An Approach for Interpretation of Self-Potential Anomalies due to Simple Geometrical Structures Using Fair Function Mini
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Pure and Applied Geophysics
An Approach for Interpretation of Self-Potential Anomalies due to Simple Geometrical Structures Using Fair Function Minimization M. TLAS1 and J. ASFAHANI1 Abstract—A quantitative interpretation method of self-potential field anomalies has been proposed. The method is designed and implemented for the estimation of center depth, electric dipole moment or magnitude of polarization, polarization angle, and geometric shape factor of a buried body from SP field data, related to simple geometric structures such as cylinders, spheres and sheetlike bodies. The proposed method is based on Fair function minimization and also on stochastic optimization modeling. This new technique was first tested on theoretical synthetic data randomly generated by a chosen statistical distribution from a known model with different random noise components. Such mathematical simulation shows a very close agreement between assumed and estimated model parameters. Being theoretically proven, it has been applied and tested on self-potential field data taken from the United States, Germany, India and Turkey. The agreement between results obtained by the suggested method and those obtained by other previous methods is good and comparable. Moreover, the depth obtained by this method is found to be in high accordance with that obtained from drilling information. Key words: Self-potential anomaly, fair function, stochastic optimization, logarithmic penalty function, inversion of self-potential field anomaly.
1. Introduction The self-potential ðSPÞ method is one of the oldest methods and has wide applications in sulphides and graphites exploration and in geophysical groundwater investigations. The interpretation methods of SP anomalies are not yet very well developed. However, the quantitative interpretation of SPanomalies is usually carried out by approximating the causative source by simple geometrically shaped models (viz, sheet, cylinder, sphere, etc.). According to this simplified concept, different interpretation techniques are
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Atomic Energy Commission, P. O. Box 6091 Damascus, Syria. E-mail: [email protected]
available in the literature for the quantitative interpretation of SP anomalies. The methods proposed by YUNGUL (1950), PAUL (1965) and BHATTACHARYA and ROY (1981) use certain characteristic points of the anomaly and hence they turned out to be less reliable in most cases. The curve-matching method proposed by MEISER (1962) is cumbersome, especially when there are many parameters to be determined. The method of least squares (SHALIVAHAN et al. 1998; ABDELRAHMAN et al. 1997; ABDELRAHMAN and SHARAFELDIN 1997) involves a series of trials in minimizing the differences between the observed and the calculated values. The interpretation made by methods based on Fourier and Hilbert transforms (ATCHUTA et al. 1982) and (SUNDARARAJAN et al. 1990, 1996, 1998) are not straightforward and are subject to some inevitable errors in the estimation of the parameters, due to the inaccurate estimation of horizontal location
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