On the Validity of Commonly Used Covariance and Variogram Functions on the Sphere

• Published in: Mathematical geosciences Vol. 43; no. 6; pp. 721 - 733
• Main Authors: Huang, Chunfeng, Zhang, Haimeng, Robeson, Scott M.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 01.08.2011; Springer; Springer Nature B.V
• Subjects: Chemistry and Earth Sciences; Computer Science; Covariance; Earth and Environmental Science; Earth Sciences; Earth, ocean, space; Exact sciences and technology; Geophysics; Geotechnical Engineering & Applied Earth Sciences; Hydrogeology; Indexing in process; Marine and continental quaternary; Mathematical analysis; Mathematical models; Physics; Radon; Statistics for Engineering; Surficial geology; Tables (data); Transforms; Spherical covariance; Variogram models; Power variogram; Stable model; sphericity; models; mathematical methods; variograms; covariance; Spherical Covariance; Radon transformation
• ISSN: 1874-8961; 1874-8953
• DOI: 10.1007/s11004-011-9344-7

Covariance and variogram functions have been extensively studied in Euclidean space. In this article, we investigate the validity of commonly used covariance and variogram functions on the sphere. In particular, we show that the spherical and exponential models, as well as power variograms with 0< α ≤1, are valid on the sphere. However, two Radon transforms of the exponential model, Cauchy model, the hole-effect model and power variograms with 1< α ≤2 are not valid on the sphere. A table that summarizes the validity of commonly used covariance and variogram functions on the sphere is provided.