Skip to main content

A parallel improved PSO algorithm with genetic operators for 2D inversion of resistivity data

A Correction to this article was published on 19 April 2022

This article has been updated

Abstract

In this paper, an improved particle swarm optimization technique known as elitist-mutated particle swarm optimization (EMPSO) was applied in the 2D electrical resistivity imaging, a complex and highly nonlinear optimization problem. The EMPSO enables better exploration of the search space, by replacing particles with a worse performance by the best particle of the swarm mutated in random positions. Nevertheless, this technique, as any other based on a population of models, costs much computation time in solving optimization problems with a large number of unknown parameters. We addressed this problem by developing a parallel version of the EMPSO that supports pure MPI and hybrid MPI-OpenMP modes, and we named as parallel elitist-mutated PSO (PEMPSO). The solution to the inverse problem is based on minimizing an objective function with a regularization term to create a mathematically stable solution. Total variation and global smoothness regularizations were used in the inversion of synthetic data obtained from simple models and a set of real data of a highly complex geological/geotechnical nature. By virtue of the features of the synthetic models and the geology of the local where the data were acquired, the inversions with total variation regularization provided the best outcomes. Additionally, we have improved the execution time significantly with our parallel solution (the pure MPI model turned out to be better than the hybrid model) in comparison with the sequential version. Cumulative frequency distribution of errors between modeled and observed apparent resistivity data for all experiments was used to validate the PEMPSO technique for estimating resistivity.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17

Change history

References

  • Arboleda-Zapata M, Guillemoteau J, Tronicke J (2022) A comprehensive workflow to analyze ensembles of globally inverted 2d electrical resistivity models. J Appl Geophys. https://doi.org/10.1016/j.jappgeo.2021.104512

    Article  Google Scholar 

  • Archie GE et al (1942) The electrical resistivity log as an aid in determining some reservoir characteristics. Trans AIME 146(01):54–62

    Article  Google Scholar 

  • Barboza FM, Medeiros WE, Santana JM (2019) A user-driven feedback approach for 2d direct current resistivity inversion based on particle swarm optimization. Geophysics 84(2):E105–E124

    Article  Google Scholar 

  • Başokur AT, Akca I (2011) Object-based model verification by a genetic algorithm approach: application in archeological targets. J Appl Geophys 74(4):167–174

    Article  Google Scholar 

  • Bertete-Aguirre H, Cherkaev E, Oristaglio M (2002) Non-smooth gravity problem with total variation penalization functional. Geophys J Int 149(2):499–507

    Article  Google Scholar 

  • Bortolozo CA, Motta MFB, de Andrade MRM et al (2019) Combined analysis of electrical and electromagnetic methods with geotechnical soundings and soil characterization as applied to a landslide study in campos do jordão city, Brazil. J Appl Geophys 161:1–14

    Article  Google Scholar 

  • Chambers JE, Kuras O, Meldrum PI et al (2006) Electrical resistivity tomography applied to geologic, hydrogeologic, and engineering investigations at a former waste-disposal site. Geophysics 71(6):B231–B239

    Article  Google Scholar 

  • Chen Z, Zhu X, Liu H et al (2017) Sequential and simultaneous joint inversion of resistivity and IP sounding data using particle swarm optimization. J Earth Sci 28(4):709–718

    Article  Google Scholar 

  • Chunduru RK, Sen MK, Stoffa PL et al (1995) Non-linear inversion of resistivity profiling data for some regular geometrical bodies1. Geophys Prospect 43(8):979–1003

    Article  Google Scholar 

  • Clerc M (1999) The swarm and the queen: towards a deterministic and adaptive particle swarm optimization. In: Proceedings of the 1999 congress on evolutionary computation-CEC99 (Cat. No. 99TH8406), IEEE, pp 1951–1957

  • Constable SC, Parker RL, Constable CG (1987) Occam’s inversion: a practical algorithm for generating smooth models from electromagnetic sounding data. Geophysics 52(3):289–300

    Article  Google Scholar 

  • Dey A, Morrison H (1979) Resistivity modeling for arbitrarily shaped two dimensional structures, part i: theoretical formulation. Lawrence Berkeley Laboratory Report (LBL-5223)

  • Eberhart RC, Shi Y (2000) Comparing inertia weights and constriction factors in particle swarm optimization. In: Proceedings of the 2000 congress on evolutionary computation. CEC00 (Cat. No. 00TH8512), IEEE, pp 84–88

  • Engelbrecht AP (2007) Computational intelligence: an introduction. Wiley

  • Farquharson CG, Oldenburg DW (1998) Non-linear inversion using general measures of data misfit and model structure. Geophys J Int 134(1):213–227

    Article  Google Scholar 

  • Farquharson CG, Oldenburg DW (2004) A comparison of automatic techniques for estimating the regularization parameter in non-linear inverse problems. Geophys J Int 156(3):411–425

    Article  Google Scholar 

  • Ferreira NR, Porsani MJ, Oliveira SPd (2003) A hybrid genetic-linear algorithm for 2d inversion of sets of vertical electrical sounding. Revista Brasileira de Geofísica 21(3):235–248

    Article  Google Scholar 

  • Gill PE, Murray W, Wright MH (2019) Practical optimization. SIAM

  • deGroot Hedlin C, Constable S (1990) Occam’s inversion to generate smooth, two-dimensional models from magnetotelluric data. Geophysics 55(12):1613–1624

    Article  Google Scholar 

  • Holland JH (1975) Adaptation in natural and artificial systems. University of Michigan Press, Ann Arbor

    Google Scholar 

  • Ingber L (1989) Very fast simulated re-annealing. Math Comput Model 12(8):967–973

