Fast generation of isotropic Gaussian random fields on the sphere

Abstract

The efficient simulation of isotropic Gaussian random fields on the unit sphere is a task encountered frequently in numerical applications. A fast algorithm based on Markov properties and fast Fourier Transforms in 1d is presented that generates samples on an n x n grid in O(n^2 log n). Furthermore, an efficient method to set up the necessary conditional covariance matrices is derived and simulations demonstrate the performance of the algorithm. An open source implementation of the code has been made available at https://github.com/pec27/smerfs .

Corrected link to software in arXiv's online abstract, added journal reference

Cited by in corpus (2)

• Surface finite element approximation of spherical Whittle--Matérn Gaussian random fields
• Galerkin--Chebyshev approximation of Gaussian random fields on compact Riemannian manifolds