Three-dimensional inversion of controlled-source electromagnetic data using general measures to evaluate data misfits and model structures

Abstract

Quantification of data misfits and model structures is an important step in the non-linear iterative inverse scheme, allowing medium parameters to be iteratively refined through minimization. This study developed a new three-dimensional controlled-source electromagnetic inversion algorithm that allows general measures to be made selectively available for this evaluation. We adopt ${\ell }_2$, ${\ell }_1$, Huber, hybrid ${\ell }_1$/${\ell }_2$, Sech, Cauchy, biweight and ${\ell }_0$ norms as general measures. The inversion implementation is based on a regularized Gauss–Newton method, and non-quadratic measures are incorporated via the use of an iteratively reweighted least-squares scheme. To exploit current computing power, forward solutions are computed on an edge finite-element discretization using a parallel version of a direct sparse solver, while dense matrix operations in inversion are optimized using the LAPACK library. The behaviours of general measures for evaluating data misfits and model structures are examined in synthetic inversion experiments, focusing on elucidating weighting mechanisms and setting user-defined parameters. A preliminary demonstration is presented, showcasing simultaneous regularization in imaging a toy model containing both sharp and smooth property changes, alongside a field data application for imaging subsurface artificial structures. Our findings highlight the seamless integration of general measures, contributing to improved robustness against data outliers and enhanced spatial properties provided in output models.