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Linear coregionalization model: Tools for estimation and choice of cross-variogram matrix 总被引：13，自引：0，他引：13
The geostatistical analysis of multivariate data involves choosing and fitting theoretical models to the empirical matrix. This paper considers the specific case of the model of linear coregionalization, and describes an automated procedure for fitting models, that are adequate in the mathematical sense, using a least-squares like technique. It also describes how to decide whether the number of parameters of the cross-variogram matrix model should be reduced to improve stability of fit. The procedure is illustrated with an analysis of the spatial relations among the physical properties of an alluvial soil. The results show the main influence of the scale and the shape of the basic models on the goodness of fit. The choice of the number of basic models appears of secondary importance, though it greatly influences the resulting interpretation of the coregionalization analysis. 相似文献
3.
因子克立格分析是研究多元地质统计学的基拙，是由因子克立格法和协区域化分析两部分组成，方法上包括了区域化变量(集)的分解和分解后每一空间分童的估值;本文阐述了因子克立格分析从产生到应用的理论发展、研究成果及应用展望。 相似文献
4.
Abstract This paper compares the performance of three geostatistical algorithms, which integrate elevation as an auxiliary variable: kriging with external drift (KED); kriging combined with regression, called regression kriging (RK) or kriging after detrending; and co-kriging (CK). These three methods differ by the way by in which the secondary information is introduced into the prediction procedure. They are applied to improve the prediction of the monthly average rainfall observations measured at 106 climatic stations in Tunisia over an area of 164 150 km2 using the elevation as the auxiliary variable. The experimental sample semivariograms, residual semivariograms and cross-variograms are constructed and fitted to estimate the rainfall levels and the estimation variance at the nodes of a square grid of 20 km?×?20 km resolution and to develop corresponding contour maps. Contour diagrams for KED and RK were similar and exhibited a pattern corresponding more closely to local topographic features when (a) the network is sparse and (b) the rainfall–elevation correlation is poor, while CK showed a smooth zonal pattern. Smaller prediction variances are obtained for the RK algorithm. The cross-validation showed that the RMSE obtained for CK gave better results than for KED or RK. Editor D. Koutsoyiannis; Associate editor C. Onof Citation Feki, H., Slimani, M., and Cudennec, C., 2012. Incorporating elevation in rainfall interpolation in Tunisia using geostatistical methods. Hydrological Sciences Journal, 57 (7), 1294–1314. 相似文献
5.
基于马尔可夫链的多元指示地质统计模型 总被引：9，自引：0，他引：9
与传统基于交叉变差函数(cross variogram)的多元指示地质统计模型相比,基于马尔可夫链的多元指示地质统计模型采用转移概率(transition probability)来描述区域化变量的空间变化,可以很好地反映复杂空间的连续性,弥补了传统地质统计模型没有考虑地质体分布存在不对称性的缺陷,简化了各向异性的处理过程,且在建立模型的过程中,融入了地质类型分布的比例、平均长度和相互间的迁移转换趋势等地质统计信息,使建模过程更直观,更易于理解。用这种方法建立的模型在理论上有比较成熟的随机理论支持,在实际应用中能更准确地反映地质体的空间分布特征。由于该模型考虑了地质体空间分布的连续性、不对称性和各向异性等特征,因此将其用于模拟地下含水层的空间结构,可以真实反映实际含水层的空间分布,为进一步模拟地下水运动提供有力支持。 相似文献
6.
Steven F. Carle 《Mathematical Geology》1997,29(2):231-244
The simulated annealing algorithm has been applied successfully to conditional simulation of categorical variables (e.g.,
rock or facies units) with the objective of improving the match between measured and modeled spatial variability. In some
implementation schemes, however, spurious features termed “artifact discontinuities” may occur near conditioning data, especially
during the “zero- temperature” case referred to as simulated quenching. This paper shows that artifact discontinuities can
be avoided by considering the anisotropy of the spatial variability model, reducing the number of lag vectors used in the
objective function, and providing a rudimentary initial configuration. Results from several test cases suggest that the artifact
discontinuities might be caused by overly precise fitting of measured to modeled spatial variability. 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
8.
Guocheng Pan 《Mathematical Geology》1993,25(5):603-631
This paper presents a regionalized method for the estimation of a favorability function through generalization of all relevant variables (explanatory and target) into random functions. The new method allows the use of cross-covariance functions in addition to ordinary covariances for extracting spatial joint information, which is virtually overlooked in the conventional analyses. The optimal weights for a favorability equation are derived from solving a generalized eigen-system established by the maximization of covariances between a favorability function and the principal components of a set of pre-selected target variables. Various correlation coefficients may be computed to assist in interpretation of the favorability estimates. Both favorability functions and correlation coefficients may be estimated for a point or a block. The regionalized favorability theory can be compared to cokriging in that both use the sample-sample covariances to account for the sample-sample relations and the point-sample covariances to account for the point-sample configurations. The new technique is demonstrated on a test case study, which involves the integration of geochemical, airborne-geophysical, and structural data sets for the target selection of hydrothermal gold-silver deposits. 相似文献
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Transition probability-based indicator geostatistics 总被引：30，自引：0，他引：30
Traditionally, spatial continuity models for indicator variables are developed by empirical curvefitting to the sample indicator (cross-) variogram. However, geologic data may be too sparse to permit a purely empirical approach, particularly in application to the subsurface. Techniques for model synthesis that integrate hard data and conceptual models therefore are needed. Interpretability is crucial. Compared with the indicator (cross-) variogram or indicator (cross-) covariance, the transition probability is more interpretable. Information on proportion, mean length, and juxtapositioning directly relates to the transition probability: asymmetry can be considered. Furthermore, the transition probability elucidates order relation conditions and readily formulates the indicator (co)kriging equations. 相似文献
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The variance-based cross-variogram between two spatial processes, Z1
(·) and Z2
(·), is var (Z1
(
u
) – Z2
(
v
)), expressed generally as a bivariate function of spatial locations
uandv. It characterizes the cross-spatial dependence between Z1
(·) and Z2
(·) and can be used to obtain optimal multivariable predictors (cokriging). It has also been called the pseudo cross-variogram; here we compare its properties to that of the traditional (covariance-based) cross-variogram, cov (Z1
(
u
) – Z1
(
v
), Z2
(
u
) – Z2
(
v
)). One concern with the variance-based cross-variogram has been that Z1
(·) and Z2
(·) might be measured in different units (apples and oranges). In this note, we show that the cokriging predictor based on variance-based cross-variograms can handle any units used for Z1
(·) and Z2
(·); recommendations are given for an appropriate choice of units. We review the differences between the variance-based cross-variogram and the covariance-based cross-variogram and conclude that the former is more appropriate for cokriging. In practice, one often assumes that variograms and cross-variograms are functions of
uandv
only through the difference
u – v. This restricts the types of models that might be fitted to measures of cross-spatial dependence. 相似文献