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A class of non-stationary covariance functions with compact support.
- Source :
-
Stochastic Environmental Research & Risk Assessment . Mar2016, Vol. 30 Issue 3, p973-987. 15p. - Publication Year :
- 2016
-
Abstract
- This article describes the use of non-stationary covariance functions with compact support to estimate and simulate a random function. Based on the kernel convolution theory, the functions are derived by convolving hyperspheres in $$\mathbb{R}^n$$ followed by a Radon transform. The order of the Radon transform controls the differentiability of the covariance functions. By varying spatially the hyperspheres radius one defines non-stationary isotropic versions of the spherical, the cubic and the penta-spherical models. Closed-form expressions for the non-stationary covariances are derived for the isotropic spherical, cubic, and penta-spherical models. Simulation of the different non-stationary models is easily obtained by weighted average of independent standard Gaussian variates in both the isotropic and the anisotropic case. The non-stationary spherical covariance model is applied to estimate the overburden thickness over an area composed of two different geological domains. The results are compared to the estimation with a single stationary model and the estimation with two stationary models, one for each geological domain. It is shown that the non-stationary model enables a reduction of the mean square error and a more realistic transition between the two geological domains. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 14363240
- Volume :
- 30
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Stochastic Environmental Research & Risk Assessment
- Publication Type :
- Academic Journal
- Accession number :
- 113305372
- Full Text :
- https://doi.org/10.1007/s00477-015-1100-y