Abstract

Spectral analysis is a very useful technique for studying geophysical problems. In earlier days, the only methods available were those of Fourier analysis or the method of Blackman and Tukey (1959) based on autocorrelation function. Recently, Burg (1967, 1968) introduced maximum entropy spectral analysis (MESA) which gives good resolution even for periods comparable to the data length. Ulrych and Bishop (1975) gave a critical appraisal of Burg’s algorithm. Several workers noticed and reported some inherent shortcomings. Thus, Chen and Stegan (1974) showed that, for truncated sinusoids, the spectral maxima showed frequency shifts sometimes as large as 20 percent, depending upon the initial phase and the length of the sample. Also, under certain conditions, the Burg spectra display line-splitting in the presence of low noise, and as the noise is increased, the multiple peaks coalesce into a single peak shifted substantially away from the correct value (Fougere et al, 1976; Fougere, 1977). These defects can be rectified by the elaborate computer program given by Fougere (1977). Another difficulty is in selection of the appropriate length of the prediction error filter (LPEF). Whereas low LPEF is generally inadequate to resolve all the peaks, high LPEF, while resolving all peaks, produces instability in the spectra and gives spurious peaks. For determining the optimum LPEF, Ulrych and Bishop (1975) suggested the use of the Akaike’s (1969) final prediction error (FPE) criterion. And if this failed, an LPEF of about 50 percent of the data length was suggested to be generally adequate. Gutowski et al (1978) suggested the use of partial correlation coefficient. Berryman (1978) suggested an empirical solution LPEF = 2N/(ln 2N) where N = number of data points. Our experience (Kane 1977, 1979) indicated that for samples containing peaks in a wide range of frequency LPEF of about 50 percent of data length was adequate to resolve frequencies exceeding the fifth harmonic, while for lower harmonics, LPEF even as high as 90 percent was sometimes needed, with the danger of peak-splitting ever present.

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