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Mathematical Geosciences

, Volume 51, Issue 8, pp 999–1020 | Cite as

Spectral Simulation of Isotropic Gaussian Random Fields on a Sphere

  • Christian LantuéjoulEmail author
  • Xavier Freulon
  • Didier Renard
Article

Abstract

A spectral algorithm is proposed to simulate an isotropic Gaussian random field on a sphere equipped with a geodesic metric. This algorithm supposes that the angular power spectrum of the covariance function is explicitly known. Direct analytic calculations are performed for exponential and linear covariance functions. In addition, three families of covariance functions are presented where the calculation of the angular power spectrum is simplified (shot-noise random fields, Yadrenko covariance functions and solutions of certain stochastic partial differential equations). Numerous illustrative examples are given.

Keywords

Spherical harmonics Angular power spectrum Yadrenko covariance functions Shot-noise random fields Chentsov model 

Notes

Acknowledgements

The support of Grant ANR-15-ASTR-0024 is gratefully acknowledged.

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Copyright information

© International Association for Mathematical Geosciences 2019

Authors and Affiliations

  • Christian Lantuéjoul
    • 1
    Email author
  • Xavier Freulon
    • 1
  • Didier Renard
    • 1
  1. 1.MinesParisTechFontainebleauFrance

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