Wavelets: analysis of seismic signals (CWI.3403)

In many disciplines which study changes in propagating waves it is often necessary to analyze (detect, recognize, classify, select, .... ) short, weak signals buried in the background noise. Fourier transformation, which is an excellent and well-exploited tool in the analysis of stationary signals, often fails when non-stationary, short-lived signals are in question. Wavelet transformation, on the other hand, offers the timing information in addition to the frequency information, and it also enables the signal analysis on various resolution levels. Of many possible applications of wavelet transformations claimed in the literature, this project concentrates on the use of wavelet transformations for signal analysis, in particular for the analysis and synthesis of seismic signals.
The wavelet transformation is an integral transformation which uses wavelets, which are short wave-like functions, as basis functions. A function (or a signal) transformed to the wavelet domain is replaced by its approximations, as well as by the detailed information extracted from these approximations. This allows the study of the signals on various resolution levels. In addition to this multi-resolution property, the wavelet transformation provides also the frequency information of both approximated and the detailed components as a function of time. These two properties, localization and multi-resolution decomposition, make the wavelet transformation an attractive method for transient signal analysis and synthesis.

The research in this project will be concentrated on the following:

1. Use the multi-scale nature of the wavelet transformation and time-frequency localization, develop and implement the methods of signal analysis and synthesis in several chosen disciplines: earthquake seismology, seismic engineering, and multi-scale modeling of geologic formations.
2. Optimal wavelet selection. A large number of functions, with different properties, belongs to the category of wavelets. The question of how to choose the 'best' wavelet is yet unanswered, and it is a subject of current research in both mathematics and application fields.

To achieve these goals, in this project we intend to, first, develop a basic software package for wavelet design and wavelet transformation (say, as an extension of existing software packages as MatLab). Secondly, we plan to develop an advanced software package for transient signals using wavelet transformation. This package should be applicable in various disciplines of signal analysis and synthesis, with the emphasis on seismic signals.

Als u meer wilt weten over dit onderzoek en de achtergrond ervan, of over de onderzoeksgroep, dan kunt u de website van het CWI over dit project raadplegen.

Eén bedrijf, twee non-profit organisaties en drie universiteiten.

Dr. N.M. Temme
Centrum voor Wiskunde en Informatica
Afdeling Analyse
Algebra en Meetkunde
Postbus 94079
1090 GB AMSTERDAM.