UBC Theses and Dissertations
Applications of prolate spheroidal function theory to geophysical data processing Rodríguez, José Antonio
Because signals that are simultaneously concentrated in time and frequency are common in geophysics, it is desirable to develop a set of basis functions with these properties to perform various types of data processing. The Prolate Spheroidal Functions (PSF's) form a complete orthonormal set, and the low-order PSF's span the space of functions which are simultaneously concentrated in time and frequency. In this study, the PSF's are utilized in three different data processing problems: spectrum estimation, signal-to-noise ratio enhancement, and wavelet estimation. All three problems are related by functions which are approximately time- and bandlimited: data tapers for spectrum estimates, time- and bandlimited signals, and seismic wavelets can all be expressed as linear combinations of the low-order PSF's. Some of the results obtained by applying the PSF's to solving these problems are encouraging. In the problems of spectrum estimation and wavelet estimation in particular, the PSF's seem to extract much of the information present in the data. The application of PSF's to solving problems in geophysical data procesing should be the focus of further research in the future.
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