A Robust Approach for Geo-Electromagnetic Sounding Data Inversion Using l1-Norm Misfit and Adaptive Moment Estimation

The choice of data misfit measure has a great impact on the convergence of electromagnetic (EM) inversion. The conventional measure based on the
$l_{2}$
-norm tends to excessively amplify the weights of a larger misfit, inadvertently neglecting data with a smaller misfit during the inversion process, thereby diminishing the resolution to a certain degree. To solve this problem, we propose a robust inversion strategy based on
$l_{1}$
-norm data misfit and adaptive moment estimation (Adam). In this scheme, we use the Ekblom-type
$l_{1}$
-norm to simplify the derivative computation of the absolute value function. The Adam algorithm is further applied to optimize this type of non-smooth objective function, which incorporates momentum terms and adaptive steps, allowing it to better adapt to the irregularities in gradient changes. The inversion results obtained from both synthetic models and field measurements demonstrate that the Adam method performs considerably better than the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method for optimizing the
$l_{1}$
-
$l_{2}$
norm of the objective function. Compared with the conventional
${l} _{2}$
-norm data misfit, the
$l_{1}$
-norm data misfit can effectively avoid excessive optimization of data with large misfits and achieve high-resolution inversion results.