Abstract
The sequential algorithm is widely used to simulate Gaussian random fields. However, a rigorous application of this algorithm is impractical and some simplifications are required, in particular a moving neighborhood has to be defined. To examine the effect of such restriction on the quality of the realizations, a reference case is presented and several parameters are reviewed, mainly the histogram, variogram, indicator variograms, as well as the ergodic fluctuations in the first and second-order statistics. The study concludes that, even in a favorable case where the simulated domain is large with respect to the range of the model, the realizations may poorly reproduce the second-order statistics and be inconsistent with the stationarity and ergodicity assumptions. Practical tips such as the ‘multiple-grid strategy’ do not overcome these impediments. Finally, extending the original algorithm by using an ordinary kriging should be avoided, unless an intrinsic random function model is sought after.
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The author would like to acknowledge the reviewers for their helpful comments and the sponsoring by Codelco-Chile for supporting this research.
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Emery, X. Testing the correctness of the sequential algorithm for simulating Gaussian random fields. Stochastic Environmental Research and Risk Assessment 18, 401–413 (2004). https://doi.org/10.1007/s00477-004-0211-7
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DOI: https://doi.org/10.1007/s00477-004-0211-7