Fast generation of isotropic Gaussian random fields on the sphere

TL;DR

This paper introduces a fast algorithm for generating isotropic Gaussian random fields on the sphere using Markov properties and FFT, enabling efficient simulations for numerical applications.

Contribution

It presents a novel, computationally efficient method for simulating Gaussian fields on the sphere, including setup of covariance matrices and implementation details.

Findings

Algorithm runs in O(n^2 log n) time for n x n grids.

Simulations confirm the efficiency and accuracy of the method.

Open source code is available for practical use.

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 .