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Mathematical Geosciences

, Volume 46, Issue 7, pp 869–885 | Cite as

A Comparison of Modified Fuzzy Weights of Evidence, Fuzzy Weights of Evidence, and Logistic Regression for Mapping Mineral Prospectivity

  • Daojun ZhangEmail author
  • Frits Agterberg
  • Qiuming ChengEmail author
  • Renguang Zuo
Article

Abstract

Weights of evidence and logistic regression are two of the most popular methods for mapping mineral prospectivity. The logistic regression model always produces unbiased estimates, whether or not the evidence variables are conditionally independent with respect to the target variable, while the weights of evidence model features an easy to explain and implement modeling process. It has been shown that there exists a model combining weights of evidence and logistic regression that has both of these advantages. In this study, three models consisting of modified fuzzy weights of evidence, fuzzy weights of evidence, and logistic regression are compared with each other for mapping mineral prospectivity. The modified fuzzy weights of the evidence model retains the advantages of both the fuzzy weights of the evidence model and the logistic regression model; the advantages being (1) the predicted number of deposits estimated by the modified fuzzy weights of evidence model is nearly equal to that of the logistic regression model, and (2) it can deal with missing data. This method is shown to be an effective tool for mapping iron prospectivity in Fujian Province, China.

Keywords

Conditional independence Mineral resource assessment Data integration GIS modeling Fujian Province 

Notes

Acknowledgements

The authors would like to give thanks to postgraduate students Shuwang Wang and Changhai Tan, who offered help in mathematical inference and data processing, respectively. The authors also sincerely thank two anonymous reviewers for their constructive comments, which have improved the manuscript. This research benefited from the joint financial support of the Program of Integrated Prediction of Mineral Resources in Covered Areas (No. 1212011085468), a research project on “Quantitative models for prediction of strategic mineral resources in China” (201211022) by the China Geological Survey, the Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan) (CUG120501, CUG120116), the National Natural Science Foundations of China (Nos. 41372007, 41272362 and 41172299).

