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Application of EBWO with chaotic mapping, reverse learning, and modified Lévy flight for joint inversion of seismic and VES data: Sea intrusion case

Fagang Wang1 ,  Liming Zhou1* ,  Daiguang Fu1
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1 Key Laboratory of Geotechnical Mechanics and Engineering of Ministry of Water Resources, Changjiang River Scientific Research Institute, Wuhan, Hubei , China
JSE, 026200086 https://doi.org/10.36922/JSE026200086
Received: 16 May 2026 | Revised: 5 August 2026 | Accepted: 10 August 2026 | Published online: 10 September 2026
© 2026 by the Author(s). This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License ( https://creativecommons.org/licenses/by/4.0/ )
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Abstract

Joint inversion of Rayleigh-wave dispersion and vertical electrical sounding (VES) data can reduce the non-uniqueness of near-surface geophysical interpretation, but its performance strongly depends on the robustness of the optimization algorithm. In this study, an Enhanced Beluga Whale Optimization (EBWO) algorithm is proposed for joint seismic–electrical inversion. EBWO improves the original Beluga Whale Optimization (BWO) by incorporating Tent chaotic mapping and reverse learning for population initialization, together with a Lévy-flight-based golden sine strategy for offspring updating. Benchmark-function tests show that EBWO provided higher optimization accuracy and stability than the original BWO. Synthetic joint inversion experiments under both noise-free and noise-contaminated conditions further demonstrate that EBWO yielded more accurate and stable estimates than BWO and Particle Swarm Optimization. Application to field data from the Besirli region in Türkiye also produced lower fitting errors and better agreement with previous geophysical interpretations. These results indicate that EBWO is an effective and reliable optimization tool for joint Rayleigh-wave and VES inversion.

Keywords
Joint Inversion
Surface wave dispersion
Vertical electrical sounding
Metaheuristics
Near-surface investigation
Funding
The study was funded by the National Key R&D Program of China (Grant No. 2024YFC3211200) and the China Railway Group Limited Science and Technology Research and Development Program (Grant No. 2025-Major-08).
Conflict of interest
The authors declare no potential conflict of interest.
References
  1. Qin Z, Wu D, Luo S, et al. A novel method to obtain permeability in a dual-pore system using geophysical logs: A case study of an Upper Triassic Formation, Southwest Ordos Basin, China. Nat Resour Res. 2020;29(4):2619-2634. doi: 10.1007/s11053-019-09612-3
  2. Park CB, Miller RD, Xia J. Multichannel analysis of surface waves. Geophysics. 1999;64(3):800-808. doi: 10.1190/1.1444590
  3. Li X, Wang S, Li Z, Yang R, Li Z. Measurement of bolt axial stress using a combination of trailing wave and shear wave ultrasound. NDT E Int. 2024;143:103056. doi: 10.1016/j.ndteint.2024.103056
  4. Wang S, Yang R, Li Z, et al. Improvement of pulse compression Rayleigh-wave EMATs. NDT E Int. 2025;155:103427. doi: 10.1016/j.ndteint.2025.103427
  5. Meng X, Lin L, Li H, Mei H, Wang Z. Influence of intense vertical component electric field with the direction away from insulation surface on streamer discharge. IEEE Trans Dielectr Electr Insul. 2025;32(3):1712-1718. doi: 10.1109/TDEI.2024.3452652
  6. Qin Z, Wu J, Wang C, et al. A novel calculation model, characteristics and applications of Archie's cementation exponent in dual porosity reservoirs with intersecting dual fractures. Geoenergy Sci Eng. 2023;231:212390. doi: 10.1016/j.geoen.2023.212390
