Comparison Study Of Different Formulations Used In 3D Magnetotelluric Modeling*

Abstract

In this study, different approaches to solve the magnetotelluric forward modelling problems are investigated. Beside classical direct electromagnetic (Direct EM) formulation, ungauged and gauged (Lorenz, Coulomb and axial) vector and scaler potential formulations are discretized using finite difference numerical solution technique. Linear matrix equations obtained from finite difference discretization for each EM field formulations are solved by using conjugate gradient iterative solution method. We compared finite different solutions of each approaches with respect to accuracy and speed. We showed that all approaches generate accurate result. However, ungauged approach gave solution with less number of CG iteration accordingly less CPU time. All stiffness matrices arising from each formulation are examined in terms of size and its type. Finite difference solution of the Coulomb gauge and ungauged approaches generates bigger size stiffness matrices than the other approaches’. Direct EM, ungauged, axial gauge approaches generates symmetric stiffness matrix. In this study, we suggest to use ungauged approach in inversion algorithms which gave fast forward solution amongst others