Chair: Willi Freeden (Germany)

Future spaceborne observation combined with terrestrial and airborne activities will provide huge datasets of the order of millions of data. A reconstruction of the gravity field from future data material requires a careful multiscale analysis of the gravity potential, fast solution techniques, and a proper stabilization of the solution by regularization. While global long-wavelength modelling can be adequately done by use of spherical harmonic expansions, harmonic splines and/or wavelets are most likely the candidates for medium and short-wavelength approximation since they are 'building blocks' that enable fast decorellation of gravitational data. Thus three features are incorporated in this way of thinking about georelevant harmonic wavelets, namely basis property, decorrelation, and fast computation. But this concept of harmonic wavelets demands its own nature in geodesy which by no means can be developed from the classical theory in Euclidean spaces. The working group intends to bring together scientists concerned with the diverse areas of geodetically relevant wavelet theory in general and its applications. An essential field of research is the specific character of geodetic multiresolution methods used in addition or in contrary to standard spectral techniques based on spherical harmonic framework.

Objectives

Theoretical research in the field of spherical and ellipsoidal wavelets as well as wavelet introduction and modelling on geodetically relevant surfaces (like spheroid, geoid, (actual) Earth’s surface). Studies of harmonic wavelets in geodetic boundary-value problems (e.g. Runge-Walsh wavelets, layer potential wavelets, etc).

- Studies on spline/wavelet kernel modeling, multiscale pyramid algorithms via kernel functions known from (least squares) collocation and spline approaches, noise cancellation, least–squares adjustment and spline smoothing vs. multiscale thresholding, etc. Development of specific numerical methods: fast wavelet transform (FWT), tree algorithms, data compression, domain decomposition techniques, fast multipole methods (FMM), panel clustering, data transmission, etc.

- Comparison of spherical harmonic and/or wavelet modeling: Combined spectral and multiscale expansion of the gravitational potential, degree variances vs. local wavelet variances, spectral and/or multiscale signal to noise thresholding, etc. Investigation of different wavelet types in geodetic pseudodifferential equations (using numerical methods such as collocation, Galerkin method, least – squares approximation, etc).

- Regularization of inverse problems by multiresolution, locally reflected multiscale vs. globally reflected spectral regularization, multiscale parameter choice strategies, multiscale modeling in SST, SGG. Time dependent multiscale modeling in boundary value and inverse problems, numerical implementation and application to GRACE–, GOCE–data.

Program of Activities

- Organization of meetings and conferences (e.g. Oberwolfach conference on "Geomathematics", May 2004, Organizers: Freeden (Kaiserslautern), Grafarend (Stuttgart), Sloan (Sydney), Svensson (Lund).
- Organizing of WG meetings or sessions, in coincidence with a larger event, if the presence of working group members appears sufficiently large.
- Email discussion and electronic exchange.
- Launching a web page for dissemination of information, expressing aims, objectives, plus providing a bibliography.
- Monitoring and presentation of activities, either of working group members or interested external individuals.

Membership

Willi Freeden (Chair) (Germany)
M. Fengler (Germany)
M. Gutting (Germany)
W. Keller (Germany)
J. Kusche (Netherlands)
D. Michel (Germany)
V. Michel (Germany)
J. Otero (Spain)
S. Pereverzev (Austria)
F. Sanso (Italy)
M. Schreiner (Switzerland)
J. Schröter (Germany)
H. Sloan (Australia)
N. Sneeuw (Canada)
L. Svensson (Sweden)
C. C. Tscherning (Denmark)