One-dimensional magnetotelluric inversion using levenberg-marquardt and particle swarm optimization algorithm

Magnetotelluric is a geophysical method which uses natural time variations of the Earth's magnetic and electric fields. One-dimensional magnetotelluric inversion was carried out to estimate the electrical resistivity distribution of rocks which varied with depth. Non-linear relationships between model parameters and observation data lead to difficulties in the inversion process. This problem can be solved with a non-linear inversion method with a global search technique. One of the global search technique that gaining interest in the inverse problem is Particle Swarm Optimization (PSO). PSO can find acceptable solutions from a very broad set of initial parameters. This study also carried out a non-linear local search technique, namely Levenberg-Marquardt (LM) which has been used globally for the geophysical problem. Then the two inversion algorithm was compared in determining the best model solution. There are two data used in this study which are generated from a three-layer model, namely data without noise and also data that has been added by Gaussian noise with 10% standard deviation. It was found that the results of the two inversions were quite good at determining the actual model. LM algorithm is an algorithm that is truly influenced by the initial value of the damping factor _ε² while PSO algorithm depends on several parameters, namely number of particles n, inertia weight w, cognitive parameter c₁ and social parameter c₂. Trial experiments suggested that the global best solution could be achieved with controlling parameters w_min = 0.4, w_max = 0.9, c₁ = 1.3 and c₂ = 1.5 without noise data and w_min = 0.7, w_max = 0.9, c₂ = 0.8 and c₂ = 1.4 for data with 10% noise.