Nonstationary wavelet simulation and estimation methods are closely related to nonstationary seismic modeling and nonstationary deconvolution. Conventional wavelet estimation and deconvolution do not deal with the nonstationarity of the wavelet. This thesis begins with an investigation of the methods for nonstationary wavelet simulation that can be used to generate realistic synthetic seismograms. Then this thesis examines methods of wavelet estimation using 1-D attenuated synthetic data and real data. These estimation approaches are the basis for Wiener deconvolution (time domain), Wiener deconvolution (frequency domain), and Gabor deconvolution. For comparison, the wavelet is also estimated from downgoing waves isolated from a VSP experiment which gives direct recordings of the nonstationary wavelet. Finally, a new approach is provided for evaluating the accuracy of the nonstationary wavelet estimates by the VSP downgoing wavelets. This result shows that the wavelets estimated from Gabor deconvolution are more stable and closer to the wavelet estimates from VSP data than those from multi-window Wiener and frequency-domain spiking deconvolution.
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