A New Algorithm for Depth Determination from Total Magnetic Anomalies due to Spheres E. M. ABDELRAHMAN, 1 T. M. EL-ARABY, 1 E. R. ABO-EZZ, 1 K. S. SOLIMAN, 1 and K. S. ESSA 1 Abstract—We have developed an automatic method to determine the depth of a buried sphere from numerical second horizontal derivative anomalies obtained from total field magnetic data. The method is based on using a relationship between the depth and a combination of observations at symmetric points with respect to the coordinate of the projection of the center of the source in the plane of the measurement points with a free parameter (graticule spacing). The problem of depth determination has been transformed into the problem of finding a solution of a nonlinear equation of f(z) = 0. Procedures are also formulated to determine the magnetic moment and the effective angle of magnetization. The method is applied to synthetic examples with and without random errors and tested on a field example from Senegal. In all cases, the depth solutions are in good agreement with the actual ones. Key words: Magnetic interpretation, Sphere model, Second derivative method, Parametric relationship. 1. Introduction Estimating the depth of a buried sphere from total magnetic anomalies has drawn considerable attention. Several good standing graphical methods have been developed for interpreting the anomalous total magnetic field caused by spherical ore bodies (SMELLIE, 1956; RADHAKRISHNA MURTHY, 1974; RAO et al., 1977; RADHAKRISHNA MURTHY and BHASKARA RAO, 1978; BHASKARA RAO and RADHAKRISHNA MURTHY, 1979; RAM BABU et al., 1983; PRAKASA RAO and SUBRAHMANYAM, 1988). These methods use characteristic points, distances, curves, and monograms for interpretation. Moreover, several numerical methods have been reported in the geophysical literature to interpret magnetic anomalies due to spheres. Most of these methods use a parametric relationship (ABDELRAHMAN and HASSANEIN, 2000), a relationship between the depths to two co-axial sources (ABDELRAHMAN et al., 2002), a least-squares minimization approach (ABDELRAHMAN et al., 2003), and a least-squares depth-shape curves method (ABDELRAH- MAN and ESSA, 2005). However, these methods can be only applied to vertical or horizontal magnetic anomalies due spheres. 1 Geophysics Department, Faculty of Science, Cairo University, Giza, Egypt. E-mail: sayed5005@yahoo.com Pure appl. geophys. 165 (2008) 967–979 Ó Birkha ¨user Verlag, Basel, 2008 0033–4553/08/050967–13 DOI 10.1007/s00024-008-0340-x Pure and Applied Geophysics