A spectral approach to simulating intrinsic random fields with power and spline generalized covariances

Abstract : This article presents an adaptation of the spectral turning bands method that allows fast and accurate simulations of isotropic self-similar intrinsic random fields, for which the generalized covariance is a power, logarithmic or spline function of the lag distance. The proposed method is applicable in any space dimension and has no restriction on the number and on the configuration of the locations where the random field has to be simulated; in particular it does not require these locations to be regularly spaced. Additionally, clues are given on how to quantify the closeness between the distribution of the generalized increments of the simulated random fields and the Gaussian distribution.