Mathematical analysis of gravity anomalies due to an infinite sheet-like structure

Gravity anomalies caused by a thin infinite sheet are interpreted quantitatively based on an integral transform approach which is elegant and simple. The proposed technique depends on the modified Hilbert transform which is called “Sundararajan transform.” The amplitudes of the well-known Hilbert transform and Sundararajan transform are exactly the same but with a phase difference of 270° between them. The interpretation of gravity anomalies due to a thin infinite sheet has been implemented using the Sundararajan transform rather than the well-known Hilbert transform, yielding a straightforward solution. Parameters such as the depth to the top of the sheet (z), the inclination angle (θ), and the amplitude coefficient (K) have been analytically determined using simple mathematical equations. The origin of the causative target can be determined by the intersection point between Hilbert and Sundararajan transforms as well as the intersection point of the amplitudes of the analytic signal of the two transforms. The proposed technique has been first applied to synthetic data where the procedures are clearly illustrated. The effect of noise on the interpretation procedures of the proposed technique has been investigated, showing in general satisfactory results especially depth estimation. However, the most sensitive parameter to noise is the dipping angle, which can be misleading in high level of noise, whereas the least sensitive parameter is the depth. Strictly speaking, the noise does not significantly distort the depth estimation obtained with this proposed technique. Finally, the interpretation of the gravity anomaly across the Mobrun ore body, Noranda, Quebec, Canada, has been carried out using the proposed technique where the parameters are estimated and compared to the results that have been published in literatures using different techniques.