Three-dimensional inversion of magnetotelluric data using Gauss-Newton method

The Gauss-Newton (GN) method has the advantage of quasi-second-order fast convergence in three-dimensional (3D) inversion of magnetotelluric (MT) data. However, this method faces two main challenges during implementation: the computation and storage of a Jacobian matrix, as well as the significant amount of memory and time required to solve the system of GN normal equations. To overcome these difficulties, we propose a sensitivity truncation criterion based on the footprint concept, which combines distance and normalized threshold. The sensitivity is stored in a sparse matrix form to significantly reduce memory usage. Transforming the GN normal equations into a least squares form and utilizing the sparse matrix least-squares QR factorization (LSQR) algorithm have reduced the time required to solve for the update direction. Simultaneously, parallel solving of the frequency and finite element coefficient matrices has further enhanced the inversion speed. The method has achieved good results in theoretical model numerical experiments.