Sundararajan Transform - a tool to interpret potential field anomalies

Abstract

The equation of the Sundararajan transform is defined in relation to the Hilbert transform. It is to be emphasised here that the magnitude of the Hilbert transform and Sundararajan transform are one and the same with a phase difference of 270°. The transforms of these two versions of the gravity anomaly due to an inclined sheet of infinite depth extent and the vertical magnetic anomaly due to 2-D horizontal circular cylinder are derived. Interpretation of the gravity and magnetic anomalies with the use of the Sundararajan transform rather than the Hilbert transform is straightforward. It is interesting to note that these two transforms intersect exactly over the origin of the causative body. The point of intersection of the amplitudes of the analytic signal of these two versions also corresponds to origin of the body. A theoretical model illustrates the procedure in each case. The effect of random noise on the interpretative process is studied. Analysis of two field examples pertaining to (a) gravity anomaly across the Mobrun ore body and (b) magnetic anomaly over a narrow band of quartz magnetite deposit near Karimnagar, Andhra Pradesh, India shows the applicability of the method.