Combination of multifractal geostatistical interpolation and spectrum–area (S–A) fractal model for Cu–Au geochemical prospects in Feizabad district, NE Iran

  • Reza Ghezelbash
  • Abbas MaghsoudiEmail author
  • Mehrdad Daviran
Original Paper


Exploration geochemical surveys seek to delimit exploration targets through the analyses of geochemical exploration data. Different methods have been applied in the delineation of geochemical anomalies including frequency-based and frequency space–based methods. The success of the latter methods depends on the modeling of the spatial distribution of geochemical data. However, selection of an appropriate method for modeling the spatial distribution of geochemical data remains a challenge. The main objective of this study is to address the foregoing challenge through a comparative study of inverse distance weighting (IDW), ordinary Kriging (OK), multifractal IDW (MIDW), and multifractal Kriging (MK) surface interpolation techniques. Initially, a set of composite sediment geochemical data from Feizabad district, NE Iran, was subjected to multivariate geochemical analysis by which a multielement geochemical signature, representing Cu–Au-related mineralization, was derived. Four above-mentioned interpolation techniques were applied to model the spatial distribution of the derived geochemical signature. The effectiveness of four interpolated models was compared by success-rate curves through which the MK model was recognized to be the superior model. The spectrum–area (S–A) fractal model was then applied on the MK model to decompose the anomalous component. The t student spatial statistics method was employed to determine proper threshold values by which the anomalous component could be discretized. The resultant crisp model was considered as the map of exploration targets.


IDW OK MIDW MK S–A fractal Student’s t value Success-rate curve 


  1. Afzal P, Khakzad A, Moarefvand P, Omran NR, Esfandiari B, Alghalandis YF (2010) Geochemical anomaly separation by multifractal modeling in Kahang (Gor Gor) porphyry system, Central Iran. J Geochem Explor 104:34–46CrossRefGoogle Scholar
  2. Afzal P, Alghalandis YF, Khakzad A, Moarefvand P, Omran NR (2011) Delineation of mineralization zones in porphyry Cu deposits by fractal concentration–volume modeling. J Geochem Explor 108:220–232CrossRefGoogle Scholar
  3. Afzal P, Alghalandis YF, Moarefvand P, Omran NR, Haroni HA (2012) Application of power-spectrum–volume fractal method for detecting hypogene, supergene enrichment, leached and barren zones in Kahang Cu porphyry deposit, Central Iran. J Geochem Explor 112:131–138CrossRefGoogle Scholar
  4. Afzal P, Harati H, Fadakar Alghalandis Y, Yasrebi AB (2013) Application of spectrumearea fractal model to identify of geochemical anomalies based on soil data in Kahang porphyry-type Cu deposit, Iran. Chem Erde 73: 533-543CrossRefGoogle Scholar
  5. Agterberg FP, Bonham-Carter GF (2005) Measuring the performance of mineral-potential maps. Nat Resour Res 14:1–17CrossRefGoogle Scholar
  6. Agterberg FP, Cheng Q, Brown A, Good D (1996) Multifractal modeling of fractures in the Lac du Bonnet batholith, Manitoba. Comput Geosci 22:497–507CrossRefGoogle Scholar
  7. Bai J, Porwal A, Hart C, Ford A, Yu L (2010) Mapping geochemical singularity using multifractal analysis: application to anomaly definition on stream sediments data from Funin Sheet, Yunnan, China. J Geochem Explor 104(1):1–11CrossRefGoogle Scholar
  8. Behroozi A (1987) Geological map of Iran 1: 100,000 series, Feizabad. Geological Survey of Iran, TehranGoogle Scholar
  9. Bonham-Carter GF, Agterberg FP, Wright DF (1990) Weights of evidence modelling: a new approach to mapping mineral potential: geological survey of Canada 89:171–183Google Scholar
  10. Carranza EJM, Hale M (1997) A catchment basin approach to the analysis of reconnaissance geochemical-geological data from Albay Province, Philippines. J Geochem Explor 60:157–171CrossRefGoogle Scholar
