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kulesh

HR: 1340h
AN: S43B-1300
TI: Geophysical Wavelet Library: Applications of the Continuous Wavelet Transform to the Polarization and Dispersion Analysis of Signals
AU: * Kulesh, M
EM: mkulesh@math.uni-potsdam.de
AF: Institute for Mathematics, University of Potsdam, Am Neuen Palais 10, Potsdam, 14469, Germany
AU: Holschneider, M
EM: hols@math.uni-potsdam.de
AF: Institute for Mathematics, University of Potsdam, Am Neuen Palais 10, Potsdam, 14469, Germany
AB: Surface wave propagation in heterogeneous media can provide a valuable source of information about the subsurface structure and its elastic properties. The processing of experimental seismic data sets related to the surface waves is computationally expensive and requires sophisticated techniques in order to infer the physical properties and structure of the subsurface from the bulk of available information. Most of the previous studies related to these problems are based on Fourier analysis. However, the frequency- dependent measurements, or time-frequency analysis offer additional insight and performance in any applications where Fourier techniques have been used. This analysis consists of examining the variation of the frequency content of a signal with time and is particularly suitable in geophysical applications. The continuous wavelet transform gives a suitable general framework for solving these types of problems; this approach is powerful and elegant, but is not the only available for the practical applications. Other methods such as the Gabor transform, the S-transform or bilinear transforms can be used as well. The relative performance of time-frequency analysis from different approaches is primarily controlled by the frequency resolution capability. To perform the time-frequency analysis of digital seismic data, we propose in this contribution a new free software package developed by the authors and based on the continuous wavelet transform. This package allows to perform the direct and inverse continuous wavelet transform, 2C and 3C polarization analysis and filtering, modeling the dispersed and attenuated wave propagation in the time-frequency domain and optimization in signal and wavelet domains. The aim of these operations is to extract polarization properties, velocities and attenuation parameters from a seismogram. The novelty of this package is that we incorporate the continuous wavelet transform into the library where the kernel is the time-frequency polarization and dispersion analysis. This library has a wide range of potential applications that we illustrate with the analysis of synthetic and real data.
UR: http://users.math.uni-potsdam.de/~gwl
DE: 0520 Data analysis: algorithms and implementation
DE: 0902 Computational methods: seismic
DE: 3280 Wavelet transform (3255, 4455)
DE: 3285 Wave propagation (0689, 2487, 4275, 4455, 6934)
DE: 7290 Computational seismology
SC: Seismology [S]
MN: 2007 Fall Meeting