KTH Geolab


A Free Scientific Software for Precise Geoid Determination Based on the Least-Squares Modification of Stokes' Formula


Why KTH approach?

Many different methods for regional geoid determination have been proposed through the years, each preferring its own set of techniques and philosophy. The Least-Squares Modification of Stokes (LSMS) integration formula is a new alternative, being one of the simplest and also practical approaches. It has been applied successfully in determining several high resolution regional geoid models in different areas. Through the LSMS approach, different heterogeneous data, e.g., gravity anomalies, a high-resolution photogrammetric/SRTM Digital Elevation Model, Global Geopotential Model and GPS/levelling data can be combined in single model in an optimum way by using the least-squares principle. The theoretical and practical aspects of this method are developed mainly by Prof. Lars E. Sjöberg since 1984 to present. The result of comparison clearly shows that the LSMS approach yields significant advantages compared to other models. This method was successfully applied in the determination of several regional geoid models: over Sweden, the Baltic countries, Iran, Zambia and Ethiopia. Notable among these studies are the applications in very rough topographic areas and in several developing countries with only limited gravity anomaly data. In all study cases the LSMS method gives good results due to the well-known potential of the LSM kernel, which matches the errors of the terrestrial gravity data, GGM and the truncation error in an optimum way. From the practical point of view, the use of precise additive correction terms, the LSMS approach is accurate, simple and computationally efficient. Also, the KTH approach can compute a geoid model with reasonable accuracy in countries with limited gravity data in the in the interior of and / or exterior to the computational area.


The KTH-GEOLAB is scientific software for precise geoid determination based on the least-squares modification of Stokes formula. The approach and software have been developed during a period of more then 20 years under the supervision of Prof. Lars Sjöberg at the Division of Geodesy in Royal Institute of Technology (KTH) in Sweden.


The KTH-GEOLAB is a package of computer programs designed to compute a precise regional geoid model according to the least-squares modification of the Stokes formula. It is made available under a license from KTH. The KTH-GEOLAB is not of commercial software, as it has been developed as a public research tool. These authors wish to make it available to other researchers for the purpose of non-commercial research and development, with the aim of continually improving the tool and distributing updates and new versions to software users. Thus, it is recommended that the recipient of the licence arrange for a workshop covering the theory, installation and use of the software package. Potential users can contact Prof. Lars E. Sjöberg to schedule the mandatory workshop and an optional course. The next workshop is planned in September 2010 in Istanbul. Once the workshop has been scheduled, please print, complete and have signed the license agreement by an authorized representative of your institution and send a fax copy and two originals of the signed license agreement to:

Prof. Lars E. Sjöberg
Head of Geodesy Division,
Royal Institute of Technology
Teknikringen 72, SE-100 44, Stockholm, Sweden
Tel: +46 8 790 7330
Fax: +46 8 790 7343

After receiving an original of the license agreement, the software and the accompanying manual will be sent.

References (PhD theses):

Ramin Kiamehr (2006) Precise Gravimetric Geoid Model for Iran Based on GRACE and SRTM Data and the Least-Squares Modification of Stokes' Formula: with Some Geodynamic Interpretations

Jonas Ågren (2004) Regional geoid determination methods for the era of satellite gradiometry

Artu Ellmann (2004) The geoid for the Baltic countries determined by the least squares modification of Stokes' formula

Addisu Hunegnaw (2001) Geoid Determination over Ethiopia with Emphasis on Downward Continuation of Gravity Anomalies

Hossein Nahavandchi (1998) Precise GPS-Gravimetric Geoid determination with Improved Topographic Corrections over Sweden

Peter Nsombo (1996) Geoid Determination over Zambia

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