A review of non-stationary spatial methods for geodetic least-squares collocation

Darbeheshti, Neda; Featherstone, Will

doi:10.1080/14498596.2010.521971

Cited by 8 publications

(1 citation statement)

References 47 publications

(49 reference statements)

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“…The second method is Least Squares Collocation (LSC). The standard LSC was originally derived for stationary processes and, later, extended to weakly stationary processes (Darbeheshti and Featherstone 2010). The quality of an LSC solution depends on the correctness of the covariance function.…”

Section: Overview Of Downward Continuation Methodsmentioning

confidence: 99%

Characterization and stabilization of the downward continuation problem for airborne gravity data

Huang

Klees

et al. 2022

J Geod

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In this study, we compare six commonly used methods for the downward continuation of airborne gravity data. We consider exact and noisy simulated data on grids and along flight trajectories and real data from the GRAV-D airborne campaign. We use simulated and real surface gravity data for validation. The methods comprise spherical harmonic analysis, least-squares collocation, residual least-squares collocation, least-squares radial basis functions, the inverse Poisson method and Moritz's analytical downward continuation method. We show that all the methods perform similar in terms of surface gravity values. For real data, the downward continued airborne gravity values are used to compute a geoid model using a Stokes-integral-based approach. The quality of the computed geoid model is validated using high-quality GSVS17 GPS-levelling data. We show that the geoid model quality is similar for all the methods. However, the least-squares collocation approach appears to be more flexible and easier to use than the other methods provided that the optimal covariance function is found. We recommend it for the downward continuation of GRAV-D data, and other methods for second check.

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Section: Overview Of Downward Continuation Methodsmentioning

confidence: 99%

Characterization and stabilization of the downward continuation problem for airborne gravity data

Huang

Klees

et al. 2022

J Geod

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On the computation of reliable formal uncertainties in the densification of GPS-levelling networks by least-squares collocation

Mysen

2014

J Geod

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HV-LSC-ex$$^2$$: velocity field interpolation using extended least-squares collocation

Steffen

Legrand

Ågren

et al. 2022

J Geod

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Least-squares collocation (LSC) is a widely used method applied in physical geodesy to separate observations into a signal and noise part but has received only little attention when interpolating velocity fields. The advantage of the LSC is the possibility to filter and interpolate as well as extrapolate the observations. Here, we will present several extensions to the traditional LSC technique, which allows the combined interpolation of both horizontal velocity components (horizontal velocity (HV)-LSC), the separation of velocity observations on different tectonic plates, and the removal of stationarity by moving variance (the latter as HV-LSC-ex(tended)$$^2$$ 2 ). Furthermore, the covariance analysis, which is required to find necessary input parameters for the LSC, is extended by finding a suitable variance and correlation length using both horizontal velocity components at the same time. The traditional LSC and all extensions are tested on a synthetic dataset to find the signal at known as well as newly defined points, with stations separated on four different plates with distinct plate velocities. The methodologies are evaluated by calculation of a misfit to the input data, and implementation of a leave-one-out cross-validation and a Jackknife resampling. The largest improvement in terms of reduced misfit and stability of the interpolation can be obtained when plate boundaries are considered. In addition, any small-scale changes can be filtered out using the moving-variance approach and a smoother velocity field is obtained. In comparison with interpolation using the Kriging method, the fit is better using the new HV-LSC-ex$$^2$$ 2 technique.

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A review of non-stationary spatial methods for geodetic least-squares collocation

Cited by 8 publications

References 47 publications

Characterization and stabilization of the downward continuation problem for airborne gravity data

Characterization and stabilization of the downward continuation problem for airborne gravity data

On the computation of reliable formal uncertainties in the densification of GPS-levelling networks by least-squares collocation

HV-LSC-ex$$^2$$: velocity field interpolation using extended least-squares collocation

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