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

Original language | British English |
---|---|

Pages (from-to) | 1659-1667 |

Number of pages | 9 |

Journal | Stochastic Environmental Research and Risk Assessment |

Volume | 33 |

Issue number | 8-9 |

DOIs | |

State | Published - 1 Sep 2019 |

## Keywords

- Addition theorem
- Bivariate spectral Matérn covariance
- Multivariate Schoenberg sequence
- Sphere
- Spherical harmonics