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. 2022 Dec 30;12:22578. doi: 10.1038/s41598-022-26265-0

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© The Author(s) 2022

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

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Inversion results of case 2 without the implementation of the SMA technique. (a) fittings between the pure residual magnetic anomaly and the responses obtained via BMO and sPSO, (b) the variation behavior of the mean RMSE values against iterations after 30 runs, (c) the variation behavior of the std of RMSE values against iterations after 30 runs, (d) calculated relative errors of model parameter solutions using BMO and sPSO for four causative sources. Error bars are given in (a) and (d).