Global Optimization for Delineation of Self-potential Anomaly of a 2D Inclined Plate

Abstract

A fast and efficient technique for explanation of self-potential anomalies is of immense importance for exploration, engineering, and environmental problems. Estimation of model parameters of ore bodies in the subsurface is the primary concern in mineral exploration. In most cases, self-potential data are delineated considering various simple or idealized structures for the interpretation of lateral and vertical variations of subsurface ore bodies. In this context, we developed an inversion algorithm to determine the different parameters associated with a 2D inclined plate-type structure, which does not require any a priori information. The developed algorithm can interpret appropriately every parameter with minimum uncertainty. The position of causative source body (x0), its half-width (w) and its depth (z) were the parameters interpreted using the developed algorithm. It was found that these parameters were well resolved within the estimated uncertainty, although solutions for w showed wide variability. The technique was verified with synthetic data without noise and with different degrees of Gaussian noise. The technique was also confirmed with three field datasets for mineral exploration, and the interpreted parameters were in fair agreement with those reported in earlier works.

This is a preview of subscription content, log in to check access.

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure 10
Figure 11
Figure 12

References

  1. Abdelazeem, M., Gobashy, M., Khalil, M. H., & Abdraboub, M. (2019). A complete model parameter optimization from self-potential data using Whale algorithm. Journal of Applied Geophysics,170, 103825.

    Google Scholar 

  2. Abdelrahman, E. M., Abdelazeem, M., & Gobashy, M. (2019). A minimization approach to depth and shape determination of mineralized zones from potential field data using the Nelder-Mead simplex algorithm. Ore Geology Reviews,114, 103123.

    Google Scholar 

  3. Abdelrahman, E. M., El-Araby, H. M., Hassanein, A. G., & Hafez, M. A. (2003). New methods for shape and depth determinations from SP data. Geophysics,68, 1202–1210.

    Google Scholar 

  4. Abdelrahman, E. M., Hassaneen, A Gh, & Hafez, M. A. (1998). Interpretation of self-potential anomalies over two-dimensional plates by gradient analysis. Pure and Applied Geophysics,152, 773–780.

    Google Scholar 

  5. Abdelrahman, E. M., & Sharafeldin, M. S. (1997). A least-squares approach to depth determination from self-potential anomalies caused by horizontal cylinders and spheres. Geophysics,62, 44–48.

    Google Scholar 

  6. Asfahani, J., & Tlas, M. (2005). A constrained nonlinear inversion approach to quantitative interpretation of self-potential anomalies caused by cylinders, spheres and sheet-like structures. Pure and Applied Geophysics,162, 609–624.

    Google Scholar 

  7. Biswas, A. (2013). Identification and resolution of ambiguities in interpretation of self-potential data: Analysis and integrated study around South Purulia Shear Zone, India. Ph.D. thesis, Department of Geology and Geophysics, Indian Institute of Technology Kharagpur, 199 pp. Retrieved May, 2020 from http://www.idr.iitkgp.ac.in/xmlui/handle/123456789/3247.

  8. Biswas, A. (2016). A comparative performance of least square method and very fast simulated annealing global optimization method for interpretation of Self-Potential anomaly over 2-D inclined sheet type structure. Journal of the Geological Society of India,88(4), 493–502.

    Google Scholar 

  9. Biswas, A. (2017). A review on modeling, inversion and interpretation of self-potential in mineral exploration and tracing Paleo-Shear zones. Ore Geology Reviews,91, 21–56.

    Google Scholar 

  10. Biswas, A. (2018). Inversion of source parameters from magnetic anomalies for mineral/ore deposits exploration using global optimization technique and analysis of uncertainty. Natural Resources Research,27(1), 77–107.

    Google Scholar 

  11. Biswas, A. (2019). Inversion of amplitude from the 2-D analytic signal of self-potential anomalies. In K. Essa (Ed.), Minerals (pp. 13–45). London: In-Tech Education and Publishing.

