3-D Forward Modeling of Semi-Airborne TEM Method With IP Effect Based on Goal-Oriented Adaptive Finite Element Algorithm

The coupling of induced polarization (IP) effects and electromagnetic induction significantly complicates the transient electromagnetic (TEM) diffusion, leading to serious distortion of the observed responses. In this article, we develop a 3-D forward modeling algorithm based on a goal-oriented adaptive finite-element method for the semi-airborne TEM method with IP effects to obtain high-precision simulation results. First, the Caputo fractional derivative is discretized by piecewise linear interpolation, and the Cole–Cole model is wholly introduced into the time-domain finite-element governing equation. Then, we simulate the semi-airborne TEM responses with IP effect directly in time domain by solving this governing equation. Because the Caputo fractional derivative depends on all historical information, it leads to a large storage and calculation. In order to solve this problem, we adopt the piecewise local time step discretization strategy to reduce the storage occupation and improve the computational efficiency. Finally, combined with the goal-oriented adaptive grid refinement technology, the forward modeling mesh is automatically optimized based on the weighted hybrid posterior error estimations. The accuracy of our codes is verified by comparing them with 1-D analytical solutions. We further simulate the electromagnetic responses of the polarizable body model with complex shape and topography to analyze the influence of the posterior error estimation method and the IP effects on the adaptive mesh.