  7. Wang Y, Song X, Zhang X. Research on nonlinear inversion of seismic surface waves based on artificial neural network algorithm. Oil Geophys Prospect. 2021;56(5):979-991. [In Chinese] doi: 10.13810/j.cnki.issn.1000-7210.2021.05.005
  8. Zhang Z, Shi Z, Ma N, et al. Deep learning inversion of Rayleigh dispersion curves. Chin J Geophys. 2022;65(6):2244-2259. [In Chinese] doi: 10.6038/cjg2022P0446
  9. Yang X-H, Han P, Yang Z, Chen X. Two-stage broad learning inversion framework for shear-wave velocity estimation. Geophysics. 2023;88(1):WA219-WA237. doi: 10.1190/geo2022-0060.1
  10. Yang X-H, Han P, Yang Z, Miao M, Sun Y-C, Chen X. Broad learning framework for search space design in Rayleigh wave inversion. IEEE Trans Geosci Remote Sens. 2022;60:1-17. doi: 10.1109/TGRS.2022.3208616
  11. Hering A, Misiek R, Gyulai A, Ormos T, Dobróka M, Dresen L. A joint inversion algorithm to process geoelectric and surface wave seismic data. Part I: basic ideas. Geophys Prospect. 1995;43(2):135-156. doi: 10.1111/j.1365-2478.1995.tb00128.x
  12. Misiek R, Liebig A, Gyulai A, Ormos T, Dobróka M, Dresen L. A joint inversion algorithm to process geoelectric and surface wave seismic data. Part II: applications. Geophys Prospect. 1997;45(1):65-85. doi: 10.1046/j.1365-2478.1997.3190241.x
  13. Gallardo LA, Meju MA. Characterization of heterogeneous near-surface materials by joint 2D inversion of dc resistivity and seismic data. Geophys Res Lett. 2003;30(13):1658. doi: 10.1029/2003GL017370
  14. Gallardo LA, Meju MA. Joint two-dimensional DC resistivity and seismic travel time inversion with cross-gradients constraints. J Geophys Res Solid Earth. 2004;109(B3):B03311. doi: 10.1029/2003JB002716
  15. Garofalo F, Sauvin G, Socco LV, Lecomte I. Joint inversion of seismic and electric data applied to 2D media. Geophysics. 2015;80:EN93-EN104. doi: 10.1190/geo2014-0313.1
  16. Garofalo F, Socco LV, Foti S. Joint inversion of seismic and electrical data in saturated porous media. Near Surf Geophys. 2022;20:64-81. doi: 10.1002/nsg.12184
  17. Senkaya M, Karslı H. Joint inversion of Rayleigh-wave dispersion data and vertical electric sounding data: synthetic tests on characteristic sub-surface models. Geophys Prospect. 2016;64(1):228-246. doi: 10.1111/1365-2478.12289
  18. Senkaya M, Karsli H, Socco LV, Foti S. Obtaining reliable S-wave velocity depth profile by joint inversion of geophysical data: the combination of active surface-wave, seismic refraction and electric sounding data. Near Surf Geophys. 2020;18(6):659-682. doi: 10.1002/nsg.12126
  19. Song X, Tang L, Lv X, Fang H, Gu H. Application of particle swarm optimization to interpret Rayleigh wave dispersion curves. J Appl Geophys. 2012;84:1-13. doi: 10.1016/j.jappgeo.2012.05.011
  20. Sun C-Y, Wang Y-Y, Wu D-S, Qin X-J. Nonlinear Rayleigh wave inversion based on the shuffled frog-leaping algorithm. Appl Geophys. 2017;14(4):551-558. doi: 10.1007/s11770-017-0641-x
  21. Yang B, Xiong Z, Zhang D, Yang Z. Rayleigh surface-wave dispersion curve inversion based on adaptive chaos genetic particle swarm optimization algorithm. Oil Geophys Prospect. 2019;54(6):1217-1227. [In Chinese] doi: 10.13810/j.cnki.issn.1000-7210.2019.06.005
  22. Yu D, Song X, Zhang X, Zhao S, Cai W. Rayleigh wave dispersion inversion based on grasshopper optimization algorithm. Oil Geophys Prospect. 2019;54(2):288-301. [In Chinese] doi: 10.13810/j.cnki.issn.1000-7210.2019.02.007
  23. Gao X, Yu J, Li X. Rayleigh wave dispersion curve inversion based on adaptive weight dragonfly algorithm. Oil Geophys Prospect. 2021;56:745-757. [In Chinese] doi: 10.13810/j.cnki.issn.1000-7210.2021.04.008
  24. Ai H, Essa KS, Ekinci YL, Balkaya Ç, Li H, Géraud Y. Magnetic anomaly inversion through the novel barnacles mating optimization algorithm. Sci Rep. 2022;12:22578. doi: 10.1038/s41598-022-26265-0
