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Journal of Applied Mathematics
Volume 2014, Article ID 319314, 12 pages
http://dx.doi.org/10.1155/2014/319314
Research Article

A Fast Independent Component Analysis Algorithm for Geochemical Anomaly Detection and Its Application to Soil Geochemistry Data Processing

1Geomathematics Key Laboratory of Sichuan Province, Chengdu University of Technology, Chengdu 610059, China
2College of Geophysics, Chengdu University of Technology, Chengdu 610059, China

Received 14 March 2014; Revised 21 June 2014; Accepted 7 July 2014; Published 23 July 2014

Academic Editor: Chongbin Zhao

Copyright © 2014 Bin Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. C. Zhao, H. B. Mühlhaus, and B. E. Hobbs, “Finite element analysis of steady-state natural convection problems in fluid-saturated porous media heated from below,” International Journal for Numerical and Analytical Methods in Geomechanics, vol. 21, no. 12, pp. 863–881, 1997. View at Publisher · View at Google Scholar · View at Scopus
  2. C. Zhao, B. E. Hobbs, and H. B. Mühlhaus, “Finite element modelling of temperature gradient driven rock alteration and mineralization in porous rock masses,” Computer Methods in Applied Mechanics and Engineering, vol. 165, no. 1–4, pp. 175–187, 1998. View at Publisher · View at Google Scholar · View at Scopus
  3. C. Zhao, B. E. Hobbs, and H. B. Mühlhaus, “Theoretical and numerical analyses of convective instability in porous media with upward throughflow,” International Journal for Numerical and Analytical Methods in Geomechanics, vol. 23, no. 7, pp. 629–646, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  4. B. E. Hobbs, Y. Zhang, A. Ord, and C. Zhao, “Application of coupled deformation, fluid flow, thermal and chemical modelling to predictive mineral exploration,” Journal of Geochemical Exploration, vol. 69-70, pp. 505–509, 2000. View at Publisher · View at Google Scholar · View at Scopus
  5. A. Ord, B. E. Hobbs, Y. Zhang et al., “Geodynamic modelling of the Century deposit, Mt Isa Province, Queensland,” Australian Journal of Earth Sciences, vol. 49, no. 6, pp. 1011–1039, 2002. View at Publisher · View at Google Scholar · View at Scopus
  6. P. Sorjonen-Ward, Y. Zhang, and C. Zhao, “Numerical modelling of orogenic processes and gold mineralisation in the southeastern part of the Yilgarn Craton, Western Australia,” Australian Journal of Earth Sciences, vol. 49, no. 6, pp. 935–964, 2002. View at Publisher · View at Google Scholar · View at Scopus
  7. P. A. Gow, P. Upton, C. Zhao, and K. C. Hill, “Copper-gold mineralisation in New Guinea: numerical modelling of collision, fluid flow and intrusion-related hydrothermal systems,” Australian Journal of Earth Sciences, vol. 49, no. 4, pp. 753–771, 2002. View at Publisher · View at Google Scholar · View at Scopus
  8. P. M. Schaubs and C. Zhao, “Numerical models of gold-deposit formation in the Bendigo-Ballarat Zone, Victoria,” Australian Journal of Earth Sciences, vol. 49, no. 6, pp. 1077–1096, 2002. View at Publisher · View at Google Scholar · View at Scopus
  9. Y. Zhang, B. E. Hobbs, A. Ord et al., “The influence of faulting on host-rock permeability, fluid flow and ore genesis of gold deposits: a theoretical 2D numerical model,” Journal of Geochemical Exploration, vol. 78-79, pp. 279–284, 2003. View at Publisher · View at Google Scholar · View at Scopus
  10. C. Zhao, B. E. Hobbs, A. Ord, S. Peng, H. B. Mühlhaus, and L. Liu, “Theoretical investigation of convective instability in inclined and fluid-saturated three-dimensional fault zones,” Tectonophysics, vol. 387, no. 1–4, pp. 47–64, 2004. View at Publisher · View at Google Scholar · View at Scopus
  11. C. Zhao, B. E. Hobbs, A. Ord, P. Hornby, S. Peng, and L. Liu, “Mineral precipitation associated with vertical fault zones: the interaction of solute advection, diffusion and chemical kinetics,” Geofluids, vol. 7, no. 1, pp. 3–18, 2007. View at Publisher · View at Google Scholar · View at Scopus
  12. C. Zhao, B. E. Hobbs, and A. Ord, Convective and Advective Heat Transfer in Geological Systems, Springer, Berlin, Germany, 2008.
