Report of International Association of Geodesy Section IV
for the period 1995-1999
Petr Holota
Research Institute of Geodesy, Topography and Cartography
250 66 Zdiby 98, Praha-východ, Czech Republic

Section IV has primarily a methodological character. It was given its present title at the 18th General Assembly of the IUGG in Hamburg, 1983. The scope of the Section is not confined to one particular topic in geodesy which would be peculiar to this section only, but rather all topics are shared in one way or another with other IAG sections, with the accent of the research pointing towards the systematic mathematical treatment of geodetic problems. In particular the by-laws of the IAG put emphasis on the following tasks of the Section: general mathematical models for geodesy, statistical and numerical analysis, data processing and management, optimization methods, least squares methods, differential and integral theories of the gravity filed.

The past four years has been a productive period with advances on many fronts. It has certainly seen a strong involvement of Section IV into most of the activities of the IAG. The structure which made it possible for this Section to fulfill its mandate consists of one special commission and five special study groups. Its is as follows:

Special Commission SC1: Mathematical and Physical Foundations of Geodesy

President: E.W. Grafarend (Germany)

SSG 4.168: Inversion of Altimetric Data

Chairman: P. Knudsen (Denmark)

SSG 4.169: Wavelets in Geodesy

Chairman: B. Benciolini (Italy)

SSG 4.170: Integrated Inverse Gravity Modelling

Chairman: L. Ballani (Germany)

SSG 4.171: Dynamic Isostasy

Chairman: L.E. Sjöberg (Sweden)

SSG 4.176: Temporal Variations of the Gravity Field

Chairman: D. Wolf (Germany)

The above structure of the Section is described with all details, terms of references and a full list of members in the Geodesist’s Handbook, pp. 940-948, which is a special issue of the Journal of Geodesy, Vol. 70, Number 12, 1996. In addition the development of the Section IV structure in the period 1979-1995 can be seen from an Appendix of this report.

Within the present structure of the Section Special Commission SC1 followed the standing concern to collect specialists on the mathematical treatment of various geodetic problems and to study those of them that are of a long term character. Special Commission SC1 was established on the basis of the decision taken by the IAG at the 20th General Assembly of the IUGG in Vienna, 1991. In the period 1995-1999 the research programme of the Special Commission was subdivided into specific tasks which were assigned to the following subcommissions of SC1:

Subcommission 1 - Statistics

Chairman: A. Dermanis (Greece)

Subcommission 2 - Numerical and Approximation Methods

Chairman: W. Freeden (Germany)

and its Working Group - Comparison of several techniques for solving geodetic boundary value problems by means of numerical experiments

Chairman: R. Klees (The Netherlands)

Subcommission 3 - Boundary Value Problems

Chairman: E.W. Grafarend (Germany)

Subcommission 4 - Geometry, Relativity, Cartography

Chairman: J. Zund (USA)

Subcommission 5 - Theory of Orbits and Dynamics of Systems

Chairman: R.J. You (Taiwan)

The task of the section president, P. Holota, and the section secretaries, B. Heck (Germany) and C. Jekeli (USA), was to coordinate and facilitate research in Section IV.

