Doc: H:\cctwp\ic-sg2.5.doc, Date: 2003-12-05.


Terms of reference and  program of work for Inter-Comission Study Group IC-SG2.5.



Aliasing in gravity field modelling. C.C.Tscherning, President.



Terms of reference.


A gravity field observable contain information about all coefficients of its associated spherical harmonic series and of other signals of time-varying character. This makes numerical gravity field procedures prone to aliasing. The effect is most clearly seen when estimating spherical harmonic coefficients, but should also be present when regional models are constructed using Fourier series.

In a first phase, only the effects related to the static gravity field will be investigated. If possible, de-aliasing and time-varying effects will be studied in a second phase.


The joint working group will initially through a series of controlled numerical experiments study the effect of alising. Simplified as well as realistic global or regional datasets will be generated using coefficients from a spherical harmonic expansion from  degree N, 2*N, 3*N etc. to a maximal degree, e.g. 1800.


Program of work.


Phase I: The static gravity field.


(a) Creation of test datasets, including re-use of the positions and attitude angles available from the SC7 datasets for CHAMP, GRACE and GOCE. The generated data will include height anomalies, gravity anomalies or disturbances, gravity gradients or potential differences.

(b) Creation of datasets with added correlated or un-correlated noise.

(c) Estimation of spherical harmonic coefficients

(d) Estimation (interpolation or extrapolation) of the generated data or of functionals of the anomalous potential.

(e) Study the magnitude and frequency distribution of the aliasing effects

(f) Study the effect of various regularisation procedures including minimum variance and minimum noise variance methods.


The datasets, or software able to create the datasets will be made available on the internet.


The members of the group will be persons having the capability of

(1)     Creating one or more of the datasets.

(2)     Carrying out global or regional gravity field modelling.

(3)     contributing  with theoretical analysis of the fundamental aliasing problem or of the results of the numerical experiments.


If phase I is succesfully completed:


Phase II:


(g) Study of de-aliasing procedures for static gravity field determination: removal of high-frequency information, such as topographic effects or filtering.

(h) Create synthetic data-sets which include time-varying effets (atmosphere, ocean, tides)

(i) Study the effect of combined gravity field modelling and the determination of (contingently time dependent) parameters.

(j) Study the effect of mixing data-types with different spectral content such as gravity and altimetry.




F.Sansō, Politecnico di Milano, e-mail:

J.Bouman, SRON,  e-mail:

Annette Eicker, e-mail:

W.Freeden, U. Kaiserslautern, e-mail:

Shin-Chan Han, OSU, e-mail:

Pieter Visser, TUDelft, e-mail:

Roland Klees, TUDelft, e-mail:

Michael Sideris, e-mail:

Nico Sneeuw, U-Calgary, e-mail:

C.C.Tscherning, UCPH, e-mail: (President)



Corresponding members:

Rene Forsberg, KMS, e-mail:

Jürgen Mueller, e-mail:





Last update 2003-12-05