  13. C. Zhao, Dynamic and Transient Infinite Elements: Theory and Geophysical, Geotechnical and Geoenvironmental Applications, Advances in Geophysical and Environmental Mechanics and Mathematics, Springer, Berlin, Germany, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  14. C. Zhao, B. E. Hobbs, and A. Ord, “Investigating dynamic mechanisms of geological phenomena using methodology of computational geosciences: an example of equal-distant mineralization in a fault,” Science in China D: Earth Sciences, vol. 51, no. 7, pp. 947–954, 2008. View at Publisher · View at Google Scholar · View at Scopus
  15. C. Zhao, B. E. Hobbs, and A. Ord, Fundamentals of Computational Geoscience: Numerical Methods and Algorithms, Springer, Berlin, Germany, 2009.
  16. S. C. Wang, Theory and Methods of Mineral Resources Prediction Based on Synthetic Information, Science Press, Beijing, China, 2002.
  17. Q. Cheng, F. P. Agterberg, and G. F. Bonham-Carter, “A spatial analysis method for geochemical anomaly separation,” Journal of Geochemical Exploration, vol. 56, no. 3, pp. 183–195, 1996. View at Publisher · View at Google Scholar · View at Scopus
  18. Q. Cheng, “Spatial and scaling modelling for geochemical anomaly separation,” Journal of Geochemical Exploration, vol. 65, no. 3, pp. 175–194, 1999. View at Publisher · View at Google Scholar · View at Scopus
  19. Q. Cheng, Y. Xu, and E. Grunsky, “Integrated spatial and spectrum method for geochemical anomaly separation,” Natural Resources Research, vol. 9, no. 1, pp. 43–52, 2000. View at Publisher · View at Google Scholar · View at Scopus
  20. Q. Cheng, “Mapping singularities with stream sediment geochemical data for prediction of undiscovered mineral deposits in Gejiu, Yunnan Province, China,” Ore Geology Reviews, vol. 32, no. 1-2, pp. 314–324, 2007. View at Publisher · View at Google Scholar · View at Scopus
  21. Q. M. Cheng, C. Lu, and C. Ko, “GIS spatial: temporal modeling of water systems in greater,” Earth Science: Journal of China University of Geosciences, vol. 15, no. 13, pp. 1–8, 2004. View at Google Scholar
  22. P. Filzmoser, K. Hron, and C. Reimann, “Interpretation of multivariate outliers for compositional data,” Computers and Geosciences, vol. 39, pp. 77–85, 2012. View at Publisher · View at Google Scholar · View at Scopus
  23. W. Wang, J. Zhao, and Q. Cheng, “Analysis and integration of geo-information to identify granitic intrusions as exploration targets in southeastern Yunnan District, China,” Computers & Geosciences, vol. 37, no. 12, pp. 1946–1957, 2011. View at Publisher · View at Google Scholar · View at Scopus
  24. Q. Cheng, F. P. Agterberg, and S. B. Ballantyne, “The separation of geochemical anomalies from background by fractal methods,” Journal of Geochemical Exploration, vol. 51, no. 2, pp. 109–130, 1994. View at Publisher · View at Google Scholar · View at Scopus
  25. R. Ghavami-Riabi, M. M. Seyedrahimi-Niaraq, R. Khalokakaie, and M. R. Hazareh, “U-spatial statistic data modeled on a probability diagram for investigation of mineralization phases and exploration of shear zone gold deposits,” Journal of Geochemical Exploration, vol. 104, no. 1-2, pp. 27–33, 2010. View at Publisher · View at Google Scholar · View at Scopus
  26. M. A. Gonçalves, A. Mateus, and V. Oliveira, “Geochemical anomaly separation by multifractal modelling,” Journal of Geochemical Exploration, vol. 72, no. 2, pp. 91–114, 2001. View at Publisher · View at Google Scholar · View at Scopus
  27. U. Kramar, “Application of limited fuzzy clusters to anomaly recognition in complex geological environments,” Journal of Geochemical Exploration, vol. 55, no. 1–3, pp. 81–92, 1995. View at Publisher · View at Google Scholar · View at Scopus