    Article  Google Scholar 

  • Jha MK, Kumar S, Chowdhury A (2008) Vertical electrical sounding survey and resistivity inversion using genetic algorithm optimization technique. J Hydrol 359(1–2):71–87

    Article  Google Scholar 

  • Juan L, Esperanza G, José P et al (2010) Pso: a powerful algorithm to solve geophysical inverse problems: application to a 1d-dc resistivity case. J Appl Geophys 71:13–25

    Article  Google Scholar 

  • Kennedy J (2006) Swarm intelligence. In: Handbook of nature-inspired and innovative computing. Springer, pp 187–219

  • Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of ICNN’95-international conference on neural networks, IEEE, pp 1942–1948

  • Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220(4598):671–680

    Article  Google Scholar 

  • Lalwani S, Sharma H, Satapathy SC et al (2019) A survey on parallel particle swarm optimization algorithms. Arab J Sci Eng 44(4):2899–2923

    Article  Google Scholar 

  • Liu B, Li S, Nie L et al (2012) 3d resistivity inversion using an improved genetic algorithm based on control method of mutation direction. J Appl Geophys 87:1–8. https://doi.org/10.1016/j.jappgeo.2012.08.002

    Article  Google Scholar 

  • Loke M, Chambers J, Rucker D et al (2013) Recent developments in the direct-current geoelectrical imaging method. J Appl Geophys 95:135–156

    Article  Google Scholar 

  • Medeiros W (1987) The resistivity method applied to the hydrogeology of crystalline terrains: A problem of two-dimensional modelling. Master’s thesis, Universidade Federal da Bahia

  • Menke W (2018) Geophysical data analysis: Discrete inverse theory. Academic press

  • Metcalfe TS, Charbonneau P (2003) Stellar structure modeling using a parallel genetic algorithm for objective global optimization. J Comput Phys 185(1):176–193

    Article  Google Scholar 

  • Moura FA, Silva SA, de Araújo JM et al (2020) Progressive matching optimisation method for FWI. J Geophys Eng 17(2):357–364

    Article  Google Scholar 

  • Nagesh Kumar D, Janga Reddy M (2007) Multipurpose reservoir operation using particle swarm optimization. J Water Resour Plann Manage 133(3):192–201

    Article  Google Scholar 

  • Pace F, Santilano A, Godio A (2019) Particle swarm optimization of 2d magnetotelluric data. Geophysics 84(3):E125–E141

    Article  Google Scholar 

  • Pace F, Santilano A, Godio A (2021) A review of geophysical modeling based on particle swarm optimization. Surv Geophys 42(3):505–549

    Article  Google Scholar 

  • Portniaguine O, Zhdanov MS (1999) Focusing geophysical inversion images. Geophysics 64(3):874–887

    Article  Google Scholar 

  • Regińska T (1996) A regularization parameter in discrete ill-posed problems. SIAM J Sci Comput 17(3):740–749

    Article  Google Scholar 

  • Rudin LI, Osher S, Fatemi E (1992) Nonlinear total variation based noise removal algorithms. Phys D: Nonlinear Phenom 60(1–4):259–268

    Article  Google Scholar 

  • Schwarzbach C, Börner RU, Spitzer K (2005) Two-dimensional inversion of direct current resistivity data using a parallel, multi-objective genetic algorithm. Geophys J Int 162(3):685–695

    Article  Google Scholar 

  • Sen MK, Stoffa PL (2013) Global optimization methods in geophysical inversion. Cambridge University Press

  • Sen MK, Bhattacharya BB, Stoffa PL (1993) Nonlinear inversion of resistivity sounding data. Geophysics 58(4):496–507

    Article  Google Scholar 

  • Sharma SP (2012) Vfsares: a very fast simulated annealing fortran program for interpretation of 1-d dc resistivity sounding data from various electrode arrays. Comput Geosci 42:177–188

    Article  Google Scholar 

  • Shaw R, Srivastava S (2007) Particle swarm optimization: a new tool to invert geophysical data. Geophysics 72(2):F75–F83. https://doi.org/10.1190/1.2432481

    Article  Google Scholar 

  • Sigdel A, Adhikari RK (2020) Application of electrical resistivity tomography (ERT) survey for investigation of the landslide: a case study from Taprang landslide, Kaski district, west-central Nepal. J Nepal Geol Soc 60:103–115

    Article  Google Scholar 

  • Szu H, Hartley R (1987) Fast simulated annealing. Phys Lett A 122(3–4):157–162

    Article  Google Scholar 

  • Tikhonov AN, Arsenin VY (1977) Solutions of ill-posed problems. New York 1:30

    Google Scholar 

  • Wahba G (1990) Spline models for observational data, siam, philadelphia, 1990. MR 91g 62028

Download references

Acknowledgements

This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001. M.Sc. Abril is also grateful to CAPES for his Ph.D. fellowship. We thank the Federal University’s High Performance Processing Nucleus (NPAD) Rio Grande do Norte (UFRN) for the computational resource used in this research. We are also thankful to the Professor Dr. Milton Porsani for providing us the 2D forward modelling resistivity code in Fortran 77.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jorge L. Abril.

Ethics declarations

Conflict of interest

The authors that developed this research notify that there is no conflict of interests by a third party.

Additional information

Edited by Prof. Bogdan Mihai Niculescu (ASSOCIATE EDITOR) / Prof. Michał Malinowski (CO-EDITOR-IN-CHIEF).

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Abril, J.L., Vasconcelos, M.A., Barboza, F.M. et al. A parallel improved PSO algorithm with genetic operators for 2D inversion of resistivity data. Acta Geophys. 70, 1137–1154 (2022). https://doi.org/10.1007/s11600-022-00760-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11600-022-00760-4

Keywords

  • Constrained inversion
  • Electrical resistivity imaging
  • Particle swarm optimization
  • Parallel computing