The joint application of metaheuristic algorithm and Bayesian Statistics approach for uncertainty and stability assessment of nonlinear Magnetotelluric data

Abstract. In this paper, we have developed the Matlab code for a weighted hybrid of particle swarm optimization (PSO) and gravitational search algorithm (GSA) known as wPSOGSA, GSA, and PSO algorithms to interpret one-dimensional magnetotelluric (MT) data for some corrupted and non-corrupted synthetic data, as well as two examples of MT field data over different geological terrains: (i) geothermal rich area, Island of Milos, Greece, and (ii) Southern Scotland due to the occurrence of a significantly high electrical conductivity anomaly under crust and upper mantle extending from the Midland Valley across the Southern Uplands into northern England. Even though the fact that many models provide a good fit in a large predefined search space, specific models do not fit well. As a result, we used a Bayesian statistical technique to construct and assess the posterior probability density function (PDF) rather than picking the global model based on the lowest misfit error. This is proceeded by 68.27 % confidence interval for selecting a region where PDF is more prevalent to estimate the mean model which is more accurate and close to the true model. For illustration, correlation matrices show a significant relationship among layer parameters. The findings indicate, the wPSOGSA is less sensitive to model parameters and produces well, more stable and reliable results with the least uncertainty in the model that is compatible with existing borehole samples. Furthermore, the present methods resolve two additional geologically significant layers, one highly conductive (less than 1.0 Ωm) and another resistive (300.0 Ωm) over the Island of Milos, Greece, characterized by alluvium and volcanic deposits, respectively, as corroborated by borehole stratigraphy.