A goal-oriented adaptive finite-element method for 3D scattered airborne electromagnetic method modeling

We have developed a goal-oriented adaptive unstructured finite-element method based on the scattered field for 3D frequency-domain airborne electromagnetic (AEM) modeling. To guarantee the EM field divergence free within each element and the continuity conditions at electrical material interfaces, we have used the edge-based shape functions to approximate the electrical field. The posterior error for finite-element adaptive meshing procedure is estimated from the continuity of the normal component of the current density, whereas the influence functions are estimated by solving a dual forward problem. Because the imaginary part of the scattered current is discontinuous and the real part is continuous, we use the latter to estimate the posterior error. For the multisources and multifrequencies problem in AEM, we calculate the weighted posterior error for each element by considering only those transmitter-receiver pairs that do not adhere to our convergence criteria. Finally, we add a minimum volume constraint to improve the stability of the adaptive procedure. To check the accuracy, we compared our adaptive results with the semianalytical solutions for AEM systems over a half-space model. To test the effectiveness of our algorithm for multiple sources and multiple frequencies of AEM, we analyzed meshes for separate frequencies and for combined frequencies. Finally, we calculated the AEM responses over a hill model with and without embedded abnormal bodies to prove the feasibility of our algorithm for AEM variable topography modeling.