A hybrid optimization scheme for self-potential measurements due to multiple sheet-like bodies in arbitrary 2D resistivity distributions

Self-potential is a passive geophysical method that can be applied in a straightforward manner with minimum requirements in the field. Nonetheless, interpretation of self-potential data is particularly challenging due to the inherited non-uniqueness present in all potential methods. Incorporating information regarding the target of interest can facilitate interpretation and increase the reliability of the final output. In the current paper, a novel method for detecting multiple sheet-like targets is presented. A numerical framework is initially described that simulates sheet-like bodies in an arbitrary 2D resistivity distribution. A scattered field formulation based on finite differences is employed that allows the edges of the sheet to be independent of the grid geometry. A novel analytical solution for two-layered models is derived and subsequently used to validate the accuracy of the proposed numerical scheme. Lastly, a hybrid optimization is proposed that couples linear least-squares with particle-swarm optimization in order to effectively locate the edges of multiple sheet-like bodies. Through numerical and real data, it is proven that the hybrid optimization overcomes local minimal that occurs in complex resistivity distributions and converges substantially faster compared to traditional particle-swarmoptimization.