A Non-Homogeneous Model for Kriging Dosimetric Data
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A Non-Homogeneous Model for Kriging Dosimetric Data Christian Lajaunie1 · Didier Renard1 Alexis Quentin2 · Vincent Le Guen2 · Yvan Caffari2
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Received: 11 October 2017 / Accepted: 13 August 2019 © International Association for Mathematical Geosciences 2019
Abstract This paper deals with kriging-based interpolation of dosimetric data. Such data typically show some inhomogeneities that are difficult to take into account by means of the usual non-stationary models available in geostatistics. By including the knowledge of suspected potential sources (such as pipes or reservoirs) better estimates can be obtained, even when no hard data are available on these sources. The proposed method decomposes the measured dose rates into a diffuse homogeneous term and the contribution from the sources. Accordingly, two random function models are introduced, the first associated with the diffuse term, and the second with the unknown and unmeasured source contribution. Estimation of the model parameters is based on cross-validation quadratic error. As a bonus, the resulting model makes it possible to estimate the source activity. The efficiency of this approach is demonstrated on data simulated according to the physical equations of the system. The method is available to researchers through an R-package provided by the authors upon request.
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Didier Renard [email protected] Christian Lajaunie [email protected] Alexis Quentin [email protected] Vincent Le Guen [email protected] Yvan Caffari [email protected]
1
Mines Paris Tech, Paris, France
2
EDF, R&D, Chatou, France
123
Math Geosci
Keywords Geostatistics · Estimation with inhomogeneous model · External drift model
1 Introduction Standard kriging assumes statistical invariance under translations in space, which means that linear combinations filtering trends are statistically homogeneous across the domain of interest. This is the case under the usual model in which the spatial function is the sum of a stationary random function and a polynomial drift. Another class of models in which this assumption holds is the IRFk model (Matheron 1973) in which only specific linear combinations of the variable have finite variance. This variance can then be computed on the basis of generalized covariances, allowing the calculation of the kriging predictor. This class of models emerges naturally when dealing with solutions of linear partial derivative equations with constant coefficients (Dong 1990). The previous assumption, while most often reasonable (see Chilès and Delfiner 2012 or Wackernagel 2003), can be ruled out in several instances. A search for another form of homogeneity compatible with statistical inference is then needed. This is particularly difficult in the case of a unique realization, as opposed to cases where repeated measurements are available over time. Another particular class of non-stationary models, introduced by Sampson and Guttorp (1992), derives from a stationary random function by space deformation. The inference
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