Several graphical, and numerical methods have been developed to interpret SP anomalies including curve matching, characteristic points, least-squares, derivative and gradient analysis, nonlinear modeling, and Fourier analysis techniques. Examples of such techniques used for interpreting the self-potential anomalies of horizontal and vertical cylinders, spheres, sheets and geological contacts are classified as follows.

(1) Methods using only a few points on the anomaly curve. These were originally developed by\ DeWitte (1948),\ Y{\"u}ng{\"u}l (1950),\ Paul (1965),\ Paul et al. (1965),\ Bhattacharya and Roy (1981),\ Atchuta Rao and Ram Babu (1983). The essential disadvantage of these methods was related to the fact that only a few points are used on the anomaly curve, and hence, the interpreted results are not reliable.

(2) Curve matching techniques. According to\ Meiser (1962),\ Satyanarayana Murty and Haricharen (1985), the field curve is compared with sets of theoretical curves either manually or using a computer. This process is cumbersome and the complexity of the method is very high especially when the variables are numerous.

(3) Least-squares methods. Here, the model parameters that give a best fit are derived using an initial presumption, as well as characteristic points and distances from the measured anomaly curve. Examples of these methods are of\ Abdelrahman and Sharafeldin (1997),\ [Abdelrahman et al., 1997b]\ and\ [Abdelrahman et al., 2003].

The above-mentioned three categories have the disadvantage of using characteristic points, distances, curves, and nomograms for interpretation, which is subject to human error in estimating these few points and distances, especially if they are derived by interpolation procedure. This can consequently lead to errors in derived parameters. Moreover, some of these methods demand knowledge of the anomalous body shape, and based on the interpreter{\textquoteright}s choice, the results could vary a lot.

(4) Methods using derivative analysis and gradients. Namely those of\ [Abdelrahman et al., 1997a],[Abdelrahman et al., 1998a],\ [Abdelrahman et al., 1998b]\ and\ [Abdelrahman et al., 2003]\ belong to this category.

(5) Methods using Fourier analysis and the wave number domain. Particularly those of\ Atchuta Rao et al. (1982)\ and\ Roy and Mohan (1984)\ belong to this group.

(6) Modeling and Inversion Methods such as those given by\ Guptasarma (1983),\ Furness (1992), and\ Shi and Morgan (1996).

The last three categories are greatly influenced by noise in measured data and can lead to serious errors.

}, month = {2004}, pages = {211 - 224}, abstract = {A least-squares minimization approach to determine the shape of a buried polarized body from a self-potential (SP) anomaly profile has been developed. By defining the anomaly value at three points on the profile, one at the origin and the others at any two symmetrical points around the origin, the problem of the shape-factor determination is transformed into the problem of finding a solution of a nonlinear equation. Procedures are also formulated to complete the quantitative interpretation by finding the depth, polarization angle, and the electric dipole moment. The validity of the new proposed method has been tested on synthetic data with and without random noise. The obtained parameters are in congruence with the model parameters when using noise free synthetic data. After adding {\textpm}5\% random error in the synthetic data, the maximum error in model parameters is less than {\textpm}5\%. Moreover, when error in profile origin position determination is studied, the method is approved to be not sensitive to it. Two oft cited field examples from Turkey have also been analyzed and interpreted by the proposed method, where an acceptable agreement has been noticed between the obtained results and other published results. The present method has the capability of avoiding noisy data points and enforcing the incorporation of points free from random errors to enhance the interpretation results.}, keywords = {Interpretation, Least-squares, Model parameters, Noise, self-potential, shape-factor}, isbn = {0926-9851}, url = {http://www.sciencedirect.com/science/article/pii/S0926985103001447}, author = {El-Araby, Hesham M.} }