Three-dimensional inversion of semi-airborne electromagnetic data with a second-order finite-element forward solver

The analysis of controlled-source electromagnetic (EM) data recorded with semi-airborne exploration systems requires advanced simulation and inversion tools that are capable of handling realistic survey geometries. Semi-airborne EM setups with elongated transmitters deployed in mountainous terrain prohibit the exploitation of secondary-field formulations in numerical approximations without producing hardly quantifiable errors. Building upon the open-source software custEM for forward modeling and pyGIMLi for geophysical inversion, we present an inverse modeling procedure based on highly accurate second-order finite-element forward solutions on irregular grids and fast-converging-Gauss-Newton minimization. Using the total-field formulation of the electric field approach in combination with a direct solver enables calculating explicit sensitivities with comparatively cheap back-substitutions for thousands of ground and airborne receiver stations in multiple flight areas. Second-order basis functions show general superiority over first-order basis-functions regarding the accuracy and performance of the forward problem. Beyond that, synthetic and real data inversion studies related to semi-airborne geometries indicate that second-order basis functions help particularly to avoid high modeling errors for the weakest field components and artifacts in the vicinity of transmitters or at the surface. This leads generally to a better convergence and final inversion results of higher robustness and quality. The presented tools are freely available such as the underlying software.