Two transforms (the Gabor transform, based on the Fourier transform, and the wavelet transform) are investigated and employed to achieve an increased temporal resolution of the seismic data. Unlike the Fourier transform, which maps a time series into a totally abstract domain, called the frequency domain, or the Fourier domain, the Gabor transform maps the time series into a joint time-frequency domain, called the Gabor domain. The Gabor domain, is suitable to analyze the data simultaneously in time and frequency, and to design, test, and evaluate new processing techniques. The hyperbolic smoother designed in the Gabor domain represents the main achievement of this thesis. It is shown that the Gabor deconvolution with the hyperbolic smoother successfully corrects the seismic data for the effects of anelastic attenuation and source signature, and effectively restores the relative amplitudes.
Two methods of using the wavelet transform in seismic signal analysis are also investigated in this research. The wavelet transform spectral whitening technique is a method introduced and investigated for the first time, similar to the classical time variant spectral whitening method. The second method, the wavelet transform filtering by semblance weighting, represents also a new technique, which demonstrates that the wavelet domain is suitable for suppressing random noise and enhancing the resolution of subtle stratigraphic features.
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