Section IV

General Theory and Methodology

 

Report of the President for the Period 1999 – 2003

 

B. Heck

 

 

Introduction and Objectives

 

According to the IAG by-laws and the terms of reference, section IV in the hitherto existing structure of the IAG covers general aspects of geodetic theory and methodology. In contrast to other lAG sections, the scope of Section IV is not confined to a specific topic in Geodesy such as positioning, or gravity field determination, or geodynamics; the accent here is rather on the systematic (mathematical) treatment of groups of problems. Therefore it is quite natural that most topics treated by the bodies in Section IV are shared in one way or another with other lAG sections, adding a different, more general point of view, but without just duplicating the work. Ideally, the mathematical problems occurring in the topic-oriented sections should be reflected upon in Section IV and solved on a general basis. Another principal scope of Section IV is to develop mathematical tools and to take up available approaches already developed in other fields of Science and to adapt them to Geodesy; a prominent historical example is Least Squares Collocation which was developed in the seventies mainly in Section IV and nowadays is a basic tool in many branches of Geodesy. In recent years, e.g. spatial statistics, robust statistical methods, fuzzy theory and the use of wavelets have been thoroughly investigated in Section IV tor applications in Geodesy; some of these approaches seem to be very promising and to become highly efficient tools in geodetic data analysis.

 

Structure

 

The principal structure as well as its title was given to Section IV at the 18th IUGG General Assembly in Hamburg 1983. In 1991 the Special Commission 1 on „Mathematical and Physical Foundations of Geodesy“ has been added as a new structure element besides the conventional Special Study Groups. This basic structure, consisting of Special Commission 1 and Special Study Groups, has been retained in the past period 1999 – 2003. While the Special Study Groups have clearly defined topics reflecting the most important aspects of contemporary geodetic theory, the Special Commission covers broader and long-term items of geodetic theory in its sub-commissions and working groups.

 

In order to achieve its objectives, Section IV has established the following structure in detail:

 

President:

          Bernhard Heck (Germany)

Secretaries:

          Christopher Jekeli (USA)

          Yuanxi Yang (China)

Special Commission SC1:

          Mathematical and Physical Foundations of Geodesy

          Chair: Petr Holota (Czech Republic)

 

Subcommission 1:

           Statistics and Optimization

          Chair: Peiliang Xu (Japan)

Working Group:

          Spatial Statistics for Geodetic Science

          Chair: Burkhard Schaffrin (USA)

Subcommission 2:

          Numerical and Approximation Methods

          Chair: Willi Freeden (Germany)

Subcommission 3:

          Boundary Value Problems

          Chair: Rüdiger Lehmann (Germany)

Subcommission 4:

          Geometry, Relativity, Cartography, GIS

          Chair: Volker Schwarze (Germany)

Subcommission 5:

          Hydrostatic/isostatic Earth reference Models

          Chair: Alexander Marchenko (Ukraine)

 

Special Study Groups

In 1999 the following five Special Study Groups have been established:

 

SSG 4.187: Wavelets in Geodesy and Geodynamics

          Chair: Wolfgang Keller (Germany)

SSG 4.188: Mass Density from Joint Inverse Gravity Modelling

          Chair. Gabriel Strykowski (Denmark)

SSG 4.189: Dynamic Theories of Deformation and Gravity Fields

          Chair: Detlef Wolf (Germany)

SSG 4.190: Non-Probabilistic Assessment in Geodetic Data Analysis

          Chair: Hansjörg Kutterer (Germany)

SSG 4.191: Theory of Fundamental Height Systems

          Chair: Christopher Jekeli (USA)

 

In 2001 another Special Study Group has been added:

 

SSG 4.195: Fractal Geometry in Geodesy

          Chair: Erik W. Grafarend (Germany)

 

A detailied description of the above structure of Section IV is provided in the Geodesist’s Handbook 2000 (Special Issue of the Journal of Geodesy, Vol 74, No. 1, pp. 106-115)

 

Major Scientific Achievements

 

The past (and simultaneously the last) four year period marked a very productive and successful period in the 20 years lifetime of Section IV, having been involved in many activities of the IAG. The great progress in geodetic theory and methodology has been made visible in presentations by Section IV members on the occasion of scientific symposia and workshops; the scientific work has also been documented by publications in peer-reviewed international journals such as Journal of Geodesy, Geophysical Journal International, Journal of Geophysical Research, and others, as well as in national journals and publication series and in Symposia Proceedings (in particular in the Springer IAG Symposia series).

 

Section IV has been represented at many IAG sponsored symposia and seminars. Only some of the most eminent events are highlighted below:

 

·    International Symposium on Gravity, Geoid and Geodynamics in Banff/Canada, July 31 – August 4, 2000,

·    Seventh International Winter Seminar in Sopron/Hungary, February 19-23, 2001,

·    IAG Symposium on Vertical Reference Systems, Cartagena/Columbia, February 20-23, 2001,

·    First International Symposium on Robust Statistics and Fuzzy Techniques in Geodesy and GIS, Zurich/Switzerland, March 12-16,2001 (Organized by SSG 4.190),

·    IAG Scientific Assembly in Budapest/Hungary, September 3-7, 2001,

·    5th Hotine-Marussi Symposium on Mathematical Geodesy in Matera/Italy, July 10-14, 2002 (which was an extremely successful meeting in the series of the traditional Section IV Symposia),

·    W.A. Heiskanen Symposium in Geodesy in Columbus/Ohio, USA, October 1-5, 2002.

