An iterative algorithm for estimating and accounting for 3D TEM modeling errors in 1D inversion

Systematic modeling errors arising from incomplete forward modeling theory in transient electromagnetic (TEM) inversion, such as using a 1D forward model to interpret data from inherently 3D subsurface structures, bias inversion results. It is difficult to identify these errors as erroneous 1D models often fit the data within the assumed noise level. A solution is to perform the inversion in a full 3D framework. However, 3D inversion is constrained by several challenges, such as a high demand for computational resources and increased regularization requirements. These challenges typically result in simplistic or smooth inversion models, the exclusion of probabilistic approaches, and an inability to handle complex prior information. We present an algorithm that iteratively refines a nonlinear estimate of the 3D modeling error, enabling the continued use of flexible 1D TEM inversion schemes, such as Bayesian inversion with complex priors, even in the presence of 3D effects. The algorithm iteratively refines an estimate of the error by projecting the inversion model onto a coarse 3D mesh and simulating a 3D response. By simulating data for the corresponding laterally homogenous (1D) model, the 3D error can be estimated and used to correct the data. We test the algorithm on synthetic 3D TEM data, inverted using a 1D probabilistic framework while using the median posterior model for the error estimate. We also present a test on a real airborne TEM dataset from Denmark, and in both synthetic and real tests we use the residual between the observed data and the 3D response of the projected inversion model as a quantitative performance measure.  The results show that the algorithm consistently improves the agreement between observed and simulated 3D data while also either removing or significantly dampening 3D artifacts in the final 1D inversion model. This iterative approach provides a solution that is otherwise typically provided by full 3D inversion, while preserving the advantages of 1D frameworks and with promising implications for improved interpretability of 3D structures in 1D inversion frameworks.