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A Robust Approach for Geo-Electromagnetic Sounding Data Inversion Using l1-Norm Misfit and Adaptive Moment Estimation | IEEE Journals & Magazine | IEEE Xplore

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


Abstract:

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 e...Show More

Abstract:

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.
Article Sequence Number: 5913612
Date of Publication: 02 May 2024

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