Advertisement

Natural Resources Research

, Volume 25, Issue 3, pp 297–314 | Cite as

Application of Global Particle Swarm Optimization for Inversion of Residual Gravity Anomalies Over Geological Bodies with Idealized Geometries

  • Anand Singh
  • Arkoprovo Biswas
Article

Abstract

A global particle swarm optimization (GPSO) technique is developed and applied to the inversion of residual gravity anomalies caused by buried bodies with simple geometry (spheres, horizontal, and vertical cylinders). Inversion parameters, such as density contrast of geometries, radius of body, depth of body, location of anomaly, and shape factor, were optimized. The GPSO algorithm was tested on noise-free synthetic data, synthetic data with 10% Gaussian noise, and five field examples from different parts of the world. The present study shows that the GPSO method is able to determine all the model parameters accurately even when shape factor is allowed to change in the optimization problem. However, the shape was fixed a priori in order to obtain the most consistent appraisal of various model parameters. For synthetic data without noise or with 10% Gaussian noise, estimates of different parameters were very close to the actual model parameters. For the field examples, the inversion results showed excellent agreement with results from previous studies that used other inverse techniques. The computation time for the GPSO procedure is very short (less than 1 s) for a swarm size of less than 50. The advantage of the GPSO method is that it is extremely fast and does not require assumptions about the shape of the source of the residual gravity anomaly.

Keywords

Residual gravity anomaly Inversion Global particle swarm optimization Exploration 

Notes

Acknowledgements

We thank the Editor-in-chief, Prof. John Carranza, Dr. Ertan Pekşen, and an anonymous reviewer for the comments and suggestion which have improved the quality of the manuscript. We are also grateful to Prof. S. P. Sharma, Geology and Geophysics, IIT Kharagpur for his keen interest and encouragement throughout the development of this work. One of the authors AB also acknowledges the necessary facilities and support from the Director of IISER Bhopal to complete this work.