  25. Fu Y, Ai H, Yao ZA. Inversion of multi-mode Rayleigh wave dispersion curves based on lightning attachment procedure optimization. Oil Geophys Prospect. 2023;58(4):830-838. [In Chinese] doi: 10.13810/j.cnki.issn.1000-7210.2023.04.008
  26. Fu Y, Ai H, Yao Z, Mei Z, Su K. Inversion of the Rayleigh wave dispersion curves based on the sine-cosine algorithm. Geophys Geochem Explor. 2023;47(6):1467-1478. [In Chinese] doi: 10.11720/wtyht.2023.1239
  27. Ekinci YL, Balkaya Ç, Ai H, Roy A, Özyalin Ş. Investigation of Kula Volcanic Field (Türkiye) through the inversion of aeromagnetic anomalies using success-history-based adaptive differential evolution with exponential population reduction strategy. Pure Appl Geophys. 2025;182(3):1333-1361. doi: 10.1007/s00024-024-03569-y
  28. Ekinci YL, Balkaya Ç, Göktürkler G, Ai H. 3-D gravity inversion for the basement relief reconstruction through modified success-history-based adaptive differential evolution. Geophys J Int. 2023;235:377-400. doi: 10.1093/gji/ggad222
  29. Peng LY, Feng WD, Xie HT, et al. An improved butterfly optimization algorithm in the inversion of Rayleigh wave dispersion curve. Geophys Geochem Explor. 2024;48(3):705-720. [In Chinese] doi: 10.11720/wtyht.2024.1116
  30. Tang S, Wu Y. Application of modified wild horse optimizer for inversion of base-mode Rayleigh wave dispersion curve. Prog Geophys. 2024;39(4):1698-1710. [In Chinese] doi: 10.6038/pg2024HH0304
  31. Balkaya Ç, Ekinci YL, Ai H, Biswas A, Göktürkler G. Fault structure reconstruction from magnetic anomalies using an improved backtracking search optimization algorithm. Earth Space Sci. 2024;11(5):e2023EA003082. doi: 10.1029/2023EA003082
  32. Su K, Ai H, Alvandi A, et al. Hunger Games Search for the elucidation of gravity anomalies with application to geothermal energy investigations and volcanic activity studies. Open Geosci. 2024;16:20220641. doi: 10.1515/geo-2022-0641
  33. Ai H, Ekinci YL, Balkaya Ç, et al. Modified Barnacles mating optimizing algorithm for the inversion of self-potential anomalies due to ore deposits. Nat Resour Res. 2024;33(3):1073-1102. doi: 10.1007/s11053-024-10331-7
  34. Ai H, Essa KS, Ekinci YL, Balkaya Ç, Géraud Y. Hunger Games Search optimization for the inversion of gravity anomalies of active mud diapir from SW Taiwan using inclined anticlinal source approximation. J Appl Geophys. 2024;227:105443. doi: 10.1016/j.jappgeo.2024.105443
  35. Ai H, Song X, Zhang X, et al. Full-parametric and joint inversion of multimode surface wave data for identifying glacial ice thickness and freezing extent in subglacial sediments via the hunger games search algorithm. Geophysics. 2025;90:KS1-KS14. doi: 10.1190/geo2023-0756.1
  36. Yang X-H, Zhou Y, Han P, Feng X, Chen X. Near-surface Rayleigh wave dispersion curve inversion algorithms: a comprehensive comparison. Surv Geophys. 2024;45(3):773-818. doi: 10.1007/s10712-024-09826-y
  37. Zhong C, Li G, Meng Z. Beluga whale optimization: A novel nature-inspired metaheuristic algorithm. Knowl Based Syst. 2022;251:109215. doi: 10.1016/j.knosys.2022.109215
  38. Shan L, Qiang H, Li J, Wang Z. Jiyu Tent yingshe de hundun youhua suanfa [Chaotic optimization algorithm based on Tent map]. Control Decis. 2005;20(2):179-182. [In Chinese] doi: 10.13195/j.cd.2005.02.60.shanl.013
  39. Zhang N, Zhao Z, Bao X, Qian J, Wu B. Gravitational search algorithm based on improved Tent chaos. Control Decis. 2020;35(4):893-900. [In Chinese] doi: 10.13195/j.kzyjc.2018.0795
  40. Yin DX, Zhang DM, Cai PC, Qin WN. An improved sparrow search optimization algorithm and its application. Comput Eng Sci. 2022;44(10):1844-1851. [In Chinese] doi: 10.3969/j.issn.1007-130X.2022.10.016
  41. Yamanaka H, Ishida H. Application of genetic algorithms to an inversion of surface-wave dispersion data. Bull Seismol Soc Am. 1996;86(2):436-444. doi: 10.1785/BSSA0860020436
  42. Xia J, Miller RD, Park CB. Estimation of near-surface shear-wave velocity by inversion of Rayleigh waves. Geophysics. 1999;64(3):691-700. doi: 10.1190/1.1444578
  43. Xia J, Miller RD, Park CB, Tian G. Inversion of high frequency surface waves with fundamental and higher modes. J Appl Geophys. 2003;52:45-57. doi: 10.1016/S0926-9851(02)00239-2
  44. Gao L, Xia J, Pan Y, Xu Y. Reason and condition for mode kissing in MASW method. Pure Appl Geophys. 2016;173(5):1627-1638. doi: 10.1007/s00024-015-1208-5
  45. Mi B, Xia J, Shen C, Wang L. Dispersion energy analysis of Rayleigh and Love waves in the presence of low-velocity layers in near-surface seismic surveys. Surv Geophys. 2018;39(2):271-288. doi: 10.1007/s10712-017-9440-4
  46. Killingbeck S, Livermore P, Booth A, West L. Multimodal layered transdimensional inversion of seismic dispersion curves with depth constraints. Geochem Geophys Geosyst. 2018;19(12):4957-4971. doi: 10.1029/2018GC008000
  47. Wang X, Feng X, Liu Q, Bai H, Dong X, Wang T. Adaptive trans-dimensional inversion of multimode dispersion curve based on slime mold algorithm. Acta Geophys. 2024;72:233-245. doi: 10.1007/s11600-023-01086-5
  48. Ai H, Song X, Zhang X, et al. Transdimensional joint inversion of surface wave, refraction, and resistivity data using Modified Barnacles Mating Optimizer (MBMO) for near-surface investigations. J Appl Geophys. 2025;241:105863. doi: 10.1016/j.jappgeo.2025.105863
  49. Li Z, Shi C, Ren H, Chen X. Multiple leaking mode dispersion observations and applications from ambient noise cross-correlation in Oklahoma. Geophys Res Lett. 2022;49:e2021GL096032. doi: 10.1029/2021GL096032
  50. Yang Z, Chen X, Pan L, Wang J, Xu J, Zhang D. Multi-channel analysis of Rayleigh waves based on the Vector Wavenumber Transformation Method (VWTM). Chin J Geophys. 2019;62(1):298-305. [In Chinese] doi: 10.6038/cjg2019M0641
  51. Song W, Feng X, Zhang G, Gao L, Yan B, Chen X. Domain adaptation in automatic picking of phase velocity dispersions based on deep learning. J Geophys Res Solid Earth. 2022;127(6):e2021JB023389. doi: 10.1029/2021JB023389
  52. Zhang D, Yang B, Yang Z, et al. Multimodal inversion of Rayleigh wave dispersion curves based on a generalized misfit function. J Appl Geophys. 2022;207:104849. doi: 10.1016/j.jappgeo.2022.104849
  53. Yan Y, Chen X, Huai N, Guan J. Modern inversion workflow of the multimodal surface wave dispersion curves: staging strategy and pattern search with embedded Kuhn–Munkres algorithm. Geophys J Int. 2022;231:47-71. doi: 10.1093/gji/ggac178
  54. Le Z, Song X, Zhang X, et al. Particle swarm optimization for Rayleigh wave frequency-velocity spectrum inversion. J Appl Geophys. 2024;222:105311. doi: 10.1016/j.jappgeo.2024.105311
  55. Zhou G, Xu J, Hu H, et al. Off-axis four-reflection optical structure for lightweight single-band bathymetric LiDAR. IEEE Trans Geosci Remote Sens. 2023;61:1-17. doi: 10.1109/TGRS.2023.3298531
  56. Zhou G, Jia G, Zhou X, et al. Adaptive high-speed echo data acquisition method for bathymetric LiDAR. IEEE Trans Geosci Remote Sens. 2024;62:1-17. doi: 10.1109/TGRS.2024.3386687
  57. Yuan Y, Qin G, Li D, Zhong M, Shen Y, Ouyang Y. Real-time joint filtering of gravity and gravity gradient data based on improved Kalman filter. IEEE Trans Geosci Remote Sens. 2024;62:1-12. doi: 10.1109/TGRS.2024.3452038
  58. Zhang H, Bao X, Zhao H, et al. High-precision deblending of 3-D simultaneous source data based on prior information constraint. IEEE Geosci Remote Sens Lett. 2025;22:1-5. doi: 10.1109/LGRS.2025.3526972
  59. Fu J, He T, Guo C, Bao Y, Li X, Liu X. An additional structure with power-law thickness for weak acoustic emission signal enhancement. Thin-Walled Struct. 2025;211:113071. doi: 10.1016/j.tws.2025.113071
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