TY - JOUR

T1 - Fourier-Hilbert versus Hartley-Hilbert transforms with some geophysical applications

AU - Sundararajan, N.

AU - Srinivas, Y.

PY - 2010/8

Y1 - 2010/8

N2 - 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.

AB - 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.

KW - Amplitude

KW - Analytic signal

KW - Hartley Hilbert transform

KW - Interpretation

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U2 - 10.1016/j.jappgeo.2010.06.005

DO - 10.1016/j.jappgeo.2010.06.005

M3 - Article

AN - SCOPUS:77955276302

SN - 0926-9851

VL - 71

SP - 157

EP - 161

JO - Journal of Applied Geophysics

JF - Journal of Applied Geophysics

IS - 4

ER -