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Relationships between correlation lengths and integral scales for covariance models with more than two parameters

M. Zukovic

Πλήρης Εγγραφή


URI: http://purl.tuc.gr/dl/dias/857114D5-BE48-4FF5-AE02-64898F5CC3E8
Έτος 2011
Τύπος Δημοσίευση σε Περιοδικό με Κριτές
Άδεια Χρήσης
Λεπτομέρειες
Βιβλιογραφική Αναφορά D. T. Hristopulos,M. Zukovic ," Relationships between correlation lengths and integral scales for covariance models with more than two parameters ", Stoch. Env. Res. and Risk As.,vol. 25, no. 1 , pp. 11-19, 2011.doi:10.1007/s00477-010-0407-y https://doi.org/10.1007/s00477-010-0407-y
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Περίληψη

In geostatistical applications, the terms correlation length and range are often used interchangeably and refer to a characteristic covariance length ξ that normalizes the lag distance in the variogram or the covariance model. We present equations that strictly define the correlation length (r c ) and integral range (ℓ c ). We derive analytical expressions for r c and ℓ c of the Whittle–Matérn, fluctuation gradient curvature and rational quadratic covariances. For these covariances, we show that the correlation length and integral range for a given model are not fully determined by ξ. We define non-trivial covariance functions, and we formulate an ergodicity index based on ℓ c . We propose using the ergodicity index to compare coarse-grained measures corresponding to non-trivial covariance functions with different parameters. Finally, we discuss potential applications of the proposed covariance models in stochastic subsurface hydrology.

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