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

This article presents a variant of the spectral turning bands method that allows fast and accurate simulation of intrinsic random fields with power, spline, or logarithmic generalized covariances. The method is applicable in any workspace dimension and is not restricted in the number and configuration of the locations where the random field is simulated; in particular, it does not require these locations to be regularly spaced. On the basis of the central limit and Berry–Esséen theorems, an upper bound is derived for the Kolmogorov distance between the distributions of generalized increments of the simulated random fields and the normal distribution.