A Least-squares Approach to Shape Determination from Residual Self-potential Anomalies

We have developed a least-squares minimization approach to determine the shape (shape-factor) of a buried polarized body from a residual self-potential anomaly profile. By defining the zero anomaly distance and the anomaly value at the origin on the profile, the problem of the shape-factor determination is transformed into the problem of finding a solution of a nonlinear equation of the form f(q) 0. Procedures are also formulated to estimate the depth of polarization angle, and the electric dipole moment. The method is applied to synthetic data with and without random noise. The obtained shape-factor agrees very well with the model shape-factor when using synthetic data. After adding 92 percent random error in the synthetic data, the shape factor obtained is within 94 percent. Finally the validity of the method is tested on a field example from the Ergani copper district, Turkey.