A very fast simulated annealing (VFSA) global optimization is used to interpret residual gravity anomaly. Since, VFSA optimization yields a large number of best-fitted models in a vast model space; the nature of uncertainty in the interpretation is also examined simultaneously in the present study. The results of VFSA optimization reveal that various parameters show a number of equivalent solutions when shape of the target body is not known and shape factor ‘q’ is also optimized together with other model parameters. The study reveals that amplitude coefficient k is strongly dependent on shape factor. This shows that there is a multi-model type uncertainty between these two model parameters derived from the analysis of cross-plots. However, the appraised values of shape factor from various VFSA runs clearly indicate whether the subsurface structure is sphere, horizontal or vertical cylinder type structure. Accordingly, the exact shape factor (1.5 for sphere, 1.0 for horizontal cylinder and 0.5 for vertical cylinder) is fixed and optimization process is repeated. After fixing the shape factor, analysis of uncertainty and cross-plots shows a well-defined uni-model characteristic. The mean model computed after fixing the shape factor gives the utmost consistent results. Inversion of noise-free and noisy synthetic data as well as field data demonstrates the efficacy of the approach

A very fast simulated-annealing (VFSA) global optimization procedure is developed for the interpretation of self-potential (SP) anomaly measured over a 2D inclined sheet-type structure. Model parameters such as electric current dipole density (k), horizontal and vertical locations of the center of the causative body (x0 and h), half-width (a), and polarization/inclination angle (α) of the sheet are optimized. VFSA optimization yields a large number of well-fitting solutions in a vast model space. Even though the assumed model space (minimum and maximum limits for each model parameter) is appropriate, it has been observed that models obtained by the VFSA process in the predefined model space could also be geologically erroneous. This offers new insight into the interpretation of self-potential data. Our optimization results indicate that there exist at least two sets of solutions that can fit the observed data equally well. The first set of solutions represents a local optimum and is geologically inappropriate. The second set of solutions represents the actual subsurface structure. The mean model estimated from the latter models represents the global solution. The efficacy of the developed approach has been demonstrated using various synthetic examples. Field data from the Surda area of Rakha Mines, India and the Bavarian woods, Germany are also interpreted. The computation time for finding this versatile solution is very short (52 s on a simple PC) and the proposed approach is found to be more advantageous than other approaches.