Estimation of Model Parameters from Self-Potential Anomalies Generated by Simple-Geometric Shaped Structures Using Bat Algorithm

Abstract

Metaheuristic methods have started to be preferred instead of derivative-based optimization methods for the inversion of geophysical data. Metaheuristic methods, inspired by nature, are used in geophysical inversion studies because of their advantages such as comprehensive exploring of the search space, the non-necessity of a good initial model, and easy adaptability to every optimization problem. In this study, the investigations are presented for the inversion of Self-Potential data using the Bat Algorithm, which is a population-based metaheuristic method. First, parameter tuning studies of the Bat Algorithm were carried out, and the control parameters determined from the tuning were used for the inversion of theoretical noise-free and noisy Self-Potential data, as well as two field data sets. Additionally, the estimated parameters were statistically tested by using the Metropolis-Hasting algorithm to determine the reliability of the model parameters of the theoretical and field data. By comparing the inversion results of the theoretical data with the true values of the data, and the inversion results of the field data with the results of other studies in the literature, it was shown that the Bat Algorithm is applicable as an effective method for the inversion of self-potential data.

Keywords

• Bat Algorithm
• Metaheuristic
• Self Potential Anomaly

Doğal Potansiyel Anomalilerini Oluşturan Basit Geometrik Şekilli Yapılarda Yarasa Algoritması Kullanılarak Model Parametre Kestirimi

Abstract

Jeofizik verilerinin ters çözümünde günümüzde türev tabanlı optimizasyon yöntemlerinin yerini metasezgisel yöntemler almaya başlamıştır. Arama uzayını kapsamlı taraması, iyi bir başlangıç modeline ihtiyaç duymaması ve her optimizasyon problemine kolay uyarlanabilmesi gibi avantajları nedeniyle doğadan esinlenerek oluşturulan birçok metasezgisel yöntem, jeofizik ters çözüm çalışmalarında kullanılmaktadır. Bu çalışmada, popülasyon tabanlı bir metasezgisel yöntem olan Yarasa Algoritmasının doğal potansiyel verilerinin ters çözümünde kullanımına yönelik incelemeler sunulmuştur. Öncelikle Yarasa Algoritmasının kontrol parametrelerini belirleme çalışmaları yapılmış, elde edilen kontrol parametreleri kullanılarak da gürültüsüz ve gürültü eklenmiş kuramsal doğal potansiyel verilerinin ve iki adet arazi verisinin ters çözümü çalışmaları gerçekleştirilmiştir. Ayrıca, kuramsal ve arazi verilerine ait model parametrelerinin güvenilirliğinin belirlenmesi amacıyla Metropolis-Hasting algoritması kullanılarak, kestirim parametrelerinin olasılık yoğunluğu histogramları, istatistiksel olarak da test edilmiştir. Kuramsal verilerin ters çözüm sonuçları ilgili verilere ait doğru değerlerle, arazi verilerine ait ters çözüm sonuçlarıysa literatürdeki diğer çalışmalarda bulunan sonuçlarla kıyaslanarak Yarasa Algoritmasının doğal potansiyel verilerinin ters çözümünde efektif bir yöntem olarak uygulanabilir olduğu görülmüştür

Keywords

• Yarasa Algoritması
• Metasezgisel
• Doğal Potansiyel Anomalisi

Supporting Institution

Herhangi bir kurum tarafından desteklenmemektedir.

Ethical Statement

Hazırlanan makalede etik kurul izni alınmasına gerek yoktur.

Thanks

Yazarlar, editör ve anonim hakemlere yorum ve önerileri için teşekkür eder. Ayrıca yazarlar çalışmada kullanılan YA algoritmasının orijinal kodu için Dr. Xin-She Yang’a teşekkürlerini sunar. YA algoritması, MATLAB® (http://www.mathworks.com/) kullanılarak çalıştırılmış ve sayısal hesaplamalar yapılmıştır.