In the reported period Section IV and its accent on systematic theoretical and methodological treatment of geodetic problems were clearly visible and well represented at a number of IAG sponsored symposia and schools. For space limitation, we will only highlight the following events:
The International Summer School of Theoretical Geodesy on Boundary Value Problems and the Modelling of the Earth s Gravity Filed in View of the One Centimeter Geoid , Como, 1996, was an important meeting attended not only by young scientists, but also by a broader community of geodesists, mathematicians, geophysiscists and representatives of other branches of related sciences. A number of key lectures and seminars at this summer school was given by members of Section IV.
The International Symposium on Gravity, Geoid, and Marine Geodesy (GraGeoMar96), Tokyo, 1996. Scientific discussions at this meeting put an emphasis on practical as well as theoretical problems. In Tokyo there were 15 scientific sessions and 7 of them were convened by colleagues intimately associated with Section IV as its active members or as its officers.
Scientific Assembly of the International Association of Geodesy (IAG97), Rio de Janeiro, 1997. The broad range of the programme of this meeting gave a considerable space to discussions of special interest to Section IV. In Rio the Section held also its Business Meeting and within the official programme of the scientific assembly the session The Geoid - Theory and Methods was entrusted to the Section IV care.
Second Continental Workshop on the Geoid in Europe, Budapest, 1998, organized by the IAG Sub-commission for the Geoid in Europe in co-operation with the Technical University of Budapest. Here again Section IV took a very active part and was also a sponsor of this workshop.
IAG School on Wavelets in the Geosciences. Delft, 1998.
From the above it is also clear that in the reported period the activities of Section IV followed the principle of equal geographical distribution. Moreover, in a sense through its contributions the Section was an ambassador participating in the work of other scientific bodies of IUGG as well as in the work of EGS (European Geophysical Society), ECGS (European Center for Geodynamnics and Seismology), ESA and others. In this way it helped to make contacts with other scientific organizations real. Members and officers of Section IV were also entrusted to act as conveners of a number of EGS Symposia. Let us mention at least:
Joint Inversion as a General Problem in Earth Sciences. 22nd General Assembly of the EGS, Vienna, 1997;
Modelling Techniques and Joint Inversion in Earth Sciences,
Ocean Modelling from Altimetry and Remote Sensing
both held on the occasion of the XXII General Assembly of the EGS, Nice, 1998, and three symposia convened at the 24th General Assembly of the EGS in The Hague, 1999:
Topography and Bathymetry in Geodetic and Geophysical,
Potential Fileds in Geodesy, Geophysics and Geology,
Mathematical Modelling and Adjustment Theory.
All the merits of the success of actions of Section IV go to its special commission, sub-commissions and its SSG s which were active and productive. Limiting now ourselves to those only that can be considered specific of Section IV, we for sure have to recall as a minimum the success of the:
Meeting of SSG 4.170 (Integrated Inverse Gravity Modelling), Walferdange, Luxembourg, 1996;
Meetings of SSG 4.176 (Temporal Variations of the Gravity Filed), Walferdange, Luxembourg, 1997 and Potsdam, 1998;
International Summer School Data Analysis and the Statistical Foundations of Geomatics , Chania, Crete, 1998 (organized by IAG SC 1);
IV Hotine-Marussi Symposium on Mathematical Geodesy, Trento, 1998.
Traditionally, Hotine-Marussi symposia are events which offer an exceptional opportunity to discuss research done within Section IV. In Trento the discussion concentrated upon boundary value problems, gravity field modelling, orbital dynamics, differential geometry in geodesy, relativity, upon the theory of cartographic projections, estimation theory, approximation theory and numerical methods, inverse problems and also problems in geodynamics with emphasis on geodetic aspects. In addition in Trento Section IV had also a broad and thorough discussion concerning its work and future plans, especially those for the period after the 22nd General Assembly of the IUGG. Special thanks go to the organizers of the IV Hotine-Marussi symposium who made it possible to devote one of the programme blocks of the symposium to the Business Meeting of Section IV.

The profile of Section IV research activities and the nature of results achieved was completed by a very successful Symposium G4 General Theory and Methodology organized by Section IV within the programme of the 22nd General Assembly of the IUGG, Birmingham, 1999. First part of this symposium was organized as a Business Meeting of the Section, were the president of the Section, the president of SC1 and the Chairmen of individual SSG’s presented their report.

It was clear from this symposium that functional-analytic aspects were strongly pronounced in the majority of mathematical studies carried out in the Section. This concerns nor only the use of methods of mathematical analysis or the use of the theory of boundary value problems, but also the use of numerical methods and a great variety of other applications. The results achieved speak about the mathematical properties of the geodetic problems discussed in a way which is more transparent, more complete and more general. We believe that these are the properties that will do geodesy good service in its future tasks.

In Birmingham in addition some of the contributions resulting from the research carried out in Section IV were presented within inter-association symposia. Section IV was also represented in the team of conveners of an inter-association symposium on Solid-Earth Geophysical Data Fusion and Analysis Method. Moreover, in Birmingham representative achievements resulting from the research in Section IV were then also presented in Symposium G6 Geodesy Beyond 2000 - The Challenges of the First Decade . This important symposium mainly oriented to future tasks gave the Section a space to discuss topics that cover problems related: to the World Geodetic Datum 2000, to studies associated with the representation of the time-varying gravity filed, to applications of the so-called direct methods for the solution of boundary value problems in physical geodesy with their tie to the minimization of a quadratic functional and the famous Lax-Milgram theorem, to studies concerning the use of wavelets in geodesy, then also to coordinate systems in four-dimensional space-time geodesy and to the recovery of the gravity filed form gravity gradient measurements.

Finally, the author would like to refer the reader of this report to detailed reports of the Special Commission and the Special Study Groups of Section IV that follow in the sequel and where the information given above are further amplified. Another important source of information are the individual issues of the SC1-Bulletin regularly published in the period 1995-1999.

Acknowledgements. Concluding this brief report, I wish to express my sincere thanks to all my colleagues from Section IV and to all officers of this Section for excellent cooperation and all the results achieved that often are associated with months or years of a great endeavor and a devoted work. My sincere thanks go also to many scientists in geodesy, in mathematics and other branches of science that have been contributing to this success and helped the Section to accomplish its mission. Honestly, in a considerable measure it is exactly the work of all these people and distinguished scientists that created a springboard for the activity of the Section in the next period. Much success and good fortune for Section IV in its further work!





