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Permissibility of fractal exponents and models of band-limited two-point functions for fGn and fBm random fields

D.T. Hristopulos

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URIhttp://purl.tuc.gr/dl/dias/B07C5CA5-0A02-4726-BA02-7C49A7B42F98-
Identifierhttps://doi.org/10.1007/s00477-003-0126-8-
Languageen-
Extent25 pagesen
TitlePermissibility of fractal exponents and models of band-limited two-point functions for fGn and fBm random fields en
CreatorD.T. Hristopulosen
PublisherSpringer-Verlagen
Content SummaryThe fractional Gaussian noise (fGn) and fractional Brownian motion (fBm) random field models have many applications in the environmental sciences. An issue of practical interest is the permissible range and the relations between different fractal exponents used to characterize these processes. Here we derive the bounds of the covariance exponent for fGn and the Hurst exponent for fBm based on the permissibility theorem by Bochner. We exploit the theoretical constraints on the spectral density to construct explicit two-point (covariance and structure) functions that are band-limited fractals with smooth cutoffs. Such functions are useful for modeling a gradual cutoff of power-law correlations. We also point out certain peculiarities of the relations between fractal exponents imposed by the mathematical bounds. Reliable estimation of the correlation and Hurst exponents typically requires measurements over a large range of scales (more than 3 orders of magnitude). For isotropic fractals and partially isotropic self-affine processes the dimensionality curse is partially lifted by estimating the exponent from measurements along fixed directions. We derive relations between the fractal exponents and the one-dimensional spectral density exponents, and we illustrate the relations using measurements of paper roughness.en
Type of ItemPeer-Reviewed Journal Publicationen
Type of ItemΔημοσίευση σε Περιοδικό με Κριτέςel
Licensehttp://creativecommons.org/licenses/by/4.0/en
Date of Item2015-09-25-
Date of Publication2003-
Bibliographic CitationD.T. Hristopulos, "Permissibility of fractal exponents and models of band-limited two-point functions for fGn and fBm random fields, Stoch. Envir. Res. and Risk Ass.,vol.17 ,no.3, pp. 191-216 ,2003.doi:10.1007/s00477-003-0126-8en

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