Change of Support for Estimating Local Block Grade Distributions     

Xavier Emery 《Mathematical Geosciences》2008,40(6):671-688

An important aspect in mineral resource evaluation is the reduction of variance when post-processing the grade distributions defined on the support (volume) of the available data into distributions defined on the support of the proposed selective mining units. Although the volume-variance relationship is well understood for the estimation of global grade distributions, it is still an unsolved issue for local estimation studies based on non-parametric geostatistical methods, such as indicator kriging, for which the support correction is not inherent to the method. To clarify this relationship, the local change of support problem is examined in the scope of two parametric models (multi-Gaussian and discrete Gaussian models). It is shown that the variance reduction factor between point and block-support local distributions depends on the block being considered and is less than the global variance reduction factor. As a consequence, post-processing the local point-support grade distributions on the basis of the latter systematically understates the importance of the change of support at the local scale and makes selective mining appear more economically attractive than it really is. In the light of these results, a methodology is proposed to post-process the local point-support distributions obtained via non-parametric (indicator) methods into block-support distributions. An application to simulated data indicates that this methodology provides an accurate estimation at the block support when dealing with diffusion-type random fields.  相似文献   

Efficient generation of conditional simulations by chebyshev matrix polynomial approximations to the symmetric square root of the covariance matrix     

C. R. Dietrich  G. N. Newsam 《Mathematical Geology》1995,27(2):207-228

Consider the problem of generating a realization y₁ of a Gaussian random field on a dense grid of points ₁ conditioned on field observations y₂ collected on a sparse grid of points ₂. An approach to this is to generate first an unconditional realization y over the grid =_{1 2}, and then to produce y₁ by conditioning y on the data y₂. As standard methods for generating y, such as the turning bands, spectral or Cholesky approaches can have various limitations, it has been proposed by M. W. Davis to generate realizations from a matrix polynomial approximations to the square root of the covariance matrix. In this paper we describe how to generate a direct approximation to the conditional realization y₁, on ₁ using a variant of Davis' approach based on approximation by Chebyshev polynomials. The resulting algorithm is simple to implement, numerically stable, and bounds on the approximation error are readily available. Furthermore we show that the conditional realization y₁ can be generated directly with a lower order polynomial than the unconditional realization y, and that further reductions can be achieved by exploiting a nugget effect if one is present. A pseudocode version of the algorithm is provided that can be implemented using the fast Fourier transform if the field is stationary and the grid ₁ is rectangular. Finally, numerical illustrations are given of the algorithm's performance in generating various 2-D realizations of conditional processes on large sampling grids.  相似文献   

图像平滑算法比较研究及改进策略   总被引：9，自引：0，他引：9  

秦志远 吴冰王艳  山海涛 《测绘学院学报》2005,22(2):103-106

图像平滑作为去除图像中含有噪声的图像增强处理技术，是各种与图像有关软件中必不可少的功能模块。文中在分析噪声模型的基础上，对均值平滑、中值平滑、边缘保持平滑等技术从图像处理空间域中的算法原理、实现方法及效率等方面进行了详细比较。针对图像中含有的不同噪声模型，通过多次试验，得出了值得从事图像处理研究者参考的结论。这将有助于提高图像处理软件开发的效率。  相似文献   

Conditional curvilinear stochastic simulation using pixel-based algorithms   总被引：7，自引：0，他引：7  

Wenlong Xu 《Mathematical Geology》1996,28(7):937-949

In geology, structures displaying differing local directions of continuity are widespread, a typical example being a flusial depositional system. Conventional pixel-based geostatistical algorithms, may fail to reproduce such curvilinear structures. Conversely, object-based algorithms can reproduce curvilinear shapes but are difficult to condition to dense local data. Local depositional directions as obtained from dipmeter data. 3D seismic data, and geological interpretation represent critical information. An improved pixel-based geostatistical algorithm is proposed to account for such directional information. Case studies demonstrate the potential and limitations of the algorithm.  相似文献   

SEDIMENT TRANSPORT MODEL OF A WATERSHED     

LI Huaien 《国际泥沙研究》1997,(1)