References

1. Seyyedabbasi A. A reinforcement learning-based metaheuristic algorithm for solving global optimization problems. Advances in Engineering Software 2023;178:103411. doi:10.1016/j.advengsoft.2023.103411.
2. Ma Z, Wu G, Suganthan PN, Song A, Luo Q. Performance assessment and exhaustive listing of 500+ nature-inspired metaheuristic algorithms. Swarm and Evolutionary Computation 2023;77:101248.
3. Glover F. Future paths for integer programming and links to artificial intelligence. Computers & Operations Research 1986;13(5):533-549. doi:10.1016/0305-0548(86)90048-1.
4. Askari Q, Saeed M, Younas I. Heap-based optimizer inspired by corporate rank hierarchy for global optimization. Expert Systems with Applications 2020;161:113702. doi:10.1016/j.eswa.2020.113702.
5. Turan-Karaoğlan S, Göktürkler G. Cuckoo Search Algorithm for model parameter estimation from self-potential data. Journal of Applied Geophysics 2021;194:104461. doi:10.1016/j.jappgeo.2021.104461.
6. Göktürkler G. A hybrid approach for tomographic inversion of crosshole seismic first-arrival times. Journal of Geophysics and Engineering 2011;8:99-108. doi:10.1088/1742-2132/8/1/012.
7. Başokur AT, Akça I, Siyam NWA. Hybrid genetic algorithms in view of the evolution theories with application for the electrical sounding method. Geophys Prospect 2007;55:393-406. doi:10.1111/j.1365-2478.2007.00588.x.
8. Balkaya Ç, Ekinci YL, Göktürkler G, Turan S. 3D non-linear inversion of magnetic anomalies caused by prismatic bodies using differential evolution algorithm. Journal of Applied Geophysics 2017;136:372-386. doi:10.1016/j.jappgeo.2016.10.040.

