Depth detection of magnetic bodies by using the analytic signal derivative

The analytic signal and its derivatives have been used in magnetic data interpretation such as estimation of the edge, depth and slope of the magnetic bodies for several years. Nabighian (1972, 1974, 1984) extensively described the principles of the analytic signal method for the location of the 2D sources. The analytic signal shape can be used to determine the depth of the magnetic sources. Atchuta et al (1981) used the anomaly width at half the amplitude to derive the depths. W. R. Roest and his collaborators used the 3D analytic signal amplitude to estimate the magnetic source depth (Roestetal.,1992) and to identify remanent magnetization (Roest and Pilkington, 1993). However, their applications and many conclusions are based on a 2D vertical- magnetic-contact model assumption. Further implementation of this technique was made by Hsu et al. (1996) who developed an enhanced analytic signal applied to a higher order vertical derivative of potential - field anomalies and thus providing a better visualization of the outlines of magnetic bodies. This enhanced analytic signal was adapted as an automatic interpretation tool (Debeglia and Corpel, 1997; Hsu et al. ,1998). Hsu et al, 1998 used the enhanced analytic signal to estimate the depth of step models and the thin dike. They also proposed an algorithm for the type of these models afterwards. Bastani and Pedersen (2001) have developed an algorithm for the automatic estimation of the source parameters, including the dip and susceptibility contrast, from the analytic signal in the case of magnetic profiles. Salem and Ravat (2003) proposed a combined method (AN-EUL) based on the Euler equation and the analytic signal. Li (2006) discussed a 3D analytic signal and proposed that, generally, in three dimensions, the analytic signal is dependent on everything that the total magnetic intensity (TMI) itself may depend on i.e. the direction of the inducing field, the direction of the remanent magnetization, the dipping angle of the source body, and the depths to the top and bottom of the source body.
    In this study, the equations of analytic signal and its derivatives were developed based on their effective parameters for contact, thin dikes and horizontal cylinder models. Afterwards, using the maximum value of the ratio of analytic signal and its derivatives, an equation for depth and structural index estimation was obtained which was exactly similar to the equations in the AN–EUL method. Then, assuming a priori knowledge about the shape of magnetic body, other equations were obtained for the depth detection of contact, thin dike and horizontal cylinder. To evaluate the precision of these methods, we have used a dike model with constant width located at deferent depths. In this modeling study, we proved that the estimated depth from the AN-EUL method was dependent on the depth-to-width ratio. Using the AN-EUL method, it is not possible to detect the depth of bodies with their depth-to-width ratio less than two. To solve this problem, we used proposed equations for different models. This method was used for the depth detection of the Aliabad iron deposit, and its results were compared to the results from drilling exploration data. The correlation coefficient between the exact depth and the estimated depth was equal to 85 percent.