scholarly journals Multi-processing least squares collocation: Applications to gravity field analysis

2013 ◽  
Vol 3 (3) ◽  
Author(s):  
E. Kaas ◽  
B. Sørensen ◽  
C. C. Tscherning ◽  
M. Veicherts
Keyword(s):  
Least Squares ◽  
Gravity Field ◽  
Field Analysis ◽  
Least Squares Collocation

scholarly journals Investigating the optimal integration of airborne, ship-borne, satellite and terrestrial gravity data for use in geoid determination

2021 ◽  
Author(s):  
◽  
Rachelle Winefield
Keyword(s):  
Least Squares ◽  
Gravity Field ◽  
Integration Method ◽  
Bouguer Anomaly ◽  
Least Squares Collocation ◽  
Integration Methods ◽  
Case Study Area ◽  
Gravity Observation ◽  
Gravity Map

<p>Each gravity observation technique has different parameters and contributes to different pieces of the gravity spectrum. This means that no one gravity dataset is able to model the Earth’s gravity field completely and the best gravity map is one derived from many sources. Therefore, one of the challenges in gravity field modelling is combining multiple types of heterogeneous gravity datasets.  The aim of this study is to determine the optimal method to produce a single gravity map of the Canterbury case study area, for the purposes of use in geoid modelling.  This objective is realised through the identification and application of a four-step integration process: purpose, data, combination and assessment. This includes the evaluation of three integration methods: natural neighbour, ordinary kriging and least squares collocation.  As geoid modelling requires the combination of gravity datasets collected at various altitudes, it is beneficial to be able to combine the dataset using an integration method which operates in a three-dimensional space. Of the three integration methods assessed, least squares collocation is the only integration method which is able to perform this type of reduction.  The resulting product is a Bouguer anomaly map of the Canterbury case study area, which combines satellite altimetry, terrestrial, ship-borne, airborne, and satellite gravimetry using least squares collocation.</p>

scholarly journals Investigating the optimal integration of airborne, ship-borne, satellite and terrestrial gravity data for use in geoid determination

2021 ◽  
Author(s):  
◽  
Rachelle Winefield
Keyword(s):  
Least Squares ◽  
Gravity Field ◽  
Integration Method ◽  
Bouguer Anomaly ◽  
Least Squares Collocation ◽  
Integration Methods ◽  
Case Study Area ◽  
Gravity Observation ◽  
Gravity Map

<p>Each gravity observation technique has different parameters and contributes to different pieces of the gravity spectrum. This means that no one gravity dataset is able to model the Earth’s gravity field completely and the best gravity map is one derived from many sources. Therefore, one of the challenges in gravity field modelling is combining multiple types of heterogeneous gravity datasets.  The aim of this study is to determine the optimal method to produce a single gravity map of the Canterbury case study area, for the purposes of use in geoid modelling.  This objective is realised through the identification and application of a four-step integration process: purpose, data, combination and assessment. This includes the evaluation of three integration methods: natural neighbour, ordinary kriging and least squares collocation.  As geoid modelling requires the combination of gravity datasets collected at various altitudes, it is beneficial to be able to combine the dataset using an integration method which operates in a three-dimensional space. Of the three integration methods assessed, least squares collocation is the only integration method which is able to perform this type of reduction.  The resulting product is a Bouguer anomaly map of the Canterbury case study area, which combines satellite altimetry, terrestrial, ship-borne, airborne, and satellite gravimetry using least squares collocation.</p>

scholarly journals The least-squares collocation method in the mechanics of deformable solids

2021 ◽  
Vol 1715 ◽  
pp. 012029
Author(s):  
Sergey Golushko ◽  
Vasily Shapeev ◽  
Vasily Belyaev ◽  
Luka Bryndin ◽  
Artem Boltaev ◽  
...  
Keyword(s):  
Least Squares ◽  
Collocation Method ◽  
Least Squares Collocation ◽  
Deformable Solids ◽  
Mechanics Of Deformable Solids

scholarly journals On the uncertainty of height anomaly differences predicted by least-squares collocation

2020 ◽  
Vol 10 (1) ◽  
pp. 53-61
Author(s):  
E. Mysen
Keyword(s):  
Least Squares ◽  
Spatial Separation ◽  
Height Anomaly ◽  
Surface Model ◽  
Least Squares Collocation ◽  
Normal Heights ◽  
Gravimetric Quasigeoid ◽  
The Difference ◽  
Grid Interpolation ◽  
Gps Observations

AbstractA network of pointwise available height anomalies, derived from levelling and GPS observations, can be densified by adjusting a gravimetric quasigeoid using least-squares collocation. The resulting type of Corrector Surface Model (CSM) is applied by Norwegian surveyors to convert ellipsoidal heights to normal heights expressed in the official height system NN2000. In this work, the uncertainty related to the use of a CSM to predict differences in height anomaly was sought. As previously, the application of variograms to determine the local statistical properties of the adopted collocation model led to predictions that were consistent with their computed uncertainties. For the purpose of predicting height anomaly differences, the effect of collocation was seen to be moderate in general for the small spatial separations considered (< 10 km). However, the relative impact of collocation could be appreciable, and increasing with distance, near the network. At last, it was argued that conservative uncertainties of height anomaly differences may be obtained by rescaling output of a grid interpolation by \sqrt \Delta, where Δ is the spatial separation of the two locations for which the difference is sought.

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