  11. Carranza EJM (2004) Usefulness of stream order to detect stream sediment geochemical anomalies. Geochem Explor Environ Anal 4:341–352CrossRefGoogle Scholar
  12. Carranza E J M (2008) Geochemical anomaly and mineral prospectivity mapping in GIS (Vol. 11). ElsevierGoogle Scholar
  13. Cheng QM (2001) Multifractal and geostatistic methods for characterizing local structure and singularity properties of exploration geochemical anomalies. J China Univ Geosci 26:161–166Google Scholar
  14. Cheng Q (1999) Multifractal interpolation. In: Proceedings of the Fifth Annual Conference of the International Association for Mathematical Geology, Trondheim, Norway, vol 1, pp 245–250Google Scholar
  15. Cheng Q (2000) Interpolation by means of multiftractal, kriging and moving average techniques. In GAC/MAC meeting of GeoCanada2000 CalgaryGoogle Scholar
  16. Cheng Q (2007) Mapping singularities with stream sediment geochemical data for prediction of undiscovered mineral deposits in Gejiu, Yunnan Province, China. Ore Geol Rev 32:314–324CrossRefGoogle Scholar
  17. Cheng Q, Xu Y, Grunsky E (1999) Integrated spatial and spectral analysis for geochemical anomaly separation. In: Lippard, S.J., Naess, A., Sinding-Larsen, R. (Eds.), Proceedings of the Fifth Annual Conference of the International Association for Mathematical Geology, Trondheim, Norway 6 e11th August. 11, pp 87-92Google Scholar
  18. Cheng Q, Xu Y, Grunsky E (2000) Integrated spatial and spectrum method for geochemical anomaly separation. Nat Resour Res 9:43-52Google Scholar
  19. Cheng Q, Agterberg FP, Ballantyne SB (1994) The separation of geochemical anomalies from background by fractal methods. J Geochem Explor 51:109–130CrossRefGoogle Scholar
  20. Cheng Q, Agterberg FP, Bonham-Carter GF (1996) A spatial analysis method for geochemical anomaly separation. J Geochem Explor 56:183–195CrossRefGoogle Scholar
  21. Cheng Q, Bonham-Carter G, Wang W, Zhang S, Li W, Qinglin X (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 37:662–669CrossRefGoogle Scholar
  22. Cheng Q, Xia Q, Li W, Zhang S, Chen Z, Zuo R, Wang W (2010) Density/area power-law models for separating multi-scale anomalies of ore and toxic elements in stream sediments in Gejiu mineral district, Yunnan Province, China. Biogeosciences 7:3019–3025CrossRefGoogle Scholar
  23. Davis CJ (2002) Statistics and data analysis geology, 3th edn. John Wiley & Sons Inc, New York, pp 342–353Google Scholar
  24. Ghezelbash R, Maghsoudi A (2018a) Comparison of U-spatial statistics and C-A fractal models for delineating anomaly patterns of porphyry-type Cu geochemical signatures in the Varzaghan district, NW Iran. C R Geosci 350:180–191CrossRefGoogle Scholar
  25. Ghezelbash R, Maghsoudi A (2018b) A hybrid AHP-VIKOR approach for prospectivity modeling of porphyry Cu deposits in the Varzaghan District, NW Iran. Arab J Geosci 11:275Google Scholar
  26. Ghezelbash R, Maghsoudi A (2018c) Application of hybrid AHP-TOPSIS method for prospectivity modeling of Cu porphyry in Varzaghan district, Iran. ULUM-I ZAMIN (In Persion) 28:33-42.
  27. Ghezelbash R, Maghsoudi A, Daviran M (2018) Prospectivity modeling of porphyry copper deposits: recognition of efficient mono-and multi-element geochemical signatures in the Varzaghan district, NW Iran. Acta Geochim 1-14Google Scholar
  28. Ghezelbash R, Maghsoudi A, Carranza EJM (2019a) Mapping of single-and multi-element geochemical indicators based on catchment basin analysis: Application of fractal method and unsupervised clustering models. J Geochem Explor 199:90-104CrossRefGoogle Scholar
  29. Ghezelbash R, Maghsoudi A, Carranza EJM (2019b) An Improved Data-Driven Multiple Criteria Decision-Making Procedure for Spatial Modeling of Mineral Prospectivity: Adaption of Prediction–Area Plot and Logistic Functions. Nat Resour Res.
  30. Ghezelbash R, Maghsoudi A, Carranza EJM (2019c) Performance evaluation of RBF-and SVM-based machine learning algorithms for predictive mineral prospectivity modeling: integration of SA multifractal model and mineralization controls. Earth Sci Inf.
