reproducing the HD, keeping the texture indicated by the TI and following the trends identified in probability maps obtained from soft data. A real case study, the Mallik methane-hydrate field, shows perfect reproduction of HD while keeping a good reproduction of the TI texture and probability trends. 相似文献
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