References

  1. Agterberg FP (1974) Automatic contouring of geological maps to detect target areas for mineral exploration. J Int Assoc Math Geol 6:373–395 CrossRefGoogle Scholar
  2. Agterberg FP (1988) Application of recent developments of regression analysis in mineral resource evaluation. In: Chung CF et al (eds) Quantitative analysis of mineral and energy resources. Reidel, Dordrecht, pp 1–28 CrossRefGoogle Scholar
  3. Agterberg FP (1989a) Computer programs for mineral exploration. Science 245:76–81 CrossRefGoogle Scholar
  4. Agterberg FP (1989b) LOGDIA—Fortran 77 program for logistic regression with diagnostics. Comput Geosci 15:599–614 CrossRefGoogle Scholar
  5. Agterberg FP (1992) Combining indicator patterns in weights of evidence modeling for resource evaluation. Nat Resour Res 1:35–50 CrossRefGoogle Scholar
  6. Agterberg FP (2011a) A modified weights-of-evidence method for regional mineral resource estimation. Nat Resour Res 20:95–101 CrossRefGoogle Scholar
  7. Agterberg FP (2011b) Principles of probabilistic regional mineral resource estimation. J China Univ Geosci 36:189–200 Google Scholar
  8. Agterberg FP, Cheng Q (2002) Conditional independence test for weights-of-evidence modeling. Nat Resour Res 11:249–255 CrossRefGoogle Scholar
  9. Agterberg FP, Bonham-Carter GF, Wright DF (1990) Statistical pattern integration for mineral exploration. In: Gaál G, Merriam DF (eds) Computer applications in resource exploration, prediction and assessment for metals and petroleum. Pergamon, Oxford, pp 1–21 CrossRefGoogle Scholar
  10. Agterberg FP, Bonham-Carter GF, Cheng QM, Wright DF (1993) Weights of evidence modeling and weighted logistic regression for mineral potential mapping. In: Davis JC, Herzfeld UC (eds) Computers in geology, 25 years of progress. Oxford University Press, New York, pp 13–32 Google Scholar
  11. Bonham-Carter GF (1994) Geographic information systems for geoscientists: modeling with GIS. Pergamon, Oxford, p 398 Google Scholar
  12. Bonham-Carter GF, Agterberg FP, Wright DF (1988) Integration of geological datasets for gold exploration in Nova Scotia. Photogramm Eng Remote Sens 54:1585–1592 Google Scholar
  13. Bonham-Carter GF, Agterberg FP, Wright DF (1989) Weights of evidence modeling: a new approach to mapping mineral potential. In: Agterberg FP, Bonham-Carter GF (eds) Statistical applications in the earth sciences, vol 89–9. Geological survey, Canada, pp 171–183 Google Scholar
  14. Carranza EJ (2004) Weights of evidence modeling of mineral potential: a case study using small number of prospects, Abra, Philippines. Nat Resour Res 13:173–185 CrossRefGoogle Scholar
  15. Cassard D, Billa M, Lambert A (2008) Gold predictivity mapping in French Guiana using an expert guided data-driven approach based on a regional-scale GIS. Ore Geol Rev 34:471–500 CrossRefGoogle Scholar
  16. Cervi F, Berti M, Borgatti L, Ronchetti F, Manenti F, Corsini A (2010) Comparing predictive capability of statistical and deterministic methods for landslide susceptibility mapping: a case study in the northern Apennines (Reggio Emilia Province, Italy. Landslides 7:433–444 CrossRefGoogle Scholar
  17. Cheng Q (1997) Fractal/multifractal and spatial analysis. In: Glahn VP (ed) Proceedings of IAMG’ 1997: international centre for numeric methods in engineering (CIMNE). 2nd conference of IAMG, Barcelona, 19–27 Sept. 1997, pp 57–72 Google Scholar
  18. Cheng Q (1999) Spatial and scaling modelling for geochemical anomaly separation. J Geochem Explor 65:175–194 CrossRefGoogle Scholar
  19. Cheng Q (2008) Non-linear theory and power-law models for information integration and mineral resources quantitative assessments. Math Geosci 40:503–532 CrossRefGoogle Scholar
  20. Cheng Q (2012a) Application of a newly developed boost weights of evidence model (BoostWofE) for mineral resources quantitative assessments. J Jilin Univ, Earth Sci Ed 42:1976–1984 (in Chinese with English abstract) Google Scholar
  21. Cheng Q (2012b) Techniques and methods for mineral resources integrated prediction in covered areas. Earth Sci-J China Univ Geosci 37:1110–1125 (in Chinese with English abstract) Google Scholar
  22. Cheng Q (2012c) Singularity theory and methods for mapping geochemical anomalies caused by buried sources and for predicting undiscovered mineral deposits in covered areas. J Geochem Explor 122:55–70 CrossRefGoogle Scholar
  23. Cheng Q (2012d) Multiplicative cascade processes and information integration for predictive mapping. Nonlinear Process Geophys 19:57–68 CrossRefGoogle Scholar
  24. Cheng Q (2013) Sequential weights of evidence as a machine learning model for mineral deposits prediction. In: Proceedings of the 15th conference of IAMG, Madrid, Spain, September 02–06, 2013, pp 157–161 Google Scholar
  25. Cheng Q, Agterberg FP (1999) Fuzzy weights of evidence method and its application in mineral potential mapping. Nat Resour Res 8:27–35 CrossRefGoogle Scholar
  26. Cheng Q, Bonham-Carter GF, Wang W, Zhang S, Li W, Xia Q (2011) A spatially weighted principal component analysis for multi-element geochemical data for mapping locations of felsic intrusions in the Gejiu mineral district of Yunnan, China. Comput Geosci 37:662–669 CrossRefGoogle Scholar
  27. Cheng Q, Chen Z, Ali K (2007) Application of fuzzy weights of evidence method in mineral resource assessment for gold in Zhenyuan district, Yunnan province, China. Earth Sci-J China Univ Geosci 32:175–184 (in Chinese with English abstract) Google Scholar
