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- Title
Regularisation and Deregularisation of Covariances and Variograms for Univariate Random Functions in One-dimensional Space.
- Authors
Lantuéjoul, Christian; Bush, David E.; Stiefenhofer, Johann; Thurston, Malcolm L.
- Abstract
The regularisation on a segment of a stationary or intrinsic variogram model is usually expressed as an integral. By introducing an auxiliary function, it is shown that this integral is a linear combination of elementary terms. This paper shows how these terms are arranged and provides a simple and safe procedure to calculate them. An important application of this procedure is the deregularisation problem, that is, the conversion of a regularised variogram to a point variogram. This ill-posed problem is tackled using an iterative optimisation algorithm designed to produce a family of point variograms that best fit the initial regularised variogram. Subsequently, each of these point variograms can be regularised on any segment, which results in a fully coherent family of simple and cross regularised variograms.
- Subjects
VARIOGRAMS; FUNCTION spaces; OPTIMIZATION algorithms
- Publication
Mathematical Geosciences, 2023, Vol 55, Issue 5, p609
- ISSN
1874-8961
- Publication type
Article
- DOI
10.1007/s11004-022-10043-9