    Google Scholar 

  12. Biswas, A., & Sharma, S. P. (2014a). Resolution of multiple sheet-type structures in self-potential measurement. Journal of Earth System Science,123(4), 809–825.

    Google Scholar 

  13. Biswas, A., & Sharma, S. P. (2014b). Optimization of Self-Potential interpretation of 2-D inclined sheet-type structures based on Very Fast Simulated Annealing and analysis of ambiguity. Journal of Applied Geophysics,105, 235–247.

    Google Scholar 

  14. Biswas, A., & Sharma, S. P. (2015). Interpretation of self-potential anomaly over idealized body and analysis of ambiguity using very fast simulated annealing global optimization. Near Surface Geophysics,13(2), 179–195.

    Google Scholar 

  15. Biswas, A., & Sharma, S. P. (2016). Integrated geophysical studies to elicit the structure associated with Uranium mineralization around South Purulia Shear Zone, India: A Review. Ore Geology Reviews,72, 1307–1326.

    Google Scholar 

  16. Biswas, A., & Sharma, S. P. (2017). Interpretation of Self-potential anomaly over 2-D inclined thick sheet structures and analysis of uncertainty using very fast simulated annealing global optimization. Acta Geodaetica et Geophysica,52(4), 439–455.

    Google Scholar 

  17. Di Maio, R., Piegari, E., Rani, P., & Avella, A. (2016a). Self-Potential data inversion through the integration of spectral analysis and tomographic approaches. Geophysical Journal International,206, 1204–1220.

    Google Scholar 

  18. Di Maio, R., Rani, P., Piegari, E., & Milano, L. (2016b). Self-potential data inversion through a Genetic-Price algorithm. Computers & Geosciences,94, 86–95.

    Google Scholar 

  19. Dmitriev, A. N. (2012). Forward and inverse self-potential modeling: A new approach. Russian Geology and Geophysics,53, 611–622.

    Google Scholar 

  20. El-Kaliouby, H. M., & Al-Garani, M. A. (2009). Inversion of self-potential anomalies caused by 2D inclined sheets using neural networks. Journal of Geophysics and Engineering,6, 29–34.

    Google Scholar 

  21. Eppelbaum, L., & Khesin, B. (2012). Methodological specificities of geophysical studies in the complex environments of the caucasus. In L. Eppelbaum & B. Khesin (Eds.), Geophysical studies in the caucasus (pp. 39–138). Berlin: Springer.

    Google Scholar 

  22. Essa, K. S. (2011). A new algorithm for gravity or self-potential data interpretation. Journal of Geophysics and Engineering,8, 434–446.

    Google Scholar 

  23. Essa, K. S., & El-Hussein, M. (2017). A new approach for the interpretation of self-potential data by 2-D inclined plate. Journal of Applied Geophysics,136, 455–461.

    Google Scholar 

  24. Essa, K., Mahanee, S., & Smith, P. D. (2008). A new inversion algorithm for estimating the best fitting parameters of some geometrically simple body to measured self-potential anomalies. Exploration Geophysics,39, 155–163.

    Google Scholar 

  25. Gobashy, M., Abdelazeem, M., Abdrabou, M., & Khalil, M. H. (2020). 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,29, 499–519.

    Google Scholar 

  26. Göktürkler, G., & Balkaya, Ç. (2012). Inversion of self-potential anomalies caused by simple geometry bodies using global optimization algorithms. Journal of Geophysics and Engineering,9, 498–507.

    Google Scholar 

  27. Hafez, M. A. (2005). Interpretation of the self-potential anomaly over a 2D inclined plate using a moving average window curves method. Journal of Geophysics and Engineering,2, 97–102.

    Google Scholar 

  28. Ingber, L., & Rosen, B. (1992). Genetic algorithms and very fast simulated reannealing: A comparison. Mathematical and Computer Modeling,16(11), 87–100.

    Google Scholar 

  29. Jagannadha, R. S., Rama, R. P., & Radhakrishna, M. I. V. (1993). Automatic inversion of self-potential anomalies of sheet-like bodies. Computers & Geosciences,19, 61–73.

