REPORT ON THE VI I I HOTINE SYMPOSIUM

ON MATHEMATICAL GEODESY

by Fernando SANSO

The VIII Hotine Symposium on Mathematical Geodesy has been held in Como from September 7 th to September 9 th, 1981.

60 scientists working in geodesy as welt as in other fields (mathematics, physics, etc.) participated in the Symposium by presenting their papers and discussing the many fascinating problems of mathematical geodesy. Prof. H. Moritz and Prof. T. Kramp who could not be present in Como, sent telegrams wishing the Symposium success. The works of the Symposium were partitioned into 9 sessions, 8 of which, were devoted to the presentation of communications, and the last one dedicated to a final free discussion.

The first session was introduced by a speech of welcome by Prof. F. Sa_ns6 on behalf of the Organizing Committee, composed of Profs. E. W. Grafarend, A. Mamssi, H. Montz and by the writer.

The session took place under the direction of Prof. A. Manlssi, who also gave an introductory speech reca!ling the history of Hotine Symposia and the importance of their contributions to the scientific growth of geodesy. The first communication too, presented by B. Chovitz, had a historical flavour, being devoted to an analysis of the contents of M. Hotine's book on Mathematical Geodesy.

The following main topics were treated in the subsequent presentations : differential geodesy (including 4 - D analysis and relativistic effects), geometrical versus physical geodesy, estimation theory, geodesy versus geophysics, numerical methods in geodesy, convergence of series in spherical harmonics, improperly posed and inverse problems in geodesy, geodetic and geodynamic boundary value problems.

The discussions during the three days of the Symposium and specially in the final free-session underlined some of the basic problems in mathematical geodesy : in particular the problem of the finite-dimensional versus the infinite-dimensional approach in estimation theory, the problem of taking into account the effects of the topography on the gravity field, however avoiding the non--rigorous old-fashioned reductions, the problem of the stability of the approximations and the opportunity of introducing geophysical constraints.

The usefulness of the theoretical analysis of the geodetic boundary value problems was also thoroughly discussed and its value in creating a firm framework for the approximation theory was underlined ; this also referring to the necessity of a "continuous treatment" of very abundant discrete data (think of the altimetry data which supply an almost continuous coverage of large areas).

The proceedings of the Symposium will be published in the Bollettino di Geodesia e Scienze Affini.

Scientific Program Monday- Sept. 7 th, 1981

- 9:00 - 10:20 Chairman : A. Mamssi.

Chovitz B. - The influence of Hot ine's "Mathematical Geodesy"

Bull. G~od, 56 (1982)pp, 177-179. 177

Georgiadou Y, Bode A, Grafarend E.W.

Livieratos E. Dermanis A.

10:50 - 12:30

Bocchio F. Grafarend E.W. Brunner F.K.

Boucher C.

Weightman J.A.

14:30 - 16:30

Baarda W.

Remmer O. Eeg J. Adam J.

Kelm R.

Fritsch D. Schaffrin B.

1 6 : 5 0 - 18:30

Svensson L, Bjerhammar A. Bertotti B. Schwarz K.P, Lachapelle G. Mainville A. Dufour H.M. Caputo M.

- Love numbers and the deformation of gravity space. ,- The tel luroid mapping based on a normal gravity potential including

the centrifugal term.

- Di latat ion, shear and rotat ion analysis of map prc;jections.

Chairman : B. Chovitz.

- On the inverse geodetic singularity problem. - The small scale structure of geometry and gravity space.

-App ra i sa l of the geometrical optics approximat ion for geodetic refraction calculations.

- Review of relativistic effects in the Solar System and their impact on geodetic models.

- Datum transformation from data w i th in a l imited area.

Chairman : E.W. Grafarend.

- S o m e comments on " A connection between geometric and gravimetric geodesy".

- T w o letters on physical geodesy. - C o n t i n u o u s methods in least squares theory. - O n the determination of simi lar i ty coordinate transformation

parameters. - Modell ing of the gravity f ield effects on geometric parameters in

local networks. - The "choice of norm" problem for the free net adjustment w i th

or ientat ion parameters.

Chairman : K. Linkwitz

-- On a new geodesy based upon inversionfree Bjerhammar predictors. - On the col location solut ion for a non-spher ical surface. - Higher order correlation funct ions for the gravity field. -- Empirical investigations into the anisotropy and non-homogene i t y

of the gravity anomaly field.

- La correction de Rudski am~lior6e. Justif ications. Appl icat ions. --Physical constraints for the estimate of strain on the Earth's

surface.

Tuesday - Sept. 8 th, 1981 14:30 - 16:30

Fell P.

Gerstl M,

Freeden W. Kleusberg A, Nagy D. Hofmann- Wellenhof B. Meissl P.

Chairman :W, Baarda

- Decreasing the influence of distant zones w i th modif icat ions to the Stokes and Vening Meinesz Kernels.

- -Numer ica l evaluation of el l ipt ic integrals for some geodetic appl ications.

- O n interpolat ion by harmonic splines. - C a r t e s i a n representation of the gravitational field. - D i r e c t gravity formulae for the GRS 1980 : a review. - Appl icat ions of sparse matr ix techniques to physical geodesy.

178

- 9:00 - 10:00

Engl H.

1 6 : 5 0 - 18:30 Chairman : A. Bjerhammar.

Tscherning C . - C . - Some geodetic applications of Clenshaw summation. Poder K.

Rummel R. -Est imat ion of gravity field parameters with stabilized integral Kernels.

Krynski J. - Processing of satel l i te-to-satel l i te tracking data for gravity field determination.

Petrovskaya M. - Representation of the Earth's potential by convergent series.

Colombo O i . - Convergence problems in spherical harmonic expansions.

Wednesday - Sept. 9 th, 1981.

Chairman : L.P. Pellinen

- O n the parameter choice problem in regularization methods for solving linear il l-posed problems.

Holota P. - On geodetic improperly posed problems and the subgroup of lAG SSG 4.57.

- An inverse problem in potential theory.

- A note on density problems and the Runge-Krarup's theorem.

Chairman : C.-C. Tscheming;

- --Effects of the Earth's ell ipticity in solving geodetic boundary value problems.

- On the free boundary value problem of physical geodesy.

- On the altimetry--gravimetry boundary problem.

- The geodynamic boundary value problem.

Pagani C.

Sans6 F.

- 11:00 - 12:40

Pellinen L,P.

Witsch K.J.

SjSberg L.

Dermanis A.

Sans6 F.

179