Comparison of the different forward modeling formulations

What is it about?

Many different partial differential equations (PDE) can be used to obtain the 3D magnetotelluric forward modeling response. In this study, we compared the five different PDEs in terms of the accuracy and the solution speed of the respective linear systems. While comparing them, we considered the finite-difference numerical technique and the iterative Krylov space solvers.

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Why is it important?

3D inversion of the Magnetotelluric data is still a challenge even for this day. An efficient and fast forward solution directly affects the speed of an inversion. That is why picking and using the fastest forward modeling algorithm is crucial. In this study, we picked four different approaches that are available in the literature and also we offered one more approach that can be used for forward modeling. In the end, we compared five of them in terms of the solution speed and accuracy. We've found out that the potential formulation with no gauge conditions is applied can be solved with least amount of time. The newly proposed approach (axial gauged formulation) is the second when it comes to the solution speed. However, it has the least amount of non-zero entries in its stiffness matrix that makes it perfect candidate for the direct solution of the linear system.

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