COMPARISON OF WALSH AND FOURIER SPECTROSCOPY OF GEOMAGNETIC REVERSALSAND NONSINUSOIDAL PALEOCLIMATIC TIME-SERIES

Higher resolving capabilities and theoretical appropriatness of Walsh spectral techniques as compared to fourier spectral analyses are prese nted for synthetic and nonsinusoidal geotime series. Walsh functions f orm a complete orthogonal set of rectangular wave-functions assuming o nly two amplitude values of +1 and -1 and possessing many other proper ties similar to Sine and Cosine functions. Theoretical developments of Walsh transform techniques and a comparative study of Walsh and Fouri er spectral estimates are presented. The Walsh spectral technique is a pplied specifically to two actual time series data of: (i) geomagnetic reversals in binary telegraphic wave form and (ii) nonsinusoidal pala eomagnetic and palaeoclimate time series. Walsh spectra reveal periodi cities in Milankovitch frequency bands and provide exceptionally well- resolved spectral lines. The possible physical significance of these o rbital periodicities are discussed. A comparative example of autocorre lation analysis in real time domain and dyadic time domain is also pre sented using a telegraphic signal model of actual geomagnetic reversal s time series and the result is briefly discussed. The computational e fficiency of the Walsh function could be exploited further for many ot her binary and nonsinusoidal geophysical/geological time series.