  28. C. Li, T. Ma, and J. Shi, “Application of a fractal method relating concentrations and distances for separation of geochemical anomalies from background,” Journal of Geochemical Exploration, vol. 77, no. 2-3, pp. 167–175, 2003. View at Publisher · View at Google Scholar · View at Scopus
  29. P. Roshani, A. R. Mokhtari, and S. H. Tabatabaei, “Objective based geochemical anomaly detection—application of discriminant function analysis in anomaly delineation in the Kuh Panj porphyry Cu mineralization (Iran),” Journal of Geochemical Exploration, vol. 130, pp. 65–73, 2013. View at Publisher · View at Google Scholar · View at Scopus
  30. P. Lenca, P. Meyer, B. Vaillant, and S. Lallich, “On selecting interestingness measures for association rules: user oriented description and multiple criteria decision aid,” European Journal of Operational Research, vol. 184, no. 2, pp. 610–626, 2008. View at Publisher · View at Google Scholar · View at Scopus
  31. T. Lee, M. Girolami, A. J. Bell, and T. Sejnowski, “A unifying information-theoretic framework for independent component analysis,” Computers & Mathematics with Applications, vol. 39, no. 11, pp. 1–21, 2000. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  32. X. C. Yu, L. W. Liu, D. Hu, and Z. N. Wang, “Robust ordinal independent component analysis (ROICA) applied to mineral resources prediction,” Journal of Jilin University (Earth Science Edition), vol. 42, no. 3, pp. 872–880, 2012. View at Google Scholar · View at Scopus
  33. C. Zhao, B. E. Hobbs, H. B. Mühlhaus, A. Ord, and G. Lin, “Convective instability of 3-D fluid-saturated geological fault zones heated from below,” Geophysical Journal International, vol. 155, no. 1, pp. 213–220, 2003. View at Publisher · View at Google Scholar · View at Scopus
  34. C. Zhao, B. E. Hobbs, A. Ord, S. Peng, H. B. Mühlhaus, and L. Liu, “Double diffusion-driven convective instability of three-dimensional fluid-saturated geological fault zones heated from below,” Mathematical Geology, vol. 37, no. 4, pp. 373–391, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  35. C. Zhao, B. E. Hobbs, and A. Ord, “Theoretical analyses of nonaqueous phase liquid dissolution-induced instability in two-dimensional fluid-saturated porous media,” International Journal for Numerical and Analytical Methods in Geomechanics, vol. 34, no. 17, pp. 1767–1796, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  36. C. Zhao, B. E. Hobbs, A. Ord, P. Hornby, and S. Peng, “Morphological evolution of three-dimensional chemical dissolution front in fluid-saturated porous media: a numerical simulation approach,” Geofluids, vol. 8, no. 2, pp. 113–127, 2008. View at Publisher · View at Google Scholar · View at Scopus
  37. C. Zhao, B. E. Hobbs, P. Hornby, A. Ord, S. Peng, and L. Liu, “Theoretical and numerical analyses of chemical-dissolution front instability in fluid-saturated porous rocks,” International Journal for Numerical and Analytical Methods in Geomechanics, vol. 32, no. 9, pp. 1107–1130, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  38. C. Zhao, B. E. Hobbs, A. Ord, P. Hornby, and S. Peng, “Effect of reactive surface areas associated with different particle shapes on chemical-dissolution front instability in fluid-saturated porous rocks,” Transport in Porous Media, vol. 73, no. 1, pp. 75–94, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  39. C. Zhao, B. E. Hobbs, A. Ord, and S. Peng, “Effects of mineral dissolution ratios on chemical-dissolution front instability in fluid-saturated porous media,” Transport in Porous Media, vol. 82, no. 2, pp. 317–335, 2010. View at Publisher · View at Google Scholar · View at Scopus
