Abstract
The paper tackles the problem of simulating isotropic vector-valued Gaussian random fields defined over the unit two-dimensional sphere embedded in the three-dimensional Euclidean space. Such random fields are used in different disciplines of the natural sciences to model observations located on the Earth or in the sky, or direction-dependent subsoil properties measured along borehole core samples. The simulation is obtained through a weighted sum of finitely many spherical harmonics with random degrees and orders, which allows accurately reproducing the desired multivariate covariance structure, a construction that can actually be generalized to the simulation of isotropic vector random fields on the d-dimensional sphere. The proposed algorithm is illustrated with the simulation of bivariate random fields whose covariances belong to the \({{{\mathcal{F}}}}\), spectral Matérn and negative binomial classes of covariance functions on the two-dimensional sphere.
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Acknowledgements
The authors are grateful to two anonymous reviewers for their constructive comments and acknowledge the support of grants CONICYT/FONDECYT/REGULAR/No. 1170290 (XE and EP) and CONICYT Project AFB180004 (XE) from the Chilean Commission for Scientific and Technological Research.
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Emery, X., Porcu, E. Simulating isotropic vector-valued Gaussian random fields on the sphere through finite harmonics approximations. Stoch Environ Res Risk Assess 33, 1659–1667 (2019). https://doi.org/10.1007/s00477-019-01717-8
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DOI: https://doi.org/10.1007/s00477-019-01717-8