References

  1. Abdelrahman, E. M., Bayoumi, A. I., Abdelhady, Y. E., Gobash, M. M., & EL-Araby, H. M. (1989). Gravity interpretation using correlation factors between successive least-squares residual anomalies. Geophysics, 54, 1614–1621.CrossRefGoogle Scholar
  2. Abdelrahman, E. M., El-Araby, T. M., El-Araby, H. M., & Abo-Ezz, E. R. (2001a). Three least squares minimization approaches to depth, shape, and amplitude coefficient determination from gravity data. Geophysics, 66, 1105–1109.CrossRefGoogle Scholar
  3. Abdelrahman, E. M., El-Araby, T. M., El-Araby, H. M., & Abo-Ezz, E. R. (2001b). A new method for shape and depth determinations from gravity data. Geophysics, 66, 1774–1780.CrossRefGoogle Scholar
  4. Abdelrahman, E. M., & Sharafeldin, S. M. (1995a). A Least-squares minimization approach to depth determination from numerical horizontal gravity gradients. Geophysics, 60, 1259–1260.CrossRefGoogle Scholar
  5. Abdelrahman, E. M., & Sharafeldin, S. M. (1995b). A least-squares minimization approach to shape determination from gravity data. Geophysics, 60, 589–590.CrossRefGoogle Scholar
  6. Alvarez, J. P. F., Martinez, F., Gonzalo, E. G., & Perez, C. O. M. (2006). Application of the particle swarm optimization algorithm to the solution and appraisal of the vertical electrical sounding inverse problem. In Proceedings of the 11th Annual Conference of the International Association of Mathematical Geology (IAMG06), Liege, Belgium, CDROM.Google Scholar
  7. Asfahani, J., & Tlas, M. (2012). Fair function minimization for direct interpretation of residual gravity anomaly profiles due to spheres and cylinders. Pure and Applied Geophysics, 169, 157–165.CrossRefGoogle Scholar
  8. Beck, R. H., & Qureshi, I. R. (1989). Gravity mapping of a subsurface cavity at Marulan, N.S.W. Exploration Geophysics, 20, 481–486.CrossRefGoogle Scholar
  9. Biswas, A. (2015). Interpretation of residual gravity anomaly caused by a simple shaped body using very fast simulated annealing global optimization. Geoscience Frontiers. doi: 10.1016/j.gsf.2015.03.001.Google Scholar
  10. Bowin, C., Scheer, E., & Smith, W. (1986). Depth estimates from ratios of gravity, geoid and gravity gradient anomalies. Geophysics, 51, 123–136.CrossRefGoogle Scholar
  11. Chau, W. K. (2008). Application of a particle swarm optimization algorithm to hydrological problems. In L. N. Robinson (Ed.), Water resources research progress (pp. 3–12). New York: Nova Science Publishers Inc.Google Scholar
  12. Eberhart, R. C., & Kennedy, J. (1995). A new optimizer using particle swarm theory. In Proceedings of the sixth international symposium on micro machine and human science. IEEE service center, Piscataway, NJ, Nagoya, Japan, 39–43.Google Scholar
  13. Eberhart, R. C., & Shi, Y. (2001). Particle swarm optimization: Developments, applications and resources. In: Proceedings of congress on evolutionary computation 2001. IEEE service center, Piscataway, NJ, Seoul, Korea.Google Scholar
  14. Elawadi, E., Salem, A., & Ushijima, K. (2001). Detection of cavities from gravity data using a neural network. Exploration Geophysics, 32, 204–208.CrossRefGoogle Scholar
  15. Essa, K. S. (2007). Gravity data interpretation using the s-curves method. Journal of Geophysics and Engineering, 4(2), 204–213.CrossRefGoogle Scholar
  16. Essa, K. S. (2012). A fast interpretation method for inverse modelling of residual gravity anomalies caused by simple geometry. Journal of Geological Research. Volume 2012, Article ID 327037.Google Scholar
  17. Essa, K. S. (2013). New fast least-squares algorithm for estimating the best-fitting parameters due to simple geometric-structures from gravity anomalies. Journal of Advanced Research, 5, 57–65.CrossRefGoogle Scholar
  18. Fedi, M. (2007). DEXP: A fast method to determine the depth and the structural index of potential fields sources. Geophysics, 72(1), I1–I11.CrossRefGoogle Scholar
  19. Grant, F. S., & West, G. F. (1965). Interpretation theory in applied geophysics. New York: McGraw-Hill Book Co.Google Scholar
  20. Gupta, O. P. (1983). A least-squares approach to depth determination from gravity data. Geophysics, 48, 357–360.CrossRefGoogle Scholar
  21. Hartmann, R. R., Teskey, D., & Friedberg, I. (1971). A system for rapid digital aeromagnetic interpretation. Geophysics, 36, 891–918.CrossRefGoogle Scholar
  22. Hinze, W. J. (1990). The role of gravity and magnetic methods in engineering and environmental studies. In S. H. Ward (Ed.), Geotechnical and environmental geophysics, vol. I: Review and tutorial. Tulsa, OK: Society of Exploration Geophysicists.Google Scholar
  23. Hinze, W. J., Von Frese, R. R. B., & Saad, A. H. (2013). Gravity and magnetic exploration: Principles, practices and applications. New York: Cambridge University Press.CrossRefGoogle Scholar
  24. Jain, S. (1976). An automatic method of direct interpretation of magnetic profiles. Geophysics, 41, 531–541.CrossRefGoogle Scholar
  25. Juan, L. F. M., Esperanza, G., José, G. P. F. Á., Heidi, A. K., & César, O. M. P. (2010). PSO: A powerful algorithm to solve geophysical inverse problems: Application to a 1D-DC resistivity case. Journal of Applied Geophysics, 71, 13–25.CrossRefGoogle Scholar
  26. Kennedy, J., & Eberhart, R. (1995). Particle swarm optimization. In IEEE international conference on neural networks, Vol. IV, Piscataway, NJ, 1942–1948.Google Scholar
  27. Kilty, T. K. (1983). Werner deconvolution of profile potential field data. Geophysics, 48, 234–237.CrossRefGoogle Scholar
  28. Lafehr, T. R., & Nabighian, M. N. (2012). Fundamentals of gravity exploration. Tulsa, OK: Society of Exploration Geophysicists.CrossRefGoogle Scholar