  28. Cho SH, Poudyal NC, Roberts RK (2008) Spatial analysis of the amenity value of green open space. Ecol Econ 66:403–416 CrossRefGoogle Scholar
  29. Chung CF, Agterberg FP (1980) Regression models for estimating mineral resources from geological map data. Math Geol 12:473–488 CrossRefGoogle Scholar
  30. Coolbaugh MF, Raines GL (2007) Estimation of undiscovered resources by incorporating spatial models of degree of exploration into data-driven models such as weights of evidence and logistic regression. In: Zhao P, Agterberg FP, Cheng Q (eds) Proceedings of IAMG’ 2007: geomathematics and GIS analysis of resources, environment and hazards. 12th conference of IAMG, Beijing, China, August 26–31, 2007, pp 90–93 Google Scholar
  31. Davis JC (2002) Statistics and data analysis in geology, 3rd edn. Wiley, New York, p 550 Google Scholar
  32. Deng M (2009) A conditional dependence adjusted weights of evidence model. Nat Resour Res 18:249–258 CrossRefGoogle Scholar
  33. Geological Survey Institute of Fujian (2010) The report of iron potential evaluation, p 148 (in Chinese) Google Scholar
  34. Gorney RM, Ferris DR, Ward AD, Williams LR (2011) Assessing channel-forming characteristics of an impacted headwater stream in Ohio, USA. Ecol Eng 37:418–430 CrossRefGoogle Scholar
  35. Journel AG (2002) Combining knowledge from diverse sources: an alternative to traditional conditional independence hypothesis. Math Geol 34:573–596 CrossRefGoogle Scholar
  36. Krishnan S, Boucher A, Journel AG (2005) Evaluating information redundancy through the Tau model. Quant Geol Geostat 14:1037–1046 CrossRefGoogle Scholar
  37. Neuhäuser B, Terhorst B (2007) Landslide susceptibility assessment using “weights-of-evidence” applied to a study area at the Jurassic escarpment (SW-Germany). Geomorphology 86:12–24 CrossRefGoogle Scholar
  38. Ozdemir A (2011) GIS-based groundwater spring potential mapping in the Sultan Mountains (Konya, Turkey) using frequency ratio, weights of evidence and logistic regression methods and their comparison. J Hydrol 411:290–308 CrossRefGoogle Scholar
  39. Ozdemir A, Altural T (2013) A comparative study of frequency ratio, weights of evidence and logistic regression methods for landslide susceptibility mapping: Sultan Mountains, SW Turkey. J Asian Earth Sci 64:180–197 CrossRefGoogle Scholar
  40. Polyakova EI, Journel AG (2007) The Nu expression for probabilistic data integration. Math Geol 39:715–733 CrossRefGoogle Scholar
  41. Porwal A, González-Álvarez I, Markwitz V, McCuaig TC, Mamuse A (2010) Weights-of-evidence and logistic regression modeling of magmatic nickel sulfide prospectivity in the Yilgarn Craton, western Australia. Ore Geol Rev 38:184–196 CrossRefGoogle Scholar
  42. Regmi NR, Giardino JR, Vitek JD (2010) Modeling susceptibility to landslides using the weight of evidence approach: western Colorado, USA. Geomorphology 115:172–187 CrossRefGoogle Scholar
  43. Romero-Calcerrada R, Luque S (2006) Habitat quality assessment using weights-of-evidence based GIS modelling: the case of Picoides tridactylus as species indicator of the biodiversity value of the Finnish forest. Ecol Model 196:62–76 CrossRefGoogle Scholar
  44. Romero-Calcerrada R, Barrio-Parra F, Millington JD, Novillo CJ (2010) Spatial modelling of socioeconomic data to understand patterns of human-caused wildfire ignition risk in the SW of Madrid (central Spain). Ecol Model 221:34–45 CrossRefGoogle Scholar
  45. Schaeben H (2012) Comparison of mathematical methods of potential modeling. Math Geosci 44:101–129 CrossRefGoogle Scholar
  46. Song H, Hiromu D, Kazutoki A, Usio K, Sumio M (2008) Modeling the potential distribution of shallow-seated landslides using the weights of evidence method and a logistic regression model: a case study of the Sabae Area. Jpn Int J Sediment Res 23:106–118 CrossRefGoogle Scholar
  47. Thiart C, Bonham-Carter GB, Agterberg FP, Cheng Q, Panahi A (2006) An application of the new omnibus test for conditional independence in weights-of-evidence modeling. In: Harris J (ed) GIS in the earth sciences, Geological association of Canada special volume, pp 131–142 Google Scholar
  48. Tukey JW Discussion of paper, Agterberg, by FP and Robinson, SC 1972 (1972) Intern Stat Bull 44:596. Google Scholar
  49. Wrigley N, Dunn R (1986) Graphical diagnostics for logistic oil exploration models. Math Geol 18:355–374 CrossRefGoogle Scholar
  50. Zhang S, Cheng Q, Zhang S, Xia Q (2009) Weighted weights of evidence and stepwise weights of evidence and their application in Sn–Cu mineral potential mapping in Gejiu, Yunnan Province, China. Earth Sci-J China Univ Geosci 34:281–286 (in Chinese with English abstract) Google Scholar
  51. Zhang D, Cheng Q, Zuo R, Wang S (2012) Application and comparison of weighted weights of evidence models. Earth Sci-J China Univ Geosci 37:1160–1168 (in Chinese with English abstract) Google Scholar
  52. Zuo R, Xia Q, Zhang D, Cheng Q (2012) Geological process-based mineral resource quantitative prediction and assessment for making type iron polymetallic deposits in Fujian. Earth Sci-J China Univ Geosci 37:1183–1190 (in Chinese with English abstract) Google Scholar

Copyright information

© International Association for Mathematical Geosciences 2013

Authors and Affiliations

  1. 1.State Key Laboratory of Geological Processes and Mineral ResourcesChina University of GeosciencesWuhanChina
  2. 2.Geological Survey of CanadaOttawaCanada
  3. 3.Department of Earth and Space Science and EngineeringYork UniversityTorontoCanada

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