Non-stationary covariance function modelling in 2D least-squares collocation |
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| Authors: | N Darbeheshti W E Featherstone |
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| Institution: | (1) Western Australian Centre for Geodesy, The Institute for Geoscience Research, Curtin University of Technology, GPO Box U1987, Perth, 6845, Australia |
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| Abstract: | 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. |
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| Keywords: | Least squares collocation (LSC) Non-stationary covariance function modelling Elliptical kernel convolution Gravity field interpolation Darling fault Australia |
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