Fast generation of isotropic Gaussian random fields on the sphere
Journal article, 2018

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

isotropic random fields

Gaussian Markov random fields

fast Fourier transform

Gaussian random fields

efficient simulation


Peter E. Creasey

University of California at Riverside

Annika Lang

University of Gothenburg

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Monte Carlo Methods and Applications

0929-9629 (ISSN) 15693961 (eISSN)

Vol. 24 1 1-11

Subject Categories

Probability Theory and Statistics

Signal Processing

Other Electrical Engineering, Electronic Engineering, Information Engineering



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