9. Kaftan İ. Interpretation of magnetic anomalies using a genetic algorithm. Acta Geophysica 2017;65:627-634. doi:10.1007/s11600-017-0060-7.
10. Hosseinzadeh S, Göktürkler G, Turan-Karaoğlan S. Inversion of self-potential data by a hybrid DE/PSO algorithm. Acta Geodaetica et Geophysica 2023;58:241-272. doi:10.1007/s40328-023-00414-x.
11. Ai H, Song X, Zhang X, Ekinci YL, Balkaya Ç, Roy A, vd. Transdimensional joint inversion of surface wave, refraction, and resistivity data using Modified Barnacles Mating Optimizer for near-surface investigations. Journal of Applied Geophysics 2025;241:105863. doi:10.1016/j.jappgeo.2025.105863.
12. Abdelazeem M, Gobashy M. Self-potential inversion using genetic Algorithm. Earth Science 2006;17:83-101. doi:10.4197/Ear.17-1.5.
13. Pekşen E, Yas T, Kayman AY, Özkan C. Application of particle swarm optimization on self-potential data. Journal of Applied Geophysics 2011;75:305-318. doi:10.1016/j.jappgeo.2011.07.0.
14. Sharma SP, Biswas A. Interpretation of self-potential anomaly over a 2D inclined structure using very fast simulated-annealing global optimization — An insight about ambiguity. Geophysics 2013;78(3):3-15. doi:10.1190/geo2012-0233.1.
15. Balkaya Ç. An implementation of differential evolution algorithm for inversion of geoelectrical data. Journal of Applied Geophysics 2013;98:160-175. doi:10.1016/j.jappgeo.2013.08.019.
16. Sungkono S, Warnana DD. Black hole algorithm for determining model parameter in self-potential data. Journal of Applied Geophysics 2018;129:178. doi:10.1016/j.jappgeo.2017.11.015.
17. Gobashy M, Abdelazeem M, Abdrabou M, Khalil MH. Estimating model parameters from self-potential anomaly of 2D inclined sheet using whale optimization algorithm: applications to mineral exploration and tracing shear zones. Natural Resources Research 2020;29(1):499-519. doi:10.1007/s11053-019-09526-0.
18. Haryono A, Sungkono S, Agustin R, Santosa BJ, Widodo A, Ramadhany B. Model parameter estimation and its uncertainty for 2-D inclined sheet structure in self-potential data using crow search algorithm. Acta Geodaetica et Geophysica 2020;55:691-715. doi:10.1007/s40328-020-00321-5.
19. Yang XS. A new metaheuristic bat-inspired algorithm. İçinde: Nature inspired cooperative strategies for optimization (NICSO 2010). Berlin, Heidelberg: Springer; 2010, s. 65-74. doi:10.1007/978-3-642-12538-6_6.
20. Yang XS, He X. Bat algorithm: literature review and applications. International Journal of Bio-Inspired Computation 2013;5:141-149. doi:10.1504/IJBIC.2013.055093.
21. Fenton MB. Bat natural history and echolocation. İçinde: Brigham RM, Elisabeth VKV, Gareth J, Stuart P, Herman AL, editörler. Bat echolocation research tools, techniques and analysis. Austin, Texas, USA: Bat Conservation International; 2004, s. 2-6.
22. Yüngül S. Interpretation of spontaneous polarization anomalies caused by spherical ore bodies. Geophysics 1950;15:237-246. doi:10.1190/1.1437597.
23. Göktürkler G, Balkaya Ç. Inversion of self-potential anomalies caused by simple geometry bodies using global optimization algorithms. Journal of Geophysics and Engineering 2012;9:498-507. doi:10.1088/1742-2132/9/5/498.
24. Fernández-Martínez JL, Fernández-Muñiz Z, Pallero JLG, Pedruelo-González LM. From Bayes to Tarantola: new insights to understand uncertainty in inverse problems. Journal of Applied Geophysics 2013;98:62-72. doi:10.1016/j.jappgeo.2013.07.005.
25. Ekinci YL, Özyalın Ş, Sındırgı P, Balkaya Ç, Göktürkler G. Amplitude inversion of the 2D analytic signal of magnetic anomalies through the differential evolution algorithm. Journal of Geophysics and Engineering 2017;14:1492-1508. doi:10.1088/1742-2140/aa7ffc.
26. Ekinci YL, Balkaya Ç, Göktürkler G, Özyalın Ş. Gravity data inversion for the basement relief delineation through global optimization: a case study from the Aegean Graben System, western Anatolia, Turkey. Geophys J Int 2021;224:923-944. doi:10.1093/gji/ggaa492.
27. Rao RM, Babu H, Sivakumar, Sinha G. A Fourier transform for the interpretation of self-potential anomalies due to two-dimensional inclined sheet of finite depth. Pure and Applied Geophysics 1982;120:365-374. doi:10.1007/BF00877042.
28. Biswas A, Sharma SP. Interpretation of self-potential anomaly over idealized bodies and analysis of ambiguity using very fast simulated annealing global optimization technique. Journal of Applied Geophysics 2015;105:235-247. doi:10.3997/1873-0604.2015005.
29. Mehanee S. An efficient regularized inversion approach for self-potential data interpretation of ore exploration using a mix of logarithmic and non-logarithmic model parameters. Ore Geology Reviews 2014;57:87-115. doi:10.1016/j.oregeorev.2013.09.002.
30. Yüngül S. Spontaneous Potential Survey of A Copper Deposit at Sarıyer, Turkey. Geophysics 1954;19(3):455. doi:10.1190/1.1438018.
31. Dobrin MB, Savit CH. Introduction to Geophysical Prospecting. 4. baskı. New York: McGraw-Hill; 1988.
32. Abdelrahman EM, Saber HS, Essa KS, Fouda MA. A least-squares approach to depth determination from numerical horizontal self-potential gradients. Pure and Applied Geophysics 2004;161:399-411. doi:10.1007/s00024-003-2446-5.
33. Tlas M, Asfahani J. An approach for interpretation of self-potential anomalies due to simple geometrical structures using fair function minimization. Pure and Applied Geophysics 2012;170:895-905. doi:10.1007/s00024-012-0594-1.
34. Abdelazeem M, Gobashy M, Khalil MH, Abdrabou M. A complete model parameter optimization from self-potential data using Whale algorithm. Journal of Applied Geophysics 2019;170:103825. doi:10.1016/j.jappgeo.2019.103825.