Three-dimensional Land FD-CSEM Regularized Inversion Based on Edge Finite-element Method

There is a desire to obtain rapid and stable inversion results and clearly reconstruct subsurface resistivity structure in frequency domain (FD) electromagnetics. Three-dimensional modeling of land FD controlled-source electromagnetic (CSEM) data is vital to improve the understanding of electromagnetic responses collected in increasingly complex geologic settings. Three-dimensional inversion of land FD-CSEM data is a mathematically non-unique problem with instability, due to the noise contained in the data and its inherent incompleteness. The main difference between our method and those from previous work is that the edge finite-element approach is applied to solve the three-dimensional FD-CSEM generated by a horizontal electric dipole source. Firstly, we formulate the edge finite-element equation through the Galerkin method, based on the Helmholtz equation of the electric fields. Secondly, in order to check the validity of the modeling code, we compare the numerical results with the analytical solutions for a homogeneous half-space model. For further tests, we calculate the electromagnetic responses for another two models with more practical structures. Finally, the three-dimensional inversion is carried out based on a regularization method with smoothness-constraints to obtain stable solutions.