Wavelets: Analysis of Seismic Signals
This research is financially supported by
Stichting Technische Wetenschappen (STW)
projectnumber CWI44.3403.
- Description of the project
- Seminar
- Course Material
- References for starters
- Related Bookmarks
- Publications & Preprints
- How to reach us
Subtitle of the project
Wavelets: Mathematical Aspects of and Applications to Geology and Seismology
Project outline
Wavelets are a relatively recent development in pure and applied mathematics;
they have, with respect to both theory and applications, strong relations
with Fourier transformations. The study of wavelets started approximately
15 years ago, and at present it has become clear that wavelets are excellent
tools for signal analysis, data compression and for developing very efficient
numerical algorithms for solving partial differential equations.
This project involves the application of wavelet techniques in the
context of seismic signals of various kinds.
The project has ended by January 1, 2000.
However, both expertise and interest are still present.
Research goals
The research in this project concentrates on the following topics:
- To develop mathematics based on wavelet methods
relevant and applicable to seismic processing.
- To develop fast and efficient algorithms based on wavelet methods for
seismic processing.
Short Description of present research activities
- Analysis of earthquake data: Phase picking methods
To detect certain phases in a seismogram an algorithm has been developed based
on a combination of the discrete wavelet transform and some well-known
parameter functions from seismics.
This research has been done in strong collaboration with the seismology
department of KNMI ,
De Bilt.
- Fractional Fourier transforms
A generalization of the fractional Fourier transform is used to
solve energy localization problems.
- Wavelet-Radon Transform in seismic preprocessing
Both the wavelet transform and the Radon transform are integral transformation
which discretized versions have found wide application in seismic processing.
The topic of research is the study of a hybrid integral transformation and
its discretizations. Also fast algorithms are being developed. Applications are
in seismic preprocessing of seismic exploration data.
- Rotation-wavelet transform
We study a combined technique composed of the two-dimensional wavelet transform,
rotation, groundroll muting strategies and interpolation of wavelet
coefficients.
- Asymptotics of filter coefficients for seismic processing
Compactly supported Daubechies wavelets are frequently used in the wavelet
analysis of seismic data. Within computational limits, the order of these
wavelets is usually taken as high as possible. An aim of research is to
find efficient asymptotic approximations of the filter coefficients for
high order Daubechies wavelets.
Note
There is a
CWI project overview available, including our formal
Project page.
The Signals & Images
Seminar
includes talks on wavelets and their applications.
If you want to be put on the mailing list in order to
receive announcements, please send your full name and E-mail address to
Radu.Stoica@cwi.nl
On November 6, 1997, we organized a one-day course on wavelets at CWI.
The course was divided in four parts:
Reference list
Wavelet bookmarks
S.J.L. van Eijndhoven, P.J. Oonincx,
Frames, Riesz systems and MRA in Hilbert spaces,
CWI Report PNA-R9701, February 1997.
Both an
abstract
,
a
PDF-version
and a
compressed postscript version
are available.
H.G. ter Morsche, P.J. Oonincx,
On the Integral representations for metaplectic operators,
RANA 99-44, TU Eindhoven, 1999.
H.G. ter Morsche, P.J. Oonincx,
Integral Representations of Affine Transformations in Phase Space
with an Application to Energy Localization Problems,
CWI Report PNA-9919, 1999.
Both an
abstract
,
a
PDF-version
and a
compressed postscript version
are available.
P.J. Oonincx,
On time-frequency analysis and time-limitedness,
CWI Report PNA-R9720, December 1997.
Both an
abstract
,
a
PDF-version
and a
compressed postscript version
are available.
P.J. Oonincx,
Automatic phase detection in seismic data using the discrete wavelet transform,
CWI Report PNA-R9811, October 1998.
Both an
abstract
,
a
PDF-version
and a
compressed postscript version
are available.
P.J. Oonincx,
A Wavelet Method for Detecting S-Waves in Seismic Data,
Computational Geosciences, 3, 111--134, 1999.
P.J. Oonincx,
Mathematical Signal Analysis:
Wavelets, Wigner Distribution and a Seismic Application.
Ph.D. Thesis, University of Amsterdam, February 2000.
P.J. Oonincx en S.J.L. van Eijndhoven,
Multiresolution Analyses in Hilbert Spaces,
Indagationes Mathematicae, 10, 369-382, 1999.
N.M. Temme,
Asymptotics and numerics of zeros of polynomials that are
related to Daubechies wavelets,
CWI Report AM-R9613, October 1996.
Both an
abstract
,
and a
compressed postscript version
are available.
Published in Applied and Computational Harmonic Analysis.
P.M. de Zeeuw, R.A. Zuidwijk,
Numerical Methods for Decomposition of 2D Signals
by Rotation and Wavelet Techniques,
CWI Report PNA-R0124, December 2001.
New! Keywords: ground-roll, wavelets, FFT, X-ray, rotation.
Both a
PDF-version
and a
compressed postscript version
are available.
R.A. Zuidwijk,
The Wavelet X-Ray Transform, CWI Report PNA-R9703, April 1997.
Both an
abstract
,
a
PDF-version
and a
compressed postscript version
are available.
R.A. Zuidwijk,
The discrete
and continuous wavelet X-ray transform,
SPIE proceedings 3169, Wavelet Applications in Signal and Image Processing V,
July-August 1997, pp. 357-366.
R.A. Zuidwijk,
Directional and time-scale wavelet analysis,
SIAM J. Mathematical Analysis, Vol. 31(2): 416--430 (2000).
R.A. Zuidwijk, P.M. de Zeeuw,
Fast Algorithm for directional Time-Scale Analysis using Wavelets ,
SPIE proceedings 3458,
Wavelet Applications in Signal and Image Processing VI, July 1998,
pp. 222-231.
R.A. Zuidwijk, P.M. de Zeeuw,
The fast wavelet X-ray transform, CWI Report PNA-R9908, September 1999.
Both an
abstract
,
a
PDF-version
and a
compressed postscript version
are available.
- Location
- Centrum voor Wiskunde en Informatica (CWI)
Dept. PNA4
Kruislaan 413
1098 SJ Amsterdam
The Netherlands
- Postal address
- Centrum voor Wiskunde en Informatica
Dept. PNA4
P.O. Box 94079
1090 GB Amsterdam
The Netherlands
- Fax
- +31 20 5924199
- E-mail
- See the list of participants
This website is maintained by
Dr. Paul M. de Zeeuw
<Paul.de.Zeeuw@cwi.nl >.
The last update has been at May 29, 2002.
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