Date of Award
J. E. Murphy
Two-dimensional power spectral estimation is an important tool for seismic data analysis and other applications. Some datasets, however, have a limited number of points in one or both dimensions. In seismic applications, there are typically fewer points in the spatial domain as compared to the temporal domain. Conventional spectral estimation techniques suffer from poor resolution on short datasets due to inherent smoothing or bias.
Ramaswamy and loup developed a one-dimensional method for the estimation of power spectra for short datasets. Constrained Iterative Spectral Deconvolution (CISD) greatly improves the power spectral resolution using a straight-forward algorithm. In a comparison to other techniques, CISD is shown to perform very well on a standard 1-D dataset.
Two modifications to the CISD method are introduced that enhance its performance. A simple modification to the algorithm, the inclusion of a relaxation parameter, speeds convergence by a factor of two. Another modification use an equivalent window to calculate multiple iterations between constraint applications. This enhancement did not improve convergence.
A method was developed that compensates the CISD technique for missing samples in the dataset. This promises to be of great practical value to real datasets. This method is demonstrated on both model and real datasets.
Finally, the CISD method is extended to the two-dimensional case, incorporating both modifications. This algorithm performs very well on a synthetic dataset and on real data from a downhole sonic tool. FORTRAN subroutines are given that implement the modified Constrained Iterative Spectral Estimation technique in both one and two dimensions.
Coggins, Jerome Leslie, "Two Dimensional Power Spectral Estimation Using Constrained Iterative Spectral Deconvolution" (1993). University of New Orleans Theses and Dissertations. 2821.