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The geoid for the Baltic countries determined by the least squares modification of Stokes´formula
KTH, Superseded Departments, Infrastructure.
2004 (English)Doctoral thesis, comprehensive summary (Other scientific)
Abstract [en]

Precise knowledge of the geoid contributes to the studies ofthe Earth’s interior, the long-term geophysical processesand to oceanography. An accurate regional geoid model, inparticular, enables the user in many cases to replace thetraditional height determination techniques by faster and morecost-effective GPS-levelling.

In regional gravimetric geoid determination, it has becomecustomary to utilize the modified Stokes formula, whichcombines local terrestrial data with a global geopotentialmodel. The Dissertation is devoted to the determination of ahighresolution geoid model for the three Baltic countries–Estonia, Latvia and Lithuania. Six differentdeterministic and stochastic modification methods are tested.These are: Wong and Gore (1969), Vincent and Marsh (1974),Vaníèek and Kleusberg (1987) and the biased, unbiasedand optimum least squares modifications by Sjöberg (1984b,1991, 2003d). Three former methods employ originally theresidual anomaly in Stokes’integral. For the sake ofcomparison these methods are expressed such that the fullgravity anomaly is utilised in all the six methods.

The contribution of different error sources for geoidmodelling is studied by means of the expected global meansquare error (MSE). The least squares methods attempt tominimise all relevant error sources in geoid modelling byspecially determined modification parameters. Part of thepresent study contributes to some important computationalaspects of the least squares parameters sn.

This study employs the new geopotential model GGM01s, whichis compiled from data of the GRACE twin-satellites. Three sets(one from each country) of GPSlevelling points were used for anindependent evaluation of computed geoid models. Generally, thepost-fit residuals from the least squares modifications areslightly smaller (up to 1 cm) than the respective values ofdeterministic methods. This could indicate that the efforts putinto minimization of the global MSE have been advantageous.

The geoid model computed by the unbiased LS modificationprovides the“best”post-fit statistics and it isthus preferred as the final representation of the joint Balticgeoid. The modification parameters of this model are calculatedfrom the following initial conditions: (1) upper limit of theGGM01s and the modification degree of Stokes’function areboth set to 67, (2) terrestrial anomaly error variance andcorrelation length are set to 1 mGal2 and 0.1°,respectively, (3) integration cap size is 2°. Thisapproximate geoid model is supplemented by separately computedadditive corrections (the combined topographic and atmosphericeffects and ellipsoidal correction), which completes the geoidmodelling procedures. The new geoid model for the Balticcountries is named BALTgeoid-04. The RMS of the GPS-levellingpost-fit residuals are as follows: 5.3 cm for the joint Balticgeoid model and 2.8, 5.6 and 4.2 cm for Estonia, Latvia andLithuania, respectively. This fit indicates the suitability ofthe new geoid model for many practical applications.

Key words: geoid:Stokes’formula, deterministicand stochastic modifications, least squares, additivecorrections, GRACE, Baltic.

Place, publisher, year, edition, pages
Stockholm: Infrastruktur , 2004. , viii, 82 p.
Trita-INFRA, ISSN 1651-0216 ; 04:013
Keyword [en]
geoid, Stokes
URN: urn:nbn:se:kth:diva-3744ISBN: 91-7323-080-4OAI: diva2:9592
Public defence
2004-05-14, 00:00
Available from: 2004-05-17 Created: 2004-05-17 Last updated: 2012-03-20

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