JSG T.26

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JSG T.26: Integral equations of potential theory for continuation and transformation of classical and new gravitational observables

Chair:Michal Šprlák (Czech Republic)
Affiliation:Commission 2 and GGOS


The geopotential height datum is realized by a gravimetric geoid/quasi-geoid model. The geoid/quasi-geoid model can now be determined with the accuracy of a few centimetres in a number of regions around the world; it has been adopted in some as a height datum to replace spirit-levelling networks, e.g., in Canada and New Zealand. A great challenge is the 1-2 cm accuracy anywhere to be compatible with the accuracy of ellipsoidal heights measured by the GNSS technology. This requires an adequate theory and its numerical realization, to be of the sub-centimetre accuracy, and the availability of commensurate gravity data and digital elevation models (DEMs).

Geoid/quasi-geoid modelling involves the combination of satellite, airborne and surface gravity data through the remove-compute-restore method, employing various modelling techniques such as the Stokes integration, least-squares collocation, spherical radial base functions or spherical harmonics. Satellite gravity data from recent gravity missions (GRACE and GOCE) enable to model the geoid components with the accuracy of 1-2 cm at the spatial resolution of 100 km. Airborne gravity data are covering more regions with a variety of accuracies and spatial resolutions such as the US GRAV-D project. They often overlap with surface gravity data which are still essential in determining the high-resolution geoid model. In the meantime, DEMs required for the gravity reduction have achieved higher spatial resolutions with a global coverage. In order to understand how accurately the geoid model can be determined, the 1 cm geoid experiment was carried out in a test region in Colorado, USA by more than ten international teams. The state-of-the-art airborne data was provided for this experiment by US NGS. The test results reveal that differences between geoid models by these teams are at the level of 2-4 cm in terms of the standard deviation with a range of decimetres. Reducing these differences is necessary for realization of geopotential height datums and the International Height Reference System (IHRS). This will require a thorough examination and assessment of both methods and data.


  • To consider different types of gravitational data, i.e., terrestrial, aerial and satellite, available today and to formulate their mathematical relation to the gravitational potential.
  • To study mathematical properties of differential operators in spherical and Jacobi ellipsoidal coordinates, which relate various functionals of the gravitational potential.
  • To complete the family of integral equations relating various types of current and foreseen gravitational data and to derive corresponding spherical and ellipsoidal Green’s functions.
  • To study accurate and numerically stable methods for upward/downward continuation of gravitational field parameters.
  • To investigate optimal combination techniques of heterogeneous gravitational field observables for gravitational field modelling at all scales.
  • To investigate conditionality as well as spatial and spectral properties of linear operators based on discretized integral equations.
  • To classify integral transformations and to propose suitable generalized notation for a variety of classical and new integral equations in geodesy.

Program of Activities

  • Presenting research results at major international geodetic and geophysical conferences, meetings and workshops.
  • Organizing a session at the forthcoming Hotine-Marussi Symposium 2017.
  • Cooperating with related IAG Commissions and GGOS.
  • Monitoring activities of JGS members as well as other scientists related to the scope of JGS activities.
  • Providing bibliographic list of relevant publications from different disciplines in the area of JSG interest.


Michal Šprlák (Czech Republic), chair
Alireza Ardalan (Iran)
Mehdi Eshagh (Sweden)
Will Featherstone (Australia)
Ismael Foroughi (Canada)
Petr Holota (Czech Republic)
Juraj Janák (Slovakia)
Otakar Nesvadba (Czech Republic)
Pavel Novák (Czech Republic)
Martin Pitoňák (Czech Republic)
Robert Tenzer (China)
Guyla Tóth (Hungary)