 

Furthermore, Section IV contributed significantly to the EGS General Assemblies held in Nice/France on an annual basis since 2000. Finally, Section IV will be represented at a number of Symposia and sessions organized on the occasion of the IUGG General Assembly in Sapporo/Japan, June 30 - July 11. In particular, a profile of the research activities and a survey of the most important results will be presented in Symposium G04 „General Theory and Methodology“ organized by Section IV, where the work of the sub-entities (Special Commission, Special Study Groups) will be reported, too.

 

Major scientific achievements have been made in particular in the various modelling aspects covering physical and mathematical modelling of geodetic observations as well as stochastic and non-stochastic methods of data evaluation. Below an attempt is made to provide a short (probably subjective and biased) summary of the most important steps of progress:

 

Physical aspects of modelling in Geodesy are related to the basic theories of Physics (Newtonian mechanics, theory of relativity, quantum theory) forming in some way the background of any modelling of geodetic observations. Significant advances in the past four-year period are visible in the theory of fundamental reference frames and height systems, in methods for the description of the Earth’s space-and time-variable gravity field and deformation, and in modelling the propagation of electromagnetic signals in refractive media; advanced models in these fields have become necessary due to the rapid development in the quality and availability of space geodetic observations.

 

The mathematical aspects of geodetic modelling refer to new developments in numerical mathematics and digital signal processing, including advanced tools such as wavelet analysis in one and two dimensions; applications in Geodesy range from time series analysis (e.g. polar motion) to feature extraction and data compression. Special emphasis has also been put into the formulation and solution of boundary value problems as well as inverse and improperly posed problems, related e.g. to downward continuation.

 

Since the foundations of least squares adjustment by C.F. Gauß stochastic methods of data evaluation have played a dominant role in Geodesy, in particular in the framework of quality analysis. Strong progress has been made in the adaption of statistical inference – including Bayesian statistics – to the fields of Geodesy and Surveying, digital Photogrammetry and image processing, and digital topography and cartography. Other topics belonging to this subject are stochastic signal analysis and geostatistics.

 

Traditionally and methodologically, a distinction is made between deterministic and stochastic signals in geodetic observations. More and more, deterministic signal analysis makes use of wavelet transforms instead of the classical Fourier techniques. Recently, the spectrum of uncertainty in geodetic data and models has been extended from the purely random status; non-random uncertainty of the data can be taken into account using interval mathematics, fuzzy data analysis and artificial neural networks.

 

Details about the progress achieved in the past four-year period can be studied in the reports by the Special Commission 1 and the Special Study Groups of Section IV that follow in the sequel.

 

The Future of Geodetic Theory in IAG

 

After having worked well for decades, the Section structure of IAG will be dissolved with the IUGG General Assembly in Sapporo and fitted to recent requirements and developments. The new IAG structure, decided at the IAG Scientific Assembly 2001 in Budapest, will bring great changes concerning the organisation of theoretical and methodological work in the IAG. The former Section structure, sometimes criticized as inconsistent, will be replaced by a Commission structure, involving four topic-oriented commissions. The task of these new commissions is to promote the advancement of science, technology and international cooperation in their field. Besides the services, the commissions will form the main scientific components of the new lAG structure.

 

In the new structure an entity like the present section IV is no more foreseen and visible at the highest level of organization below the EC, the level of the commissions and services. But this by no means should indicate that geodetic theory and methodology will not play a fundamental role anymore. Since one of the major tasks of the new commissions is the promotion of science, these bodies will be responsible for the development of theory in their respective fields, too. Of course, this procedure cannot include the development of general, topic-independent approaches of data analysis and mathematical-physical foundations, methodology and "general" theory of Geodesy. After many discussions a solution of this problem could be found consisting of the creation of the creation of an Inter-Commission Committee on Theory, reporting directly to the EC. It is expected that the existence of such a committee will make sure that e.g. mathematically interested geodesists and application-oriented mathematicians and physicists furthermore will find a home and meeting-place within IAG.

 

Furthermore, the Inter-Commission Committee on Theory should provide a channel of cooperation amongst the different commissions, on the ground of methodology, and support a closer collaboration between „theoreticians“ and „practicioners“ in the topic-oriented work of the Commissions. Finally, this Committee is intended to serve as an interface to other fields of Science, in particular Mathematics, Physics and Earth Sciences.

 

Acknowledgements

 

Concluding this general report, I wish to express my sincere thanks to all officers and colleagues having contributed to the extremely successful work of Section IV in the past four-year period. It is the work of many scientists in Geodesy, Mathematics and other branches of Science, often associated with months and years of great effort, which produced the outstanding results achieved in Section IV and helped the Section to accomplish its mission for the benefit of the IAG as a whole. My personal thanks go also to the officers of Section IV for the excellent cooperation. Finally, it is my sincere wish and hope that geodetic theory and methodology will find its due position in the new structure of IAG.