Fourier-Hilbert versus Hartley-Hilbert transforms with some geophysical applications

N. Sundararajan, Y. Srinivas

Research output: Contribution to journalArticle

16 Citations (Scopus)

Abstract

An intimate mathematical relation between Hartley and Hilbert transforms is given here in contrast with the well known Fourier and Hilbert transform relations. It is interesting to note that the Fourier-Hilbert and Hartley-Hilbert transforms while possessing the same magnitude differ in phase by 270°. The inverse Hartley-Hilbert transform returns the original function unlike the Fourier-Hilbert transform which results the negative of the original function. Further, it may be realized that the envelope defined here of the analytic signal in both Fourier-Hilbert and Hartley-Hilbert domains numerically remain the same while differing in polarity. The feasibility of Hartley-Hilbert transform for a straight forward interpretation, total magnetic anomaly due to a thin plate from Tejpur, India and self potential data of the Sulleymonkey anomaly in the Ergani Copper district, Turkey are illustrated in contrast with the Fourier-Hilbert transform. This pair of transforms have innumerable geophysical applications.

Original languageEnglish
Pages (from-to)157-161
Number of pages5
JournalJournal of Applied Geophysics
Volume71
Issue number4
DOIs
Publication statusPublished - Aug 2010

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Keywords

  • Amplitude
  • Analytic signal
  • Hartley Hilbert transform
  • Interpretation

ASJC Scopus subject areas

  • Geophysics

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