Application of BICGSTAB algorithm with incomplete LU decomposition preconditioning to two-dimensional magnetotelluric forward modeling

Based on the finite element method of quadratic interpolation in a rectangular element to solve the two-dimensional magnetotelluric forward problem, no-uniform mesh based magnetotelluric responses calculation formula was derived. Based on the fact that the finite element method was used to form a linear equation, and the coefficient matrix was a large sparse, banded, symmetric, conditioned and complex matrix, its condition number is far larger than 1, and it was an ill-conditioned matrix, solving large scale ill-conditioned linear equation was very difficult, and so the BICGSTAB (Bi-conjugate gradient stabilized method) algorithm with incomplete LU decomposition for preconditioning was used to solve this system linear equation. This approach was verified through the calculations of layered earth model and two-dimensional earth model. The results show that the BICGSTAB algorithm has high speed, high precision and stability. The apparent resistivity curves and the impedance phase curves are very accurate to synthetic magnetotelluric responses.