MTAINV3D: A Three-dimensional Adaptive Magnetotelluric Inversion Tool Using Unstructured Grids

Abstract

Currently, 3D magnetotelluric inversion often uses a fixed inversion grid. Too sparse inversion grids cannot approximate the complex subsurface conductivity distribution, and may also lead to inversion results failing to converge. Too dense inversion grids will increase not only the computational cost, but also the non-uniqueness of the inversion. Aiming at the above problems, we have developed a three-dimensional magnetotelluric adaptive inversion strategy with unstructured finite element and limited memory BFGS (L-BFGS) algorithms. Firstly, based on the unstructured finite element method, the high accuracy forward responses of the 3D geo-electric model with arbitrary complex terrain and conductivity distributions can be obtained. Then, the forward and inversion meshes are decoupled by using the nested forward and inversion tetrahedral meshes. The Thikhonov regularization objective function with smooth constraints is established and minimized by L-BFGS optimization algorithm with inexact line search procedure, where the gradient of the objective function is solved by using the adjoint principle. Most importantly, an inversion grid adjustment strategy based on the dual constraints of sensitivity matrix and model gradient is proposed, which are used to guide the automatic refinement of inversion grid in the optimization process. Finally, a topographic model is used to validate and test the performance of the proposed adaptive inversion algorithm.