Generating random fields with a truncated power-law variogram: A comparison of several numerical methods

In this study we describe and compare four numerical methods for the generation of random fields with a truncated power-law variogram; the Fourier method, the Randomization method, the Hybrid method as well as the Fourier-Wavelet method. We evaluate these methods with respect to their ability to represent the variogram function over a number of spatial scales as well as the Gaussianity of the generated fields. We furthermore compare these methods with respect to computational costs and investigate structural features.Results show that the Randomization method performs well if only a few number of spatial scales (4-6 orders of magnitude) need to be represented. Due to its simpler implementation it can be preferred over the Fourier-Wavelet method. For a larger interval of spatial scales (9-12 orders of magnitude) however, the Randomization method fails to represent the variogram. Under such circumstances the Hybrid method or the Fourier-Wavelet method should be used.The Matlab code, used for the simulations can be accessed on our institution website at http://www.ufz.de/index.php?en=32179. We investigate the generation of random fields with a truncated power-law variogram.Several methods are compared with respect to different criteria.The variogram function is reproduced over several spatial scales by the Hybrid method and the Fourier-Wavelet method.The reproduction of the variogram function strongly depends on its heavy tailing.The scale-invariance for structural properties in the fractal regime is achieved best by the Hybrid method.

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