REPORT OF THE
SSG 4.187
WAVELETS
IN GEODESY AND GEODYNAMICS
Chair: W. Keller
The
main fields of the SSG activities have been
- publications
- software
development
- education
- comparison
of different wavelet based algorithms
1 Publications
The
members of the SSG have published so far 22 papers in scientific
journals and on conferences. These contributions can be divided into
four groups
- pattern
recognition,
- spherical
wavelets,
- filtering
and prediction,
- enhancement
of numerical processes.
1.1
Pattern recognition
Most
of the publications about wavelet applications belong to this field.
The goal is to find certain signatures which, on different scales, are
hidden in the signal.
One
group of pattern recognition techniques deals with the interpretation
of signal registration from different geodetic measuring systems :
Superconducting gravimeters, airborne gravimeters and so on.The
publications [3],[9],[19] and [21] can be counted to this group.
A
more exotic application of pattern recognition using wavelets is the
study of atmospheric turbulence and seafloor topography as reported in
[2] and [4].
Last
but not least, wavelets are frequently used for gravity field
modeling. A topic which is discussed in the contributions [5] and
[10].
1.2
Spherical wavelets
This
topic is the main focus of the Kaiserslautern University Group with W.
Freeden as its head. The group aims at a construction of a wavelet
analysis on the sphere. Among the many publications of this group the
contributions [1], [6]and [7] should be mentioned.
1.3
Filtering and prediction
The
ability of wavelets to decompose a given signal into a sequence of
non-overlapping (or slightly overlapping) frequency bands can be used
for an optimization of prediction and filtering algorithms. The
publications [13], [14], [15], [16] and [17] deal with this problem.
The
time-frequency resolution property of wavelets is the key for the
extension of the known filtering algorithms from the stationary to the
non-stationary case. These questions are discussed in the publications
[11] and [12].
1.4
Enhancement of numerical processes
Numerical
algorithms do not take effect uniformly on all scales. Usually their
main effect is concentrated on a certain scale-range. Wavelets can be
used to decompose the numerical process in a number of sub-processes,
each of them operating on a certain scale-range. Neglecting the minor
effective sub-processes can improve the numerical performance of the
whole process considerably. This idea is studied in the contributions
[8] and [20].
2 Software development
In
order to provide the geodetic community with ready-to-use tools for
wavelet analysis the most important wavelet-related algorithms as
4 Comparison of algorithms
In
order to provide a scale for comparison of different wavelet
algorithms a synthetic polar motion test data-set was created by Dr.
Schmidt and was made available to the SSG via the SSG home-page. The
members of the SSG were requested to analyze the data with their own
algorithms and to submit the results. From the results conclusions
about the strength and the weakness of different algorithms should be
drawn. Unfortunately, the resonance to this project was
disappointingly low.
References
[1]Bayer
M. , Freeden W., Maier T.: WAVELET ANALYSIS OF THE GEOMAGNETIC FIELD
WITHIN SOURCE REGIONS OF IONOSPHERIC AND MAGNETOSPHERIC CURRENTS
Berichte der Arbeitsgruppe Technomathematik, N0.: 217 University of
Kaiserslautern, September 1999
[2]Beth,
S. ;Boos, T.; Freeden, W.; Casott, N.; Deussen, D.; Witte, B: On the
wavelet determination of scale exponents in energy spectra and
structure functions and their application to CCD camera data In: K.-P.
Schwarz (Ed.) Geodesy Beyond 2000: The Challenges of the First Decade
Birmingham, 1999 IAG General Assembly Birmingham , July 19 - 30, 1999
pp. 221 - 226 Springer-Verlag Berlin Heidelberg 2000
[3]Bruton,
A.M.; Schwarz, K.-P.,Skaloud,J.: The use of wavelets for the analysis
and de-noising of kinematic geodetic measurements In: K.-P. Schwarz
(Ed.) Geodesy Beyond 2000: The Challenges of the First Decade
Birmingham, 1999 IAG General Assembly Birmingham , July 19 - 30, 1999
pp. 227 - 232 Springer-Verlag Berlin Heidelberg 2000
[4]Dreher,
S.; Lalancette, M.F.: Estimating Lithosphere Characteristics With
Wavelet Admittance and Coherence of Gravity and Seafloor Topography.
