Abstract
The turning bands method (TBM) generates realizations of isotropic Gaussian random fields by summing contributions from line processes. We consider two-dimensional simulations and study the correlation bias attributable to the use of only a finite number L of lines. Our analytical and numerical results confirm that the maximal bias is of order 1/L, and that L = 64 lines suffice for excellent covariance reproduction. The notorious banding observed in simulations with an insufficient number of lines is a related but different phenomenon and depends strongly on the choice of the line simulation technique. Clear-cut recommendations for the number of lines necessary to avoid the effect can only be based on practical experience with the specific code at hand.
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Gneiting, T. The Correlation Bias for Two-Dimensional Simulations by Turning Bands. Mathematical Geology 31, 195–211 (1999). https://doi.org/10.1023/A:1007561801981
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DOI: https://doi.org/10.1023/A:1007561801981