Constrained least-squares spectral analysis: application to seismic data
This dissertation describes a new method called Constrained Least-Squares Spectral Analysis (CLSSA), an inversion-based algorithm for computing the time-frequency analysis of reflection seismograms. CLSSA is formulated and applied to modeled seismic waveforms and real seismic data. The Fourier Series coefficients are computed as a function of time directly by inverting a basis of truncated sinusoidal kernels for a moving time window. The method results in spectra that have reduced window smearing for a given window length relative to the Discrete Fourier Transform irrespective of window shape, and a time-frequency analysis with a combination of time and frequency resolution that is superior to both the Short-time Fourier Transform and the Continuous Wavelet Transform. The reduction in spectral smoothing enables better determination of the spectral characteristics of interfering reflections within a short window. The degree of resolution improvement relative to the Short-time Fourier Transform increases as window length decreases. As compared to the Continuous Wavelet Transform, the method has greatly improved temporal resolution, particularly at low frequencies.