  29. Lasmar, R. N., Guellala, R., Naouali, B. S., Triki, L., & Inoubli, M. H. (2014). Contribution of geophysics to the management of water resources: Case of the Ariana agricultural sector (Eastern Mejerda Basin, Tunisia). Natural Resources Research, 23, 367–377.CrossRefGoogle Scholar
  30. Lines, L. R., & Treitel, S. (1984). A review of least-squares inversion and its application to geophysical problems. Geophysical Prospecting, 32, 159–186.CrossRefGoogle Scholar
  31. Long, L. T., & Kaufmann, R. D. (2013). Acquisition and analysis of terrestrial gravity data. New York: Cambridge University Press.CrossRefGoogle Scholar
  32. Mehanee, S. A. (2014). Accurate and efficient regularized inversion approach for the interpretation of isolated gravity anomalies. Pure and Applied Geophysics, 171, 1897–1937.CrossRefGoogle Scholar
  33. Mohan, N. L., Anandababu, L., & Roa, S. (1986). Gravity interpretation using the Melin transform. Geophysics, 51, 114–122.CrossRefGoogle Scholar
  34. Monteiro Santos, F. A. (2010). Inversion of self-potential of idealized bodies’ anomalies using particle swarm optimization. Computers & Geosciences, 36, 1185–1190.CrossRefGoogle Scholar
  35. Nettleton, L. L. (1962). Gravity and magnetics for geologists and seismologists. AAPG, 46, 1815–1838.Google Scholar
  36. Nettleton, L. L. (1976). Gravity and magnetics in oil prospecting. New York: McGraw-Hill Book Co.Google Scholar
  37. Odegard, M. E., & Berg, J. W. (1965). Gravity interpretation using the Fourier integral. Geophysics, 30, 424–438.CrossRefGoogle Scholar
  38. Pekşen, E., Yas, T., Kayman, A. Y., & Özkan, C. (2011). Application of particle swarm optimization on self-potential data. Journal of Applied Geophysics, 75(2), 305–318.CrossRefGoogle Scholar
  39. Pekşen, E., Yas, T., & Kıyak, A. (2014). 1-D DC resistivity modeling and interpretation in anisotropic media using particle swarm optimization. Pure and Applied Geophysics, 171(9), 2371–2389.CrossRefGoogle Scholar
  40. Perez, R. E., & Behdinan, K. (2007). Particle swarm approach for structural design optimization. Computers & Structures, 85, 1579–1588.CrossRefGoogle Scholar
  41. Roy, L., Agarwal, B. N. P., & Shaw, R. K. (2000). A new concept in Euler deconvolution of isolated gravity anomalies. Geophysical Prospecting, 48, 559–575.CrossRefGoogle Scholar
  42. Salem, A., Elawadib, E., & Ushijima, K. (2003). Depth determination from residual gravity anomaly data using a simple formula. Computers & Geosciences, 29, 801–804.CrossRefGoogle Scholar
  43. Salem, A., & Ravat, D. (2003). A combined analytic signal and Euler method (AN-EUL) for automatic interpretation of magnetic data. Geophysics, 68(6), 1952–1961.CrossRefGoogle Scholar
  44. Salem, A., Ravat, D., Mushayandebvu, M. F., & Ushijima, K. (2004). Linearized least-squares method for interpretation of potential-field data from sources of simple geometry. Geophysics, 69(3), 783–788.CrossRefGoogle Scholar
  45. Sanyi, Y., Shangxu, W., & Nan, T. (2009). Swarm intelligence optimization and its application in geophysical data inversion. Applied Geophysics, 6, 166–174.CrossRefGoogle Scholar
  46. Sharma, B., & Geldart, L. P. (1968). Analysis of gravity anomalies of two-dimensional faults using Fourier transforms. Geophysical Prospecting, 16, 77–93.CrossRefGoogle Scholar
  47. Shaw, R. K., & Agarwal, B. N. P. (1990). The application of Walsh transforms to interpret gravity anomalies due to some simple geometrically shaped causative sources: A feasibility study. Geophysics, 55, 843–850.CrossRefGoogle Scholar
  48. Shaw, R., & Srivastava, S. (2007). Particle swarm optimization: A new tool to invert geophysical data. Geophysics, 72(2), 75–83.CrossRefGoogle Scholar
  49. Shi, Y. & Eberhart, R. (1998). A modified particle swarm optimizer. In IEEE international conference on evolutionary computation (pp. 69–73). IEEE Press, Piscataway, NJ.Google Scholar
  50. Siegel, H. O., Winkler, H. A., & Boniwell, J. B. (1957). Discovery of the Mobrun Copper Ltd. sulphide deposit, Noranda Mining District, Quebec. In: Methods and case histories in mining geophysics. 6th Commonwealth Mining Met. Congress (pp. 237–245), Vancouver.Google Scholar
  51. Sweilam, N. H., Gobashy, M. M., & Hashem, T. (2008). Using particle swarm optimization with function stretching (SPSO) for inverting gravity data: A visibility study. Proceedings of the Mathematical and Physical Society of Egypt, 86(2), 259–281.Google Scholar
  52. Telford, W. M., Geldart, L. P., & Sheriff, R. E. (1990). Applied geophysics (2nd ed.). London: Cambridge University Press.CrossRefGoogle Scholar
  53. Thompson, D. T. (1982). EULDPH—A new technique for making computer-assisted depth estimates from magnetic data. Geophysics, 47, 31–37.CrossRefGoogle Scholar
  54. Tlas, M., Asfahani, J., & Karmeh, H. (2005). A versatile nonlinear inversion to interpret gravity anomaly caused by a simple geometrical structure. Pure and Applied Geophysics, 162, 2557–2571.CrossRefGoogle Scholar
  55. Toushmalani, R. (2013a). Gravity inversion of a fault by particle swarm optimization (PSO). Springer Plus, 2, 315.CrossRefGoogle Scholar
  56. Toushmalani, R. (2013b). Comparison result of inversion of gravity data of a fault by particle swarm optimization and Levenberg-Marquardt methods. Springer Plus, 2, 462.CrossRefGoogle Scholar

Copyright information

© International Association for Mathematical Geosciences 2015

Authors and Affiliations

  1. 1.Department of Geology and GeophysicsIndian Institute of Technology KharagpurKharagpurIndia
  2. 2.Department of Earth and Environmental SciencesIndian Institute of Science Education and Research (IISER) BhopalBhopalIndia

Personalised recommendations