  31. Hengl T (2006) Finding the right pixel size. Comput Geosci 32:1283–1298CrossRefGoogle Scholar
  32. Hu D, Liu D, Xue S (1995) Explanatory text of geochemical map of Feizabad (7760). Geological Survey of Iran, TehranGoogle Scholar
  33. Hu S, Cheng Q, Wang L, Xu D (2013) Modeling land price distribution using multifractal IDW interpolation and fractal filtering method. Landscape Urban Plan 110:25–35CrossRefGoogle Scholar
  34. Jolliffe IT (2002) Principal component analysis, second ed. Springer, New York, 547 NY, 487ppGoogle Scholar
  35. Journel AG, Huijbregts CJ (1978) Mining geostatistics. Academic pressGoogle Scholar
  36. Kaiser HF (1960) The application of electronic computers to factor analysis. Educ Psychol Meas 20:141–151CrossRefGoogle Scholar
  37. Li C, Ma T, Shi J (2003) Application of a fractal method relating concentrations and distances for separation of 386 geochemical anomalies from background. J Geochem Explor 77:167–175CrossRefGoogle Scholar
  38. Li Q (2005) Multifractal-krige interpolation method. Adv Earth Sci 20:248–255Google Scholar
  39. Lima A, De Vivo B, Cicchella D, Cortini M, Albanese S (2003) Multifractal IDW interpolation and fractal filtering method in environmental studies: an application on regional stream sediments of (Italy), Campania region. Appl Geochem 18:1853–1865CrossRefGoogle Scholar
  40. Lima A, Plant JA, De Vivo B, Tarvainen T, Albanese S, Cicchella D (2008) Interpolation methods for geochemical maps: a comparative study using arsenic data from European stream waters. Geochem Explor Env 8:41–48CrossRefGoogle Scholar
  41. Lin YP (2002) Multivariate geostatistical methods to identify and map spatial variations of soil heavy metals. Environ Geol 42:1–10CrossRefGoogle Scholar
  42. Macklin MG, Ridgway J, Passmore DG, Rumsby BT (1994) The use of overbank sediment for geochemical mapping and contamination assessment: results from selected welsh flood plains. Appl Geochem 9:698–700CrossRefGoogle Scholar
  43. Mandelbrot BB, Pignoni R (1983) The fractal geometry of nature, vol 173. WH freeman, New YorkGoogle Scholar
  44. Muller J, Kylander M, Martinez-Cortizas A, Wüst RA, Weiss D, Blake K, Garcia-Sanchez R (2008) The use of principle component analyses in characterising trace and major elemental distribution in a 55kyr peat deposit in tropical Australia: implications to paleoclimate. Geochim Cosmochim Acta 72:449–463CrossRefGoogle Scholar
  45. Oliver MA, Webster R (1990) Kriging: a method of interpolation for geographical information systems. Int J Geogr Inf Syst 4:313–332CrossRefGoogle Scholar
  46. Parsa M, Maghsoudi A, Yousefi M (2017c) An improved data-driven fuzzy mineral prospectivity mapping procedure; cosine amplitude-based similarity approach to delineate exploration targets. Int J Appl Earth Obs Geoinf 58:157–167CrossRefGoogle Scholar
  47. Parsa M, Maghsoudi A, Ghezelbash R (2016c) Decomposition of anomaly patterns of multi-element geochemical signatures in Ahar area, NW Iran: a comparison of U-spatial statistics and fractal models. Arab J Geosci 9:260CrossRefGoogle Scholar
  48. Parsa M, Maghsoudi A, Yousefi M, Carranza EJM (2017a) Multifractal interpolation and spectrum–area fractal 404 modeling of stream sediment geochemical data: implications for mapping exploration targets. J Afr Earth Sci 128:5–15CrossRefGoogle Scholar
  49. Parsa M, Maghsoudi A, Yousefi M, Sadeghi M (2017b) Multifractal analysis of stream sediment geochemical data: implications for hydrothermal nickel prospection in an arid terrain, eastern Iran. J Geochem Explor 181:305–317CrossRefGoogle Scholar
  50. Parsa M, Maghsoudi A, Yousefi M, Sadeghi M (2016a) Prospectivity modeling of porphyry-Cu deposits by identification and integration of efficient mono-elemental geochemical signatures. J Afr Earth Sci 114:228–241CrossRefGoogle Scholar
  51. Parsa M, Maghsoudi A, Yousefi M, Sadeghi M (2016b) Recognition of significant multi-element geochemical signatures of porphyry Cu deposits in Noghdouz area, NW Iran. J Geochem Explor 165:111–124CrossRefGoogle Scholar
  52. Shuguang Z, Kefa Z, Yao C, Jinlin W, Jianli D (2015) Exploratory data analysis and singularity mapping in geochemical anomaly identification in Karamay, Xinjiang, China. J Geochem Explor 154:171–179CrossRefGoogle Scholar
  53. Sinclair AJ (1974) Selection of threshold values in geochemical data using probability graphs. J Geochem Explor 3:129–149CrossRefGoogle Scholar
  54. Sinclair AJ (1976) Applications of probability graphs in mineral exploration (no. 4). In: Association of Exploration GeochemistsGoogle Scholar
  55. Sinclair AJ (1991) A fundamental approach to threshold estimation in exploration geochemistry: probability plots revisited. J Geochem