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JSG 0.13: 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 description of the Earth's gravitational field and its temporal variations belongs to fundamental pillars of modern geodesy. The accurate knowledge of the global gravitational field is important in many applications including precise positioning, metrology, geophysics, geodynamics, oceanography, hydrology, cryospheric and other geosciences. Various observation techniques for collecting gravitational data have been invented based on terrestrial, marine, airborne and more recently, satellite sensors. On the other hand, different parametrization methods of the gravitational field were established in geodesy, however, with many unobservable parameters. For this reason, the geodetic science has traditionally been formulating various gravitational parameter transformations, including those based on solving boundary/initial value problems of potential theory, through Fredholm's integral equations.

Traditionally, Stokes’s, Vening-Meinesz’s and Hotine’s integrals have been of interest in geodesy as they accommodated geodetic applications. In recent history, new geodetic integral transformations were formulated. This effort was mainly initiated by new gravitational observables that became gradually available to geodesists with the advent of precise GNSS (Global Navigation Satellite Systems) positioning, satellite altimetry and aerial gravimetry/gradiometry. The family of integral transformations has enormously been extended with satellite-to-satellite tracking and satellite gradiometric data available from recent gravity-dedicated satellite missions.

Besides numerous efforts in developing integral equations to cover new observables in geodesy, many aspects of integral equations remain challenging. This study group aims for systematic treatment of integral transformation in geodesy, as many formulations have been performed by making use of various approaches. Many solutions are based on spherical approximation that cannot be justified for globally distributed satellite data and with respect to requirements of various data users requiring gravitational data to be distributed the reference ellipsoid or at constant geodetic altitude. On the other hand, the integral equations in spherical approximation possess symmetric properties that allow for studying their spatial and spectral properties; they also motivate for adopting a generalized notation. New numerically efficient, stable and accurate methods for upward/downward continuation, comparison, validation, transformation, combination and/or for interpretation of gravitational data are also of high interest with increasing availability of large amounts of new 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)