paper given at the IAG International Symposium on Gravity, Geodesy and
Geodynamics held in Banff, July 31 - August 4, 2000
[5]Doufexopopolou,
M.G. ; Bartha, G.C.: A Strategy to Approach a Multi-scale Space/Time
Problem by Only data Information.paper given at the IAG International
Symposium on Gravity, Geodesy and Geodynamics held in Banff, July 31 -
August 4, 2000
[6]Freeden
W. , Michel V. : LEAST SQUARES GEOPOTENTIAL APPROXIMATIONBY WINDOWED
FOURIER TRANSFORM AND WAVELET TRANSFORM Berichte der Arbeitsgruppe
Technomathematik, N0.: 216 University of Kaiserslautern, September
1999
[7]Freeden
W.: Multiscale Modelling of Spaceborne Geodata B.G. Teubner Verlag,
Stuttgart, 1999
[8]Gilbert
A., Keller W.: Deconvolution with Wavelets Journal of Geodesy. Journal
of Geodesy 2000(74) pp. 306-320
[9]Haagmans,R.H.N.;
Dorst, L.L.; Francis, O.: Wavelets and Statistical Testing for
Improved Analysis of Super Conducting Gravimeter Data at the main
Tidal Frequencies.paper given at the IAG International Symposium on
Gravity, Geodesy and Geodynamics held in Banff, July 31 - August 4,
2000
[10]Horowitz,
F.G., Strykowski, P.; Hornby, P.; Boschetti, F.; Cox, S.J.D.: A
Multiskale Skeletonization of The EGM96 Gravity Disturbances, Locally
Compared with Australian Geophysical data.paper given at the IAG
International Symposium on Gravity, Geodesy and Geodynamics held in
Banff, July 31 - August 4, 2000
[11]Keller
W.: A Wavelet Approach to Non-Stationary Collocation In: K.-P. Schwarz
(Ed.) Geodesy Beyond 2000: The Challenges of the First Decade
Birmingham, 1999 IAG General Assembly Birmingham , July 19 - 30, 1999
pp. 208 - 213 Springer-Verlag Berlin Heidelberg 2000
[12]Keller,
W.: A Wavelet Solution to Non-stationary 2D Collocation. data.paper
given at the IAG International Symposium on Gravity, Geodesy and
Geodynamics held in Banff, July 31 - August 4, 2000
[13]Keller,
W.: Wavelets in Geodesy and Geodynamics Lecture Notes, Universtity of
Calgary 2000
[13]Kotsakis
C.: The Multiresolution Character of Collocation Journal of Geodesy in
print
[14]Kotsakis
C.: The Role of Statistical Collocation as a Tool for Constructing
Generalized Multiresolution Analyses in the L2(R) Hilbert Space
Bolletina di Geodesia e Scienze Affini in press
[15]Kotsakis
C.: Wavelets and Collocation: An Interesting Similarity In: K.-P.
Schwarz (Ed.) Geodesy Beyond 2000: The Challenges of the First Decade
Birmingham, 1999 IAG General Assembly Birmingham , July 19 - 30, 1999
pp. 227 - 232 Springer-Verlag Berlin Heidelberg 2000
[16]Kotsakis,
C.: Multiresolution Aspects of Linear Approximation Methods in Hilbert
Spaces Using Gridded Data Department of Geomatics Engineering UCGE
Reports Number 20138
[17]Kotsakis,
C.; Sideris M.G.: Aliasing Error Modelling in Single-input
Single-output Linear Estimation Systems. paper given at the IAG
International Symposium on Gravity, Geodesy and Geodynamics held in
Banff, July 31 - August 4, 2000
[19]Liu,
L.T.; Hsu, H.T. ; Sun H.P.: Wavelet-characterized Approach to Harmonic
Analysis of Tide Gravity Observations.paper given at the IAG
International Symposium on Gravity, Geodesy and Geodynamics held in
Banff, July 31 - August 4, 2000
[20]Salamonowitcz,
P.H.: A Wavelet Based Gravity Model with Application to the Evaluation
of Stoke's Integral.paper given at the IAG International Symposium on
Gravity, Geodesy and Geodynamics held in Banff, July 31 - August 4,
2000
[21]Liu,L.T.;Hsu,H.T.:
Wavelet application in Airborne Gravimetry..paper given at the IAG
International Symposium on Gravity, Geodesy and Geodynamics held in
Banff, July 31 - August 4, 2000
[22]Klees, R.;
Haagmanns,R.: Wavelets in the Geosciences. Lecture Notes in Earth
Sciences, Springer-Verlag, Berlin, Heidelberg, New York, 2000