Multi-level down-sampling scheme for accelerated solution in magnetotelluric forward modelling

Abstract

The efficiency of the forward modelling procedure in three-dimensional electromagnetic methods is one of the keys of successful inversion applications, especially on small-scale computation platforms. To improve the computational efficiency, we propose a multi-level down-sampling algorithm based on finite difference method for accelerating the computation of electric fields. This scheme reduces the number of the discrete electric fields horizontally in the original grid to form a reduced electromagnetic system, without introducing coarser grids as in the multi-resolution methods. After the reduced electromagnetic system is solved, the fields abandoned in this scheme can be recovered with a simple interpolation operation. For maximum efficiency and accuracy, we propose a way to automatically determine the applicable down-sampling domain in a specific discrete model for a given period of the electromagnetic field. Additionally, we prove that the discretized derivatives for the electric fields are first-order accurate in our scheme. The scheme is verified by test cases with both synthetic and real-world three-dimensional models. The results show that the electromagnetic field calculated with our scheme is accurate compared to solutions from the standard staggered-grid scheme. An up to 35% acceleration is observed for high-frequency calculations in the real-world three-dimensional model test.