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Least-squares collocation with covariance-matching constraints

Content Provider	Springer Nature Link
Author	Kotsakis, Christopher
Copyright Year	2007
Abstract	Most geostatistical methods for spatial random field (SRF) prediction using discrete data, including least-squares collocation (LSC) and the various forms of kriging, rely on the use of prior models describing the spatial correlation of the unknown field at hand over its domain. Based upon an optimal criterion of maximum local accuracy, LSC provides an unbiased field estimate that has the smallest mean squared prediction error, at every computation point, among any other linear prediction method that uses the same data. However, LSC field estimates do not reproduce the spatial variability which is implied by the adopted covariance (CV) functions of the corresponding unknown signals. This smoothing effect can be considered as a critical drawback in the sense that the spatio-statistical structure of the unknown SRF (e.g., the disturbing potential in the case of gravity field modeling) is not preserved during its optimal estimation process. If the objective for estimating a SRF from its observed functionals requires spatial variability to be represented in a pragmatic way then the results obtained through LSC may pose limitations for further inference and modeling in Earth-related physical processes, despite their local optimality in terms of minimum mean squared prediction error. The aim of this paper is to present an approach that enhances LSC-based field estimates by eliminating their inherent smoothing effect, while preserving most of their local prediction accuracy. Our methodology consists of correcting a posteriori the optimal result obtained from LSC in such a way that the new field estimate matches the spatial correlation structure implied by the signal CV function. Furthermore, an optimal criterion is imposed on the CV-matching field estimator that minimizes the loss in local prediction accuracy (in the mean squared sense) which occurs when we transform the LSC solution to fit the spatial correlation of the underlying SRF.
Starting Page	661
Ending Page	677
Page Count	17
File Format	PDF
ISSN	09497714
Journal	Journal of Geodesy
Volume Number	81
Issue Number	10
e-ISSN	14321394
Language	English
Publisher	Springer-Verlag
Publisher Date	2007-02-03
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Least-squares collocation Spatial random field Prediction Smoothing Covariance matching Math. Applications in Geosciences Geophysics/Geodesy
Content Type	Text
Resource Type	Article
Subject	Geophysics Geochemistry and Petrology Computers in Earth Sciences

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