NATIONAL REPORT OF THE FEDERAL REPUBLIC OF ... - IAG Office

152 Inter-commission committees (ICC) – ICC on Theory (ICCT)
2004), while W. FREEDEN and V. MICHEL published Multiscale
Potential Theory (With Applications to Geoscience)
in Birkhäuser Verlag, Boston/Basel/Berlin 2004. Furthermore,
E. GRAFAREND and F. KRUMM completed the comprehensive
textbook on Map Projections – Cartographic
Information Systems (Springer Verlag, Berlin 2006).
Finally, the monograph by A. TEUSCH Einführung in die
Spektral– und Zeitreihenanalyse mit Beispielen aus der
Geodäsie (Introduction into Spectral and Time Series
Analysis with Examples from Geodesy, Deutsche Geodätische
Kommission, Reihe A, Heft Nr. 120, Munich 2006)
should be mentioned.
The following sub-chapters on Physical Aspects of Geodetic
Modelling and Relativity, Mathematical Aspects of
Geodetic Modelling, and Quality Measures and Control
report about the work related to the objectives of the ICCT,
which was carried out in Germany in the period 2003 –
2007.
The physical aspects of geodetic modelling have been
strongly focused on the deformable Earth; due to the
deformability of the Earth the geometry of the Earth’s
surface and its external gravity field are time-dependent.
While formerly the geometrical deformation and the change
of the gravity field had been treated as separate phenomena,
a unified view has been attempted in the past 4-year period,
aiming at dynamic theories of deformation and gravity field
as well as at an integrated theory for crustal deformation.
Significant advances can also be realized in the theory of
the determination of the external gravitational field from
recent and new satellite missions such as CHAMP, GRACE
and GOCE, for the steady-state part as well as for the timevariable
components. With respect to the structure of the
ICCT reference is made to WG-ICCT2 and IC-WG2/IC-
WG3.
The mathematical aspects of geodetic modelling cover both
the deterministic and the stochastic model. In the deterministic
part main emphasis has been put on the approximation
and representation of the Earth’s time-variable gravitational
field by harmonic and non-harmonic base functions
such as classical and spherical wavelets. These base
functions have also been used for other applications such
as data compression, the regularization of inverse problems,
and the investigation of deformations. Great progress has
been achieved in adapting wavelets to various fields of
Geodesy; high-performance computing is a necessary
prerequisite for the use of these new tools. Deterministic
aspects of mathematical modelling have mainly been
studied within WG-ICCT1, WG-ICCT3, IC-SG2.5 and IC-
SG2.6.
Adjustment theory had been the classical tool for quality
analysis in Geodesy. In recent years this field has been
strongly extended from stochastic to non-stochastic
methods of data evaluation, covering parameter estimation,
filtering techniques, hypothesis testing, numerical simulation
as well as fuzzy data analysis and neuronal networks.
More classical fields are mixed linear models, containing
e.g. also integer-valued unknowns with applications to GPS
ambiguity solutions and the derivation of displacements
from InSAR. It can be stated that the arsenal for the analysis
of the quality of geodetic measurements and quality control
has been strongly increased. The most recent trends concentrate
on a unique view of the complete process from data
acquisition to provision of final results, comprising measures
for integrity, reliability and precision. Studies related
to stochastic and non-stochastic methods of data evaluation
have been embedded in the work of IC-SG4.2 and IC-WG1.