A goal-oriented adaptive algorithm for 3D magnetotelluric forward modeling

Magnetotelluric (MT) exploration has been widely used in geological survey, mineral and oil and gas exploration, and the research on deep structures of the earth. With the models in the MT method becoming more and more complicated, conventional modeling methods based on structured grids cannot satisfy the accuracy requirement. To better simulate the complex earth, we adopt unstructured grids in the MT modeling. Since an effective mesh can greatly improve the modeling accuracy and save the cost, we present a goal-oriented unstructured adaptive finite element method for MT modeling. Starting from the frequency-domain Maxwell's equations, a vector Helmholtz equation is obtained for a stable solution with existing air. We use the Galerkin method to discretize the Helmholtz equation. The continuity condition for normal current density is used to evaluate the posterior error, while the weighted coefficient is obtained by solving a dual forward modeling problem. Besides, we multiply the weighted coefficients proposed by previous researches by the conductivity that proves to be more effective for grid refinement. Finally, we define a convergence rule to determine receivers used to calculate the weighted coefficients in the next refinement. The response of a homogeneous half-space model is simulated by both the goal-oriented and global adaptive finite element methods to verify the accuracy and to demonstrate advantages of our goal-oriented adaptive method over the global one. We further calculate MT response for a classical model to check the effectiveness of our method on topography models. Then, we calculate the response for a topographic model with an abnormal body embedded to demonstrate that our method can not only refine meshes near the source on the topographic earth surface but also refine meshes on physical interfaces between the abnormal body and surrounding medium. From the adaptive meshes and modeling results we can draw the following conclusions: 1) Our goal-oriented adaptive finite-element algorithm for MT modeling can obtain higher accuracy with less grids in comparison to the global method. 2) Our algorithm is effective for MT topographic modeling. 3) The algorithm presented in this paper can not only effectively refine the meshes close to the topographic surface with receivers, but also refine the meshes near the abnormal body in the earth. 4) The improved weighted coefficient is more effective than the traditional one in terms of grids refinement.