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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical geology 31 (1999), S. 85-103 
    ISSN: 1573-8868
    Keywords: dispersion covariances ; Pearson correlation ; multivariate geostatistics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract This paper extends the concept of dispersion variance to the multivariate case where the change of support affects dispersion covariances and the matrix of correlation between attributes. This leads to a concept of correlation between attributes as a function of sample supports and size of the physical domain. Decomposition of dispersion covariances into the spatial scales of variability provides a tool for computing the contribution to variability from different spatial components. Coregionalized dispersion covariances and elementary dispersion variances are defined for each multivariate spatial scale of variability. This allows the computation of dispersion covariances and correlation between attributes without integrating the cross-variograms. A correlation matrix, for a second-order stationary field with point support and infinite domain, converges toward constant correlation coefficients. The regionalized correlation coefficients for each spatial scale of variability, and the cases where the intrinsic correlation hypothesis holds are found independent of support and size of domain. This approach opens possibilities for multivariate geostatistics with data taken at different support. Two numerical examples from soil textural data demonstrate the change of correlation matrix with the size of the domain. In general, correlation between attributes is extended from the classic Pearson correlation coefficient based on independent samples to a most general approach for dependent samples taken with different support in a limited domain.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical geology 31 (1999), S. 701-722 
    ISSN: 1573-8868
    Keywords: dispersion covariances ; spatial support ; Pearson correlation ; spatial scales of variability ; PCA ; matrix variogram
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Principal component analysis (PCA) is commonly applied without looking at the “spatial support” (size and shape, of the samples and the field), and the cross-covariance structure of the explored attributes. This paper shows that PCA can depend on such spatial features. If the spatial random functions for attributes correspond to largely dissimilar variograms and cross-variograms, the scale effect will increase as well. On the other hand, under conditions of proportional shape of the variograms and cross-variograms (i.e., intrinsic coregionalization), no scale effect may occur. The theoretical analysis leads to eigenvalue and eigenvector functions of the size of the domain and sample supports. We termed this analysis “growing scale PCA,” where spatial (or time) scale refers to the size and shape of the domain and samples. An example of silt, sand, and clay attributes for a second-order stationary vector random function shows the correlation matrix asymptotically approaches constants at two or three times the largest range of the spherical variogram used in the nested model. This is contrary to the common belief that the correlation structure between attributes become constant at the range value. Results of growing scale PCA illustrate the rotation of the orthogonal space of the eigenvectors as the size of the domain grows. PCA results are strongly controlled by the multivariate matrix variogram model. This approach is useful for exploratory data analysis of spatially autocorrelated vector random functions.
    Type of Medium: Electronic Resource
    Library Location Call Number Volume/Issue/Year Availability
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