Journal of Geodesy

, Volume 83, Issue 6, pp 495–508

Non-stationary covariance function modelling in 2D least-squares collocation


DOI: 10.1007/s00190-008-0267-0

Cite this article as:
Darbeheshti, N. & Featherstone, W.E. J Geod (2009) 83: 495. doi:10.1007/s00190-008-0267-0


Standard least-squares collocation (LSC) assumes 2D stationarity and 3D isotropy, and relies on a covariance function to account for spatial dependence in the observed data. However, the assumption that the spatial dependence is constant throughout the region of interest may sometimes be violated. Assuming a stationary covariance structure can result in over-smoothing of, e.g., the gravity field in mountains and under-smoothing in great plains. We introduce the kernel convolution method from spatial statistics for non-stationary covariance structures, and demonstrate its advantage for dealing with non-stationarity in geodetic data. We then compared stationary and non- stationary covariance functions in 2D LSC to the empirical example of gravity anomaly interpolation near the Darling Fault, Western Australia, where the field is anisotropic and non-stationary. The results with non-stationary covariance functions are better than standard LSC in terms of formal errors and cross-validation against data not used in the interpolation, demonstrating that the use of non-stationary covariance functions can improve upon standard (stationary) LSC.


Least squares collocation (LSC) Non-stationary covariance function modelling Elliptical kernel convolution Gravity field interpolation Darling fault, Australia 

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Western Australian Centre for Geodesy, The Institute for Geoscience ResearchCurtin University of TechnologyPerthAustralia

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