Advertisement

Triangular Grid-Based Fuzzy Cross-Update Inversion of Gravity Data: Case Studies from Mineral Exploration

  • Anand SinghEmail author
Original Paper
  • 163 Downloads

Abstract

In mineral exploration, geophysical inversion is a common mathematical tool to obtain reliable information on subsurface density properties based on gravity measurements. Many inversion algorithms were developed to obtain the density distribution in the Earth’s subsurface. Recovered density values are usually lower/higher than the actual density as a consequence of inversion algorithm. This paper presents the use of a fuzzy cross-update inversion (FCUI) procedure to improve the subsurface density model based on a triangular grid. The algorithm is written in MATLAB and uses fuzzy c means clustering to improve the density modeling result per iteration. Two additional input parameters are added, namely the number of geologic units in the model (i.e., number of clusters) and the cluster center values of the geologic units (mean density value of each geologic unit). Inversion results from the FCUI are presented and compared with conventional inversion. The effectiveness of the developed technique is tested for the interpretation of synthetic data and two sets of field data. The FCUI approach shows improvement over conventional inversion approaches in differentiating geologic units. Further, FCUI was performed to reduce ambiguity of interpretation for the delineation of chromite and uranium deposits as the first and second case studies, respectively. We integrated favorable information and show the efficacy of FCUI over conventional inversion for the field datasets.

Keywords

Fuzzy cross-update inversion Conventional inversion Fuzzy c means clustering Gravity data Triangular grid Mineral exploration 

Notes

Acknowledgments

The author is thankful to the Prof. John Carranza (Editor-in-Chief), Prof. Colin Farquharson, and anonymous reviewers for the reviews and numerous suggestions which greatly improved the paper. The author is also thankful to Dr. Shuang Liu, China University of Geosciences (Wuhan), for his 2D-CDTGMI code to compare the results. The author is extremely grateful to the IRCC-IITB for the financial support to carry out this study in the form of a Seed Grant Project (Project code- RD/0518-IRCCSH0-022).

References

  1. Baranwal, V. C., Franke, A., Borner, R. U., & Spitzer, K. (2011). Unstructured grid based 2-D inversion of VLF data for models including topography. Journal of Applied Geophysics, 75, 363–372.CrossRefGoogle Scholar
  2. Blakely, R. J. (1995). Potential theory in gravity and magnetic applications. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  3. Böhm, G., Galuppo, P., & Vesnaver, A. (2000). 3D adaptive tomography using Delaunay triangles and Voronoi polygons. Geophysical Prospecting, 48, 723–744.CrossRefGoogle Scholar
  4. Burger, H. R., Sheehan, A. F., & Jones, C. H. (2006). Introduction to applied geophysics. New York: W. W Norton and Company.Google Scholar
  5. Carrillo, J., & Gallardo, L. A. (2018). Joint two-dimensional inversion of magnetotelluric and gravity data using correspondence maps. Geophysical Journal International, 214(2), 1061–1071.CrossRefGoogle Scholar
  6. Carter-McAuslan, A., Lelièvre, P. G., & Farquharson, C. G. (2015). A study of fuzzy c-means coupling for joint inversion, using seismic tomography and gravity data test scenarios. Geophysics, 80(1), W1–W15.CrossRefGoogle Scholar
  7. Ellis, R. G., & Oldenburg, D. W. (1994). The pole-pole 3-D DC resistivity inverse problem: Conjugate gradient approach. Geophysical Journal International, 119, 187–194.CrossRefGoogle Scholar
  8. Farquharson, C. G., Ash, M. R., & Miller, H. G. (2008). Geologically constrained gravity inversion for the Voisey’s Bay ovoid deposit. The Leading Edge, 27, 64–69.CrossRefGoogle Scholar
  9. Franke, A., Borner, R., & Spitzer, K. (2007). Adaptive unstructured grid finite element simulation of two-dimensional magnetotelluric fields for arbitrary surface and seafloor topography. Geophysical Journal International, 171, 71–86.CrossRefGoogle Scholar
  10. Günther, T., Rucker, C., & Spitzer, K. (2006). Three-dimensional modeling and inversion of dc resistivity data incorporating topography-II. Inversion. Geophysical Journal International, 166, 506–517.CrossRefGoogle Scholar
  11. Heincke, B., Jegen, M., Moorkamp, M., & Chen, J. (2010). Adaptive coupling strategy for simultaneous joint inversion that use petrophysical information as constraints. In 80th Annual International Meeting, SEG, Expanded Abstracts (pp. 2805–2809).Google Scholar
  12. Johnson, C., & Erikson, K. (1991). Finite element methods for parabolic problems I: A linear model problem. SIAM Journal on Numerical Analysis, 28, 43–77.CrossRefGoogle Scholar
  13. Key, K., & Ovall, J. (2011). A parallel goal-oriented adaptive finite element method for 2.5-D electromagnetic modeling. Geophysical Journal International, 186, 137–154.CrossRefGoogle Scholar
  14. Lane, R., FitzGerald, D., Guillen, A., Seikel, R., & Mclnerey, P. (2007). Lithologically constrained inversion of magnetic and gravity data sets. Preview, 129, 11–17.Google Scholar
  15. Last, B. J., & Kubik, K. (1983). Compact gravity inversion. Geophysics, 48, 713–721.CrossRefGoogle Scholar
  16. Lelièvre, P. G., & Farquharson, C. G. (2013). Gradient and smoothness regularization operators for geophysical inversion on unstructured meshes. Geophysical Journal International, 195, 330–341.CrossRefGoogle Scholar
  17. Lelièvre, P. G., Farquharson, C. G., & Hurich, C. A. (2011). Inversion of first-arrival seismic travel times without rays, implemented on unstructured grids. Geophysical Journal International, 185, 749–763.CrossRefGoogle Scholar
  18. Lelièvre, P. G., Farquharson, C. G., & Hurich, C. A. (2012). Joint inversion of seismic travel times and gravity data on unstructured grids with application to mineral exploration. Geophysics, 77(1), K1–K15.CrossRefGoogle Scholar
  19. Lelièvre, P. G., Oldenburg, D. W., & Williams, N. C. (2009). Integrating geological and geophysical data through advanced constrained inversions. Exploration Geophysics (Collingwood, Australia), 40, 334–341.CrossRefGoogle Scholar
  20. Li, Y., & Oldenburg, D. W. (1998). 3-D inversion of gravity data. Geophysics, 63, 109–119.CrossRefGoogle Scholar
  21. Liu, S., Hu, X., Liu, T., Feng, J., Gao, W., & Qiu, L. (2013). Magnetization vector imaging for borehole magnetic data based on magnitude magnetic anomaly. Geophysics, 78, D429–D444.CrossRefGoogle Scholar
  22. Liu, S., Hu, X., Xi, Y., & Liu, T. (2015). 2D inverse modeling for potential fields on rugged observation surface using constrained Delaunay triangulation. Computers and Geosciences, 76, 18–30.CrossRefGoogle Scholar
  23. Maag, E., & Li, Y. (2018). Discrete-valued gravity inversion using the guided fuzzy c-means clustering technique. Geophysics, 83(4), G59–G77.CrossRefGoogle Scholar
  24. Mandal, A., Mohanty, W. K., Sharma, S. P., Biswas, A., Sen, J., & Bhatt, A. K. (2015). Geophysical signatures of uranium mineralization and its subsurface validation at Beldih, Purulia District, West Bengal, India: a case study. Geophysical Prospecting, 63, 713–726.CrossRefGoogle Scholar
  25. Mohanty, W. K., Mandal, A., Sharma, S. P., Gupta, S., & Misra, S. (2011). Integrated geological and geophysical studies for delineation of chromite deposits: A case study from Tangarparha, Orissa. IndiaChromite exploration at Tangarparha. Geophysics, 76(5), B173–B185.Google Scholar
  26. Paasche, H., & Tronicke, J. (2007). Cooperative inversion of 2D geophysical data sets: A zonal approach based on fuzzy c-means cluster analysis. Geophysics, 72(3), A35–A39.CrossRefGoogle Scholar
  27. Paasche, H., Tronicke, J., Holliger, K., Green, A. G., & Maurer, H. (2006). Integration of diverse physical-property models: Subsurface zonation and petrophysical parameter estimation based on fuzzy c-means cluster analyses. Geophysics, 71(3), H33–H44.CrossRefGoogle Scholar
  28. Piggott, M. D., Gorman, G. J., Pain, C. C., Allison, P. A., Candy, A. S., Martin, B. T., et al. (2008). A systematic approach to unstructured mesh generation for ocean modeling using GMT and Terre no. Computer and Geosciences, 34, 1721–1731.CrossRefGoogle Scholar
  29. Pilkington, M. (1997). 3-D magnetic imaging using conjugate gradients. Geophysics, 62, 1132–1142.CrossRefGoogle Scholar
  30. Pilkington, M. (2009). 3D magnetic data-space inversion with sparseness constraints. Geophysics, 74(1), L7–L15.CrossRefGoogle Scholar
  31. Ramarao, P., & Murthy, I. V. R. (1989). Two FORTRAN 77 function subprograms to calculate gravity anomalies of bodies of finite and infinite strike length with the density contrast differing with depth. Computer and Geosciences, 15(8), 1265–1277.CrossRefGoogle Scholar
  32. Ren, Z., Kalscheuer, T., Greenhalgh, S., & Maurer, H. (2013). A goal-oriented adaptive finite-element approach for plane wave 3-D electromagnetic modeling. Geophysical Journal International, 194, 700–718.CrossRefGoogle Scholar
  33. Rodi, W., & Mackie, R. L. (2001). Nonlinear conjugate gradients algorithm for 2D magnetotelluric inversion. Geophysics, 66, 174–187.CrossRefGoogle Scholar
  34. Roy, K. K. (2007). Potential theory in applied geophysics. Berlin: Springer-Verlag.Google Scholar
  35. Singh, A., & Biswas, A. (2016). Application of global particle swarm optimization for inversion of residual gravity anomalies over geological bodies with idealized geometries. Natural Resources Research, 25(3), 297–314.CrossRefGoogle Scholar
  36. Singh, A., Mishra, P. K., & Sharma, S. P. (2019). 2D Cooperative inversion of direct current resistivity and gravity data: A case study of uranium bearing target rock. Geophysical Prospecting.  https://doi.org/10.1111/1365-2478.12763.Google Scholar
  37. Singh, A., & Sharma, S. P. (2016). Interpretation of very low frequency electromagnetic measurements in terms of normalized current density over variable topography. Journal of Applied Geophysics, 133, 82–91.CrossRefGoogle Scholar
  38. Singh, A., & Sharma, S. P. (2017). Modified zonal cooperative inversion of gravity data-a case study from uranium mineralization. In Society of Exploration Geophysicists Technical Program Expanded Abstracts (pp. 1744–1749).Google Scholar
  39. Singh, A., & Sharma, S. P. (2018). Identification of different geologic units using fuzzy constrained resistivity tomography. Journal of Applied Geophysics, 148, 127–138.CrossRefGoogle Scholar
  40. Singh, A., Sharma, S. P., Akca, İ., & Baranwal, V. C. (2018). Fuzzy constrained Lp-norm inversion of direct current resistivity data. Geophysics, 83(1), E11–E24.CrossRefGoogle Scholar
  41. Spitzer, K. (1995). A 3-D finite difference algorithm for DC resistivity modelling using conjugate gradient methods. Geophysical Journal International, 123, 903–914.CrossRefGoogle Scholar
  42. Sun, J., & Li, Y. (2015). Multidomain petrophysically constrained inversion and geology differentiation using guided fuzzy c-means clustering. Geophysics, 80(4), ID1–ID18.CrossRefGoogle Scholar
  43. Sun, J., & Li, Y. (2016). Joint inversion of multiple geophysical data using guided fuzzy c-means clustering. Geophysics, 81(3), ID37–ID57.CrossRefGoogle Scholar
  44. Sun, J., & Li, Y. (2017). Joint inversion of multiple geophysical and petrophysical data using generalized fuzzy clustering algorithms. Geophysical Journal International, 208(2), 1201–1216.CrossRefGoogle Scholar
  45. Wang, J., Meng, X., & Li, F. (2015). A computationally efficient scheme for the inversion of large scale potential field data: Application to synthetic and real data. Computers and Geosciences, 85, 102–111.CrossRefGoogle Scholar
  46. Williams, N. C. (2008). Geologically-constrained UBC-GIF gravity and magnetic inversions with examples from the Agnew-Wiluna Greenstone Belt, Western Australia. Ph.D. thesis, University of British Columbia.Google Scholar
  47. Wilson, C. R. (2009). Modeling unstructured meshes. London: Imperial College London.Google Scholar
  48. Zhang, J., Mackie, R. L., & Madden, T. R. (1995). 3-D resistivity forward modeling and inversion using conjugate gradients. Geophysics, 60, 1313–1325.CrossRefGoogle Scholar

Copyright information

© International Association for Mathematical Geosciences 2019

Authors and Affiliations

  1. 1.Department of Earth SciencesIndian Institute of Technology BombayBombayIndia

Personalised recommendations