Scaling variances, correlation and principal components with multivariate geostatistics
A new concept of dispersion (cross) covariance has been introduced for the modeling of spatial scale dependent multivariate correlations. Such correlations between attributes depend on the spatial size of the domain and size of samples in the population and have been modeled by first time in this re...
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| Language: | en_US |
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The University of Arizona.
1998
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| Online Access: | http://hdl.handle.net/10150/282813 |
| Summary: | A new concept of dispersion (cross) covariance has been introduced for the modeling of spatial scale dependent multivariate correlations. Such correlations between attributes depend on the spatial size of the domain and size of samples in the population and have been modeled by first time in this research. Modeled correlations have been used to introduce a new scale dependent principal component analysis (PCA) method. This method is based on computation of eigen values and vectors from dispersion covariance matrices or scale dependent correlations which can be modeled from integrals of matrix variograms. For second order stationary random functions this PCA converges for large domains to the classic PCA. A new technique for computing variograms from spatial variances have also been developed using derivatives. For completeness, a deeper analysis of the linear model of coregionalizations widely used in multivariate geostatistics has been included as well. This last part leads to a new more sophisticated model we termed "linear combinations coregionalization model." This whole research explains the relationship between different average states and the micro- state of vector random functions in the framework of geostatistics. Examples have been added to illustrate the practical application of the theory. This approach will be useful in all earth sciences and particularly in soil and environmental sciences. |
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