ChinaisoneOfthecountrieswhichsufferfromthemostserioussoilerosionintheworld,andthehillyandgullyareasof~PlateauinthemiddlereachesOftheYellowRiverarethemostseriouserosionareainChina.Inthisarea,themainerosivefactorsarerainfallandrunoff.Sometimes,thesedimentyieldinasinglefloodeventcanbe40%oftheannualsedimentload.Therefore,itisveryimPOrtanttostudytheyieldandgraphOfSedimentOfsinglefindevent.Forthispn~,thispaperiswritten.AInongsedimentmodelsforsinglefloodevent,moreandmoreattentionwaspaidtOunitse…  相似文献   

Transformation of Residuals to Avoid Artifacts in Geostatistical Modelling with a Trend   总被引：1，自引：0，他引：1  

Oy Leuangthong  Clayton V. Deutsch 《Mathematical Geology》2004,36(3):287-305

Trend modelling is an important part of natural resource characterization. A common approach to account for a variable with a trend is to decompose it into a relatively smoothly varying trend and a more variable residual component. Then, the residuals are stochastically modelled independent of the trend. This decomposition can result in values outside the plausible range of variability, such as grades below zero or ratios that exceed 1.0. We transform the residuals conditional to the trend component to explicitly remove these complex features prior to geostatistical modelling. Back transformation of the modelled residual values allows the complex relations to be reproduced. A petroleum-related application shows the robustness of the proposed transformation. Furthermore, a mining application shows that when this conditional transformation is applied to the original variable, instead of the residual, simulated values are assured to be nonnegative.  相似文献   

Histogram and variogram inference in the multigaussian model   总被引：1，自引：4，他引：1  

Xavier Emery  Julián M. Ortiz 《Stochastic Environmental Research and Risk Assessment (SERRA)》2005,19(1):48-58

Several iterative algorithms are proposed to improve the histogram and variogram inference in the framework of the multigaussian model. The starting point is the variogram obtained after a traditional normal score transform. The subsequent step consists in simulating many sets of gaussian values with this variogram at the data locations, so that the ranking of the original values is honored. The expected gaussian transformation and the expected variogram are computed by an averaging operation over the simulated datasets. The variogram model is then updated and the procedure is repeated until convergence. Such an iterative algorithm can adapt to the case of tied data and despike the histogram. Two additional issues are also examined, referred to the modeling of the empirical transformation function and to the optimal pair weighting when computing the sample variogram.  相似文献   

Lame surfaces as a generalisation of the triaxial ellipsoid     

Z. Nadenik 《Studia Geophysica et Geodaetica》2005,49(3):277-288

In modern geodesy the triaxial ellipsoid as a generalisation of the ellipsoid of revolution has a significant position in studying the figure of the Earth. Lame surfaces represent a generalisation of the triaxial ellipsoid. The following paragraphs are devoted to curvatures of the Lame surfaces.  相似文献   

Conditional Simulation of Random Fields with Bivariate Gamma Isofactorial Distributions   总被引：5，自引：0，他引：5  

Xavier Emery 《Mathematical Geology》2005,37(4):419-445

This work focuses on a random function model with gamma marginal and bivariate isofactorial distributions, which has been applied in mining geostatistics for estimating recoverable reserves by disjunctive kriging. The objective is to widen its use to conditional simulation and further its application to the modeling of continuous attributes in geosciences. First, the main properties of the bivariate gamma isofactorial distributions are analyzed, with emphasis in the destructuring of the extreme values, the presence of a proportional effect (higher variability in high-valued areas), and the asymmetry in the spatial correlation of the indicator variables with respect to the median threshold. Then, we provide examples of stationary random functions with such bivariate distributions, for which the shape parameter of the marginal distribution is half an integer. These are defined as the sum of squared independent Gaussian random fields. An iterative algorithm based on the Gibbs sampler is proposed to perform the simulation conditional to a set of existing data. Such ‘multivariate chi-square’ model generalizes the well-known multigaussian model and is more flexible, since it allows defining a shape parameter which controls the asymmetry of the marginal and bivariate distributions.  相似文献   

An algebraic solution of maximum likelihood function in case of Gaussian mixture distribution     

J. L. Awange  B. Palancz  R. Lewis  T. Lovas  B. Heck  Y. Fukuda 《Australian Journal of Earth Sciences》2016,63(2):193-203

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