Period 1979-1983
Title of the Section:

President: L.P. Pellinen (USSR)

Secretaries: E.W. Grafarend (Fed. Rep. of Germany)

F. Halmos (Hungary)

Special Study Group 4.56

Differential Geometry of the Gravity Field

Chairman: E.W. Grafarend (Fed. Rep. of Germany)

Sub-Group: Relativistic Aspects of Differential Geodesy

Chairman: C. Boucher (France)

Special Study Group 4.57

Boundary Value and Convergence Problems in Physical Geodesy

Chairman: F. Sanso (Italy)

Sub-Group: Improperly Posed Problems

Chairman: P. Holota (Czechoslovakia)

Special Study Group 4.58

Representation of the Gravity Field

Chairman: H.M. Dufour (France)

Special Study Group 4.60

Statistical Methods for Estimation and Testing of Geodetic Data

Chairman: K.R. Koch (Germany)

Special Study Group 4.65

Force Function of Two or More General Bodies: Application for Geodynamics

Chairman: E. Tengström (Sweden)

Special Study Group 4.66

Management of Geodetic Data

Chairman: C.C.Tscherming (Denmark)

Special Study Group 4.70

Gravity Field Approximation Techniques

Chairman: K.P. Schwarz (Canada)

Special Study Group 4.71

Optimization of Geodetic Networks

Chairman: G. Schmitt (Germany)

Period 1983-1987


President: E.W. Grafarend (Fed. Rep. of Germany)

Secretaries: K.-P. Schwarz (Canada)

F. Sanso (Italy)

Special Study Group 4.56

Differential Geometry of the Gravity Field

Chairman: E. Livieratos (Greece)

Special Study Group 4.57

Boundary Value and Convergence Problems in Physical Geodesy

Chairman: P. Holota (Czechoslovakia)

Special Study Group 4.60

Statistical Methods for Estimation and Testing of Geodetic Data

Chairman: D. Fritsch (Fed. Rep. of Germany)

Special Study Group 4.66

Geodetic Data Base Management

Chairman: A.U. Frank (USA)

Special Study Group 4.71

Optimal Design Problems

Chairman: G. Schmitt (Germany)

Special Study Group 4.91

Local Gravity Field Approximation

Chairman: H. Sünkel (Austria)

Special Study Group 4.92

Global Gravity Field Approximation

Chairman: L. Sjöberg (Sweden)

Special Study Group 4.93

Wave Propagation in Refractive Media

Chairman: P. Forsyth (Canada)

Special Study Group 4.94

Theory of Geodetic Reference Frames

Chairman: J. Wahr (USA)

Special Study Group 4.95

Multi Force Function: Geodetic Aspects of Astrodynamics

Chairman: K.H. Ilk (Fed. Rep. of Germany)

Special Study Group 4.96

Models for Time-Dependent Geodetic Positioning

Chairman: P. Vanicek (Canada)

  Period 1987-1991


President: K.-P. Schwarz (Canada)

Secretaries: F. Sanso (Italy)

P. Holota (Czech Republic)

Special Study Group 4.91

Local Gravity Field Approximation

Chairman: R. Forsberg (Denmark)

Special Study Group 4.92

Global Gravity Field Approximation

Chairman: H.-G. Wenzel (Germany)

Special Study Group 4.93

Wave Propagation in Refractive Media

Chairman: F.K. Brunner (Austria)

Special Study Group 4.115

Mathematical Analysis of Geodetic Boundary Value Problems

Chairman: F. Sacerdote (Italy)

Special Study Group 4.116

Kinematic and Dynamic System Modelling in Geodesy

Chairman: K.-P. Schwarz (Canada)

Special Study Group 4.117

Optimization of Modern Positioning Techniques

Chairman: D. Delikaraoglu (Canada)

Special Study Group 4.118

Inverse Geodetic Problems

Chairman: K.H. Ilk (Germany)

Special Study Group 4.119

Relativistic Effects in Geodesy

Chairman: E.W. Grafarend (Germany)

Special Study Group 4.120

Non-Linear Adjustment

Chairman: P.J.G. Teunissen (The Netherlands)

Period 1991-1995


President: F. Sanso (Italy)

Secretaries: P. Holota (Czech Republic)

P.J.G. Teunissen (The Netherlands)

Special Commission SC1

Mathematical and Physical Foundations of Geodesy

President: E.W. Grafarend (Germany)

Subcommission 1: Statistics

Chairman: B. Schaffrin (USA)

Subcommission 2: Numerical and Approximation Methods

Chairman: R. Klees (Germany)

Subcommission 3: Boundary Value Problems

Chairman: F. Sacerdote (Italy)

Subcommission 4: Differential Geometry

Chairman: J. Zund (USA)

Subcommission 5: Theory of Orbits and Dynamics of Systems

Chairman: A. Drozyner (Poland)

Special Study Group 4.138

Modelling and Quality Control for Precise Integrated Navigation

Chairman: A. Kleusberg (Canada)

Special Study Group 4.139

The Role of Terrain in Gravity Field Modelling

Chairman: A. Geiger (Switzerland)

Special Study Group 4.140

Tomography of the Atmosphere by Geodetic Measurements

Chairman: T. Spoelstra (The Netherlands)

Special Study Group 4.141

Integrated Inverse Gravity Modelling

Chairman: R. Barzaghi (Italy)

Special Study Group 4.142

Application of the Boundary Value Problem Techniques to Space and Airborne Gravity Field Observations

Chairman: B. Heck (Germany)