An improved spectral turning-bands algorithm for simulating stationary vector Gaussian random fields

• Published in: Stochastic environmental research and risk assessment Vol. 30; no. 7; pp. 1863 - 1873
• Main Authors: Emery, Xavier, Arroyo, Daisy, Porcu, Emilio
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2016; Springer Nature B.V
• Subjects: Algorithms; Aquatic Pollution; Chemistry and Earth Sciences; Computation; Computational Intelligence; Computer Science; Computer simulation; Earth and Environmental Science; Earth Sciences; Environment; Fields (mathematics); Math. Appl. in Environmental Science; Mathematical analysis; Mathematical models; Normal distribution; Original Paper; Physics; Probability Theory and Stochastic Processes; Random variables; Spectra; Statistics for Engineering; Stochastic processes; Variance analysis; Vector space; Waste Water Technology; Water Management; Water Pollution Control; Matérn covariance; Compactly supported covariance; Spectral density; Matrix-valued covariance functions; Importance sampling
• ISSN: 1436-3240; 1436-3259
• DOI: 10.1007/s00477-015-1151-0

We propose a spectral turning-bands approach for the simulation of second-order stationary vector Gaussian random fields. The approach improves existing spectral methods through coupling with importance sampling techniques. A notable insight is that one can simulate any vector random field whose direct and cross-covariance functions are continuous and absolutely integrable, provided that one knows the analytical expression of their spectral densities, without the need for these spectral densities to have a bounded support. The simulation algorithm is computationally faster than circulant-embedding techniques, lends itself to parallel computing and has a low memory storage requirement. Numerical examples with varied spatial correlation structures are presented to demonstrate the accuracy and versatility of the proposal.