High degree spherical harmonic expansion of gravity data

1981 ◽  
Vol 55 (1) ◽  
pp. 86-93 ◽  
Author(s):  
Dezsö Nagy
Keyword(s):  
Spherical Harmonic ◽  
Gravity Data ◽  
Spherical Harmonic Expansion ◽  
High Degree

scholarly journals A New Method to Build Covariance of Gravity Anomaly Along with its Simulation Experience

2015 ◽  
Vol 9 (1) ◽  
pp. 913-918
Author(s):  
Jianbo Wang ◽  
jinyun Guo ◽  
Youge Xie
Keyword(s):  
Least Squares ◽  
Gravity Anomaly ◽  
Covariance Matrix ◽  
High Precision ◽  
Spherical Harmonic ◽  
Simulation Experiment ◽  
Gravity Data ◽  
Spherical Harmonic Expansion ◽  
New Method

In this paper , we proposed a new method to build covariance matrix of gravity anomaly based on the spherical harmonic expansion of gravity anomaly , and then combined with the measured gravity data we can realize the fast and high precision interpolation and extrapolation of gravity anomaly according to the principle of least squares and the remove-compute-restore technique. The feasibility of this method is proved through the simulation experiment.

scholarly journals Unbiased least-squares modification of Stokes’ formula

2020 ◽  
Vol 94 (9) ◽  
Author(s):  
Lars E. Sjöberg
Keyword(s):  
Gravity Data ◽  
Harmonic Series ◽  
Local Error ◽  
Data Sets ◽  
Spherical Cap ◽  
Local Variance ◽  
Error Covariance ◽  
Stokes Formula ◽  
Gravity Signal ◽  
High Degree

Abstract As the KTH method for geoid determination by combining Stokes integration of gravity data in a spherical cap around the computation point and a series of spherical harmonics suffers from a bias due to truncation of the data sets, this method is based on minimizing the global mean square error (MSE) of the estimator. However, if the harmonic series is increased to a sufficiently high degree, the truncation error can be considered as negligible, and the optimization based on the local variance of the geoid estimator makes fair sense. Such unbiased types of estimators, derived in this article, have the advantage to the MSE solutions not to rely on the imperfectly known gravity signal degree variances, but only the local error covariance matrices of the observables come to play. Obviously, the geoid solution defined by the local least variance is generally superior to the solution based on the global MSE. It is also shown, at least theoretically, that the unbiased geoid solutions based on the KTH method and remove–compute–restore technique with modification of Stokes formula are the same.

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