    Google Scholar 

  30. Jardani, A., Revil, A., Boleve, A., & Dupont, J. P. (2008). Three-dimensional inversion of self-potential data used to constrain the pattern of groundwater flow in geothermal fields. Journal of Geophysical Research-Solid Earth,113, B09204.

    Google Scholar 

  31. Kaikkonen, P., & Sharma, S. P. (1998). 2-D nonlinear joint inversion of VLF and VLF-R data using simulated annealing. Journal of Applied Geophysics,39, 155–176.

    Google Scholar 

  32. Kulessa, B., Hubbard, B., & Brown, G. H. (2003). Cross-coupled flow modeling of coincident streaming and electrochemical potentials and application to sub-glacial self-potential data. Journal of Geophysical Research,108(B8), 2381.

    Google Scholar 

  33. Lile, O. B. (1994). Modeling self-potential anomalies from electric conductors. In EAGE 56th meeting and technical exhibition (Vienna, Austria).

  34. Mehanee, S. (2014). 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,57, 87–115.

    Google Scholar 

  35. Mehanee, S. (2015). Tracing of paleo-shear zones by self-potential data inversion: case studies from the KTB, Rittsteig, & Grossensees graphite-bearing fault planes. Earth, Planets and Space,67, 14–47.

    Google Scholar 

  36. Mehanee, S., Essa, K. S., & Smith, P. D. (2011). A rapid technique for estimating the depth and width of a two-dimensional plate from self-potential data. Journal of Geophysics and Engineering,8, 447–456.

    Google Scholar 

  37. Mendonca, C. A. (2008). Forward and inverse self-potential modeling in mineral exploration. Geophysics,73, F33–F43.

    Google Scholar 

  38. Monteiro Santos, F. A. (2010). Inversion of self-potential of idealized bodies anomalies using particle swarm optimization. Computers & Geosciences,36, 1185–1190.

    Google Scholar 

  39. Mosegaard, K., & Tarantola, A. (1995). Monte Carlo sampling of solutions to inverse problems. Journal of Geophysical Research,100(B7), 12431–12447.

    Google Scholar 

  40. Murthy, B. V. S., & Haricharan, P. (1984). Self-potential anomaly over double line of poles—interpretation through log curves. Proceedings Indian Academy of Science (Earth and Planetary Science),93, 437–445.

    Google Scholar 

  41. Murthy, B. V. S., & Haricharan, P. (1985). Nomograms for the complete interpretation of spontaneous potential profiles over sheet like and cylindrical 2D structures. Geophysics,50, 1127–1135.

    Google Scholar 

  42. Murthy, I. V. R., Sudhakar, K. S., & Rao, P. R. (2005). A new method of interpreting self- potential anomalies of two-dimensional inclined sheets. Computers & Geosciences,31, 661–665.

    Google Scholar 

  43. Paul, M. K. (1965). Direct interpretation of self-potential anomalies caused by inclined sheets of infinite extension. Geophysics,30, 418–423.

    Google Scholar 

  44. Paul, M. K., Data, S., & Banerjee, B. (1965). Interpretation of SP anomalies due to localized causative bodies. Pure and Applied Geophysics,61, 95–100.

    Google Scholar 

  45. Rao, A. D., Babu, H., & SivakumarSinha, G. D. (1982). A Fourier transform method for the interpretation of self-potential anomalies due to two-dimensional inclined sheet of finite depth extent. Pure and Applied Geophysics,120, 365–374.

    Google Scholar 

  46. Rao, B. S. R., Murthy, I. V. R., & Reddy, S. J. (1970). Interpretation of self-potential anomalies of some simple geometrical bodies. Pure and Applied Geophysics,78, 60–77.

    Google Scholar 

  47. Rothman, D. H. (1985). Nonlinear inversion, statistical mechanics and residual statics estimation. Geophysics,50, 2784–2796.

    Google Scholar 

  48. Rothman, D. H. (1986). Automatic estimation of large residual statics correction. Geophysics,51, 337–346.

    Google Scholar 

  49. Roudsari, M. S., & Beitollahi, A. (2013). Forward modeling and inversion of self-potential anomalies caused by 2D inclined sheets. Exploration Geophysics,44, 176–184.

    Google Scholar 

  50. Roudsari, M. S., & Beitollahi, A. (2015). Laboratory modelling of self-potential anomalies due to spherical bodies. Exploration Geophysics,46, 320–331.

    Google Scholar 

  51. Roy, S. V. S., & Mohan, N. L. (1984). Spectral interpretation of self-potential anomalies of some simple geometric bodies. Pure and Applied Geophysics,78, 66–77.

    Google Scholar 

  52. Sato, M., & Mooney, H. M. (1960). The electrochemical mechanism of sulfide self-potentials. Geophysics,25, 226–249.

    Google Scholar 

  53. Sen, M. K., & Stoffa, P. L. (1996). Bayesian inference, Gibbs sampler and uncertainty estimation in geophysical inversion. Geophysical Prospecting,44, 313–350.

    Google Scholar 

  54. Sen, M. K., & Stoffa, P. L. (2013). Global optimization methods in geophysical inversion (2nd ed.). London: Cambridge Publisher.

    Google Scholar 

  55. Sharma, S. P. (2012). VFSARES—A very fast simulated annealing FORTRAN program for interpretation of 1-D DC resistivity sounding data from various electrode array. Computers & Geosciences,42, 177–188.

    Google Scholar 

  56. Sharma, S. P., & Biswas, A. (2013). Interpretation of self-potential anomaly over 2D inclined structure using very fast simulated annealing global optimization–An insight about ambiguity. Geophysics,78(3), WB3–WB15.

    Google Scholar 

  57. Sundararajan, N., Arun Kumar, I., Mohan, N. L., & SeshagiriRao, S. V. (1990). Use of Hilbert transform to interpret self-potential anomalies due to two dimensional inclined sheets. Pure Applied Geophysics,133, 117–126.

    Google Scholar 

  58. Sundararajan, N., Srinivasa Rao, P., & Sunitha, V. (1998). An analytical method to interpret self-potential anomalies caused by 2D inclined sheets. Geophysics,63, 1551–1555.

    Google Scholar 

  59. Tlas, M., & Asfahani, J. (2007). A best-estimate approach for determining self-potential parameters related to simple geometric shaped structures. Pure and Applied Geophysics,164, 2313–2328.

    Google Scholar 

  60. Tlas, M., & Asfahani, J. (2013). An approach for interpretation of self-potential anomalies due to simple geometrical structures using flair function minimization. Pure and Applied Geophysics,170, 895–905.

    Google Scholar 

  61. Trivedi, S., Kumar, P., Parija, M. P., & Biswas, A. (2020). Global optimization of model parameters from the 2-D analytic signal of gravity and magnetic anomalies. In A. Biswas & S. P. Sharma (Eds.), Advances in modeling and interpretation in near surface geophysics (pp. 189–221). Berlin: Springer.

    Google Scholar 

Download references

Acknowledgments

We would like to thank the Editor-in-Chief Prof. John Carranza and two anonymous reviewers for their comments, which have helped to improve the work. This work forms a part of the Ph.D. thesis of KR, who thank the Council of Scientific and Industrial Research (CSIR), New Delhi, for the research fellowship. This work is a result of a modeling approach in connection with the prospective proposal on the interpretation of mineral exploration study for submission to the Institute of Eminence (IoE) research grant, BHU by AB.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Arkoprovo Biswas.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Rao, K., Jain, S. & Biswas, A. Global Optimization for Delineation of Self-potential Anomaly of a 2D Inclined Plate. Nat Resour Res (2020). https://doi.org/10.1007/s11053-020-09713-4

Download citation

Keywords

  • Self-potential
  • 2D plate
  • VFSA
  • Mineral exploration