Non-stationary covariance function modelling in 2D least-squares collocation
Standard least-squares collocation (LSC) assumes 2D stationarity and 3D isotropy, and relies on a covariance function to account for spatial dependence in the ob-served data. However, the assumption that the spatial dependence is constant through-out the region of interest may sometimes be violated....
| Main Authors: | , |
|---|---|
| Format: | Journal Article |
| Published: |
Springer - Verlag
2009
|
| Subjects: | |
| Online Access: | http://hdl.handle.net/20.500.11937/42464 |
| _version_ | 1848756426822909952 |
|---|---|
| author | Darbeheshti, Neda Featherstone, Will |
| author_facet | Darbeheshti, Neda Featherstone, Will |
| author_sort | Darbeheshti, Neda |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | Standard least-squares collocation (LSC) assumes 2D stationarity and 3D isotropy, and relies on a covariance function to account for spatial dependence in the ob-served data. However, the assumption that the spatial dependence is constant through-out 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 fordealing 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. |
| first_indexed | 2025-11-14T09:12:01Z |
| format | Journal Article |
| id | curtin-20.500.11937-42464 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T09:12:01Z |
| publishDate | 2009 |
| publisher | Springer - Verlag |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-424642017-09-13T16:05:51Z Non-stationary covariance function modelling in 2D least-squares collocation Darbeheshti, Neda Featherstone, Will gravity field interpolation elliptical kernel convolution non-stationary covariance function Darling Fault Australia modelling Least squares collocation (LSC) Standard least-squares collocation (LSC) assumes 2D stationarity and 3D isotropy, and relies on a covariance function to account for spatial dependence in the ob-served data. However, the assumption that the spatial dependence is constant through-out 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 fordealing 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. 2009 Journal Article http://hdl.handle.net/20.500.11937/42464 10.1007/s00190-008-0267-0 Springer - Verlag fulltext |
| spellingShingle | gravity field interpolation elliptical kernel convolution non-stationary covariance function Darling Fault Australia modelling Least squares collocation (LSC) Darbeheshti, Neda Featherstone, Will Non-stationary covariance function modelling in 2D least-squares collocation |
| title | Non-stationary covariance function modelling in 2D least-squares collocation |
| title_full | Non-stationary covariance function modelling in 2D least-squares collocation |
| title_fullStr | Non-stationary covariance function modelling in 2D least-squares collocation |
| title_full_unstemmed | Non-stationary covariance function modelling in 2D least-squares collocation |
| title_short | Non-stationary covariance function modelling in 2D least-squares collocation |
| title_sort | non-stationary covariance function modelling in 2d least-squares collocation |
| topic | gravity field interpolation elliptical kernel convolution non-stationary covariance function Darling Fault Australia modelling Least squares collocation (LSC) |
| url | http://hdl.handle.net/20.500.11937/42464 |