Gauss-Newton with preconditioned conjugate gradient magnetotelluric inversion for 3D axial anisotropic conductivities

We present a regularized inversion method for three-dimensional (3D) magnetotelluric (MT) data with axial anisotropic conductivities based on the edge-based finite element (FE) method. The Gauss–Newton (GN) approach is used to minimize the inversion objective function. To speed up the inversion calculation, a hybrid direct–iterative solver combined with a block-diagonal preconditioner that has not yet been applied in anisotropic inversion is developed to accelerate the solutions for the sparse linear system resulting from forward modeling and sensitivity computations. In each GN iteration, a preconditioned conjugate gradient (PCG) method is adopted to overcome the difficulty of the sensitivity matrix storage for the anisotropic scene and obtain a model update without explicitly calculating and storing the sensitivity matrix. Numerical experiments illustrate the effectiveness of the inversion method.