  40. C. Zhao, B. E. Hobbs, and A. Ord, “Theoretical analyses of the effects of solute dispersion on chemical-dissolution front instability in fluid-saturated porous media,” Transport in Porous Media, vol. 84, no. 3, pp. 629–653, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  41. C. Zhao, B. E. Hobbs, and A. Ord, “Effects of medium and pore-fluid compressibility on chemical-dissolution front instability in fluid-saturated porous media,” International Journal for Numerical and Analytical Methods in Geomechanics, vol. 36, no. 8, pp. 1077–1100, 2012. View at Publisher · View at Google Scholar · View at Scopus
  42. C. Zhao, Physical and Chemical Dissolution Front Instability in Porous Media: Theoretical Analyses and Computational Simulations, Springer, Berlin, Germany, 2014.
  43. C. Zhao, L. B. Reid, K. Regenauer-Lieb, and T. Poulet, “A porosity-gradient replacement approach for computational simulation of chemical-dissolution front propagation in fluid-saturated porous media including pore-fluid compressibility,” Computational Geosciences, vol. 16, no. 3, pp. 735–755, 2012. View at Publisher · View at Google Scholar · View at Scopus
  44. C. Zhao, B. E. Hobbs, and A. Ord, “Theoretical analyses of acidization dissolution front instability in fluid-saturated carbonate rocks,” International Journal for Numerical and Analytical Methods in Geomechanics, vol. 37, no. 13, pp. 2084–2105, 2013. View at Publisher · View at Google Scholar · View at Scopus
  45. C. Zhao, B. E. Hobbs, and A. Ord, “Effects of medium permeability anisotropy on chemical-dissolution front instability in fluid-saturated porous media,” Transport in Porous Media, vol. 99, no. 1, pp. 119–143, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  46. A. Hyvärinen, P. O. Hoyer, and M. Inki, “Topographic independent component analysis,” Neural Computation, vol. 13, no. 7, pp. 1527–1558, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  47. C. Jutten and J. Herault, “Blind separation of sources, part I: an adaptive algorithm based on neuromimetic architecture,” Signal Processing, vol. 24, no. 1, pp. 1–10, 1991. View at Publisher · View at Google Scholar · View at Scopus
  48. P. Comon, “Independent component analysis, A new concept?” Signal Processing, vol. 36, no. 3, pp. 287–314, 1994. View at Publisher · View at Google Scholar · View at Scopus
  49. C. Zhao, L. B. Reid, and K. Regenauer-Lieb, “Some fundamental issues in computational hydrodynamics of mineralization: a review,” Journal of Geochemical Exploration, vol. 112, pp. 21–34, 2012. View at Publisher · View at Google Scholar · View at Scopus
  50. C. Zhao, B. E. Hobbs, and A. Ord, “Theoretical and numerical investigation into roles of geofluid flow in ore forming systems: integrated mass conservation and generic model approach,” Journal of Geochemical Exploration, vol. 106, no. 1–3, pp. 251–260, 2010. View at Publisher · View at Google Scholar · View at Scopus
  51. T. W. Anderson, An Introduction to Multivariate Statistical Analysis, John Wiley & Sons, New York, NY, USA, 1984. View at MathSciNet
  52. R. J. Serfling, Approximation Theorems of Mathematical Statistics, John Wiley & Sons, New York, NY, USA, 1980. View at MathSciNet
  53. E. Masry, “The estimation of the correlation coefficient of bivariate data under dependence: convergence analysis,” Statistics & Probability Letters, vol. 81, no. 8, pp. 1039–1045, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus