Simulating isotropic vector-valued Gaussian random fields on the sphere through finite harmonics approximations

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 F , spectral Matérn and negative binomial classes of covariance functions on the two-dimensional sphere.