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Spectral analysis of digitized seismic data

THE GEOTECHNICAL CORPORATION, 3401 SHILOH ROAD, GARLAND, TEXAS

Abstract

Techniques of spectral analysis used for digitized data are discussed in this article from a nonstatistical viewpoint. By a generalization of the theory of linear equations and a truncation of Fourier series, a unique relationship similar to the Fourier Transform Theorem for continuous functions can be derived. Application of this theorem to Fourier series shows how aliasing of frequency occurs. Further application to digitized Fourier transforms indicates loss of aperiodicity in general. Depending upon the choice of fundamental frequencies, we will be able to perform data stacking. Some simple examples shown in the text reveal dependence of phase spectra on different modes of digitization. The phenomenon is associated with analysis of discontinuous functions by a digital method. Only deterministic investigations are conducted in this article.

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