Abstract: In the audio-frequency magnetotelluric (AMT) forward modeling, the conventional finite element method (FEM) is inherently constrained by the trade-off between computational accuracy and efficiency. To address this issue, this study proposes an adaptive finite element method  based on super convergent patch recovery (SPR). This method utilizes a posteriori error estimation to dynamically identify elements that require refinement, enabling robust local mesh optimization, and directly employs the high-accuracy recovered gradient values obtained from the SPR computation for auxiliary field calculation, thereby substantially enhancing the overall forward modeling precision. A series of systematic numerical experiments were conducted to comprehensively validate the algorithm’s accuracy and computational efficiency. First, comparative accuracy results with conventional FEM in horizontally layered media demonstrate that the  root mean square relative error is reduced to just 1.02% after five iterations, fully confirming its high precision. Second, in forward modeling of a composite high- and low-resistivity model, the apparent resistivity values progressively approach the true model resistivity as the iteration proceeds, verifying the algorithm's robust convergence behavior. Finally, simulations of complex geoelectrical structures confirm the algorithm’s strong adaptability to heterogeneous geological models models. The results conclusively show that the SPR-based posteriori error estimation method effectively identifies elements for refinement and significantly improves the accuracy of auxiliary field calculation, thus substantially elevating the accuracy of AMT forward modeling.

Key words: super convergent patch recovery, a posteriori error estimate, adaptive finite element method; , audio-frequency magnetotelluric  , forward modeling