Three-dimensional CSEM forward modeling using edge-based finite element method based on unstructured meshes and divergence correction

The iterative computation with a system of linear equations derived from the three-dimensional (3D) controlled-source electromagnetic(CSEM) forward modeling of the electric field equation suffers from slow convergence. Moreover, unstructured meshes can make the system of linear equations more ill-posed. In view of this, we propose an algorithm for finite element forward modeling based on unstructured tetrahedral meshes and divergence correction. Starting from the divergence equation of current density, we derive the corrected divergence equation of the potential on geo-electrical interfaces. Solving the system of linear equations is accelerated with the preconditioned quasi-minimal residual (QMR) method and the alternate divergence correction during the iteration. A three-layer medium model is subjected to the forward modeling under two conditions (with/without divergence correction) to verify the reliability of the proposed algorithm. The iterative convergence and the accuracy of numerical solution of the system of linear equations indicate that the divergence correction is effective to accelerate the iteration and improve the forward modeling accuracy. On this basis, a 3D geo-electric model is built, the electromagnetic response of which is employed for the comparison of numerical solutions between the proposed algorithm and the forward modeling based on the quadratic coupling potential equation. It further confirms the high accuracy of the algorithm in this study. The modeling of a complex oil and gas monitoring system demonstrates the application potential of the CSEM method in oil and gas monitoring. © 2021, Editorial Department OIL GEOPHYSICAL PROSPECTING. All right reserved.