Analysis of Regularly and Irregularly Sampled Spatial, Multivariate, and Multi-temporal Data
This thesis describes different methods that are useful in the analysis of multivariate data. Some methods focus on spatial data (sampled regularly or irregularly), others focus on multitemporal data or data from multiple sources. The thesis covers selected and not all aspects of relevant data analy...
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| Format: | Book |
| Language: | English |
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Technical University of Denmark
1994
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| Online Access: | https://orbit.dtu.dk/en/publications/a96f3c3d-df7a-4e71-ac2e-146132edd6ea https://backend.orbit.dtu.dk/ws/files/2831793/imm296.pdf |
| Summary: | This thesis describes different methods that are useful in the analysis of multivariate data. Some methods focus on spatial data (sampled regularly or irregularly), others focus on multitemporal data or data from multiple sources. The thesis covers selected and not all aspects of relevant data analysis techniques in this context. Geostatistics is described in Chapter 1. Tools as the semivariogram, the cross-semivariogram and different types of kriging are described. As an independent re-invention 2-D sample semivariograms, cross-semivariograms and cova functions, and modelling of 2-D sample semi-variograms are described. As a new way of setting up a well-balanced kriging support the Delaunay triangulation is suggested. Two case studies show the usefulness of 2-D semivariograms of geochemical data from areas in central Spain (with a geologist's comment) and South Greenland, and kriging/cokriging of an undersampled variable in South Greenland, respectively. Chapters 2 and 3 deal with various orthogonal transformations. Chapter 2 describes principal components (PC) analysis and two related spatial extensions, namely minimum/maximum autocorrelation factors (MAF) and minimum noise fractions (MNF) analysis. Whereas PCs maximize the variance represented by each component, MAFs maximize the spatial autocorrelation represented by each component, and MNFs maximize a measure of signal-to-noise ratio represented by each component. In the literature MAF/MNF analysis is described for regularly gridded data only. Here, the concepts are extended to irregularly sampled data via the Delaunay triangulation. As a link to the methods described in Chapter 1 a new type of kriging based on MAF/MNFs for irregularly spaced data is suggested. Also, a new way of removing periodic, salt-and-pepper and other types of noise based on Fourier filtering of MAF/MNFs is suggested. One case study successfully shows the effect of the MNF Fourier restoration. Another case shows the superiority of the MAF/MNF analysis over ordinary non-spatial factor ... |
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