Abstract
The aim of this work is to investigate whether retrieving the model parameters of self-potential (SP) anomalies using a combination of differential evolution (DE) and particle swarm optimization (PSO) is possible. This approach hybridizes DE and PSO in a parallel way. Each algorithm is self-contained and obtains a [premature] solution after a user-defined generation number. This hybrid algorithm (DE/PSO) selects the best individual in DE and PSO populations and carries it to the next iteration. Cooperation of DE and PSO can significantly improve the results. Simulations through noise-free synthetic anomalies show that the DE/PSO hybrid algorithm is successful in providing more accurate solutions than those obtained using each single metaheuristic. The algorithm also speeds up the rate of convergence to get the optimum solution. We implemented the algorithm in R programming environment using available metaheuristics packages. Then, the reliability of the code was investigated using some mathematical test functions having two and higher dimensions (unknowns). The performance of the hybrid to invert SP anomalies was tested by synthetic and field data sets. The true model parameters were well-recovered from synthetic data sets including noise-free and noisy data. In the tests with field data, SP anomalies over a shallow ore deposit in Süleymanköy (Türkiye), a deep ore deposit in Arizona (USA), and multiple sources of graphite deposits in KTB borehole site (Germany) were inverted. Low misfit values between the observed and calculated SP anomalies were obtained during the test studies.
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Data availability
The synthetic data (noise-free, and noisy) highlighted in this article will be shared by the corresponding author on reasonable requests. The field data including Süleymanköy, Safford, and KTB anomalies were derived from the following sources: https://doi.org/10.1111/j.1365-2478.1981.tb01013.x; https://doi.org/10.1088/1742-2132/9/5/498; https://doi.org/10.1016/j.oregeorev.2017.10.024.
Notes
The reference manual of NMOF package is available on: https://cran.project.org/web/packages/NMOF/NMOF.pdf.
The information and R implementations of the functions are available at http://www.sfu.ca/~ssurjano/optimization.html.
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Acknowledgements
All of the test studies in this work were carried out using R programming language. Some of the figures were created using MATLAB®, the software for numerical computation (http://www.mathworks.com/). This study is part of the PhD thesis of S. Hosseinzadeh. The Editor thanks the Reviewers and the Associate Editor for their constructive comments and work.
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Appendix
Appendix
Figures
The visual comparison between the results of the present study and some prior studies from the Süleymanköy anomaly
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The visual comparison between the results of the present study and some prior studies from the Safford deposit anomaly
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Hosseinzadeh, S., Göktürkler, G. & Turan-Karaoğlan, S. Inversion of self-potential data by a hybrid DE/PSO algorithm. Acta Geod Geophys 58, 241–272 (2023). https://doi.org/10.1007/s40328-023-00414-x
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DOI: https://doi.org/10.1007/s40328-023-00414-x