A Constrained Nonlinear Programming Technique for Interpretation of Self-Potential Anomalies due to Two- Dimensional Inclined Sheets of Finite Depth Extent

A new and simple method based on constrained nonlinear programming concepts is being proposed in this research to interpret the self-potential (SP) anomaly due to two-dimensional inclined sheets of finite depth extent. A constrained nonlinear model has been formulated to describe the geophysical problem related to this buried inclined structure. Thereafter this model has been solved by the famous Frank and Wolfe algorithm in order to estimate the geophysical parameters of the modeled sheets which are: the depth of upper and lower edges h and H, inclination angle θ, and electrical dipole moment k. This algorithm is chosen for being robust and also because its application to SP data converges rapidly towards the optimal estimation of parameters. To prove the efficiency of this new constrained nonlinear programming technique, three theoretical models with a random noise of 2% have been studied, and as a result, a very close and satisfactory agreement has been obtained between the assumed and evaluated parameters. The validity of this new proposed method is tested on a practical field example from India, where available SP data existed and has been previously analyzed by a spectral analysis approach. Moreover, a statistical analysis has been carried out to confirm the superiority of this method in comparison with that suggested by Atchuta et al. (1982). All acquired results indicate clearly its precision and accuracy. The advantages of the proposed technique have also been discussed and demonstrated comparing them with other published interpretative techniques.