Least-Squares Collocation can be used to integrate the two data-types, but you have to obtain the error-estimates of both quantities. Using GOCE models it is possible, since the full variance-covariance matrix is available for the potential coefficients, and ESA has in the GUT software a program, which can be used to calculate the error estimates. For the terrestrial data, the error estimates must be available together with the data (which always should be the case). However the best procedure is to use the coefficients of the spherical harmonic model as observations. See e.g. my old publication http://cct.gfy.ku.dk/publ_cct/cct45.pdf . The process is integrated in GRAVSOFT.

Kind regards

Christian

You can also use co kriging (the 2 variables are the terrestrial gravimetry data and the global model). Not easy to do but efficient.

For the gravity field kriging or co-kriging should never be used. The method uses variograms and estimates the error through the nugget effect. But the gravity field is associated with a harmonic function with finite variance, so collocation with covariance functions and error-estimates associated with the individual data is the correct method to use. It also permits the use of coefficients of the spherical harmonic expansion (the global model) to be used as observations.

Variograms of field with a Laplacian potential are well known (analytic equation are avalaible) so kriging and cokriging are good solutions.

Nugget effect is just a way to take in account the error of measurements.

As i know, a lot of research were done using integration of gravimetry data and gravity data from global model, but they mostly use global model gravity values for the gap zone in the region, the least square based algorithms are the well-known method to do that.

Ismael.

The problem with kriging is that the normal equations are nor positive definit, so usual numerically optimal equation solution procedures do not work. But I do not understand why Guillen Antonio insist on promoting Kriging, because for the gravity field the norm of the function is finite, so covariance functions can be estimated without problems, and then Kriging becomes a special case of optimal linear estimation. Please look into Advanced Physical Geodesy by H.Moritz, for the

development of optimal linear prediction in a reproducing kernel Hilbert Space.

Christian

Thanks for your answers. I would like to know more about using gravsoft proposed by Dr. Tscherning

Dear Miguel, GRAVSOFT is available free of charge for scientific or educational purpose. It includes manuals and test data. If you send an e-mail to [email protected] I will inform you how to access the software. Then I will help you setting up a run using the programs. Kind regards

Christian

Dear Professor Tscherning,

I would be pleaded if i can access to Gravsoft and having your help about that, because actually i probably need to use it for my program

I will send email too,

Thank you in advance,

Ismael,

Thanks for all for the very beneficial discussions a bout the integration of gravimetry and geopotential model?.. But I have question, could I know the minimum data necessary to be integrated, I mean how size of the gravmetry data is needed to be compared with geoptential model?

the model has a max resolutiom equal to 180/maximal degree, for egm98 degrer

360 corrrspomd to 0,5 deg. So the gravity anomaly data should at least coversuch

an area, so the mean of the differemces is close to zero if eberything is ok

Christian

Thanks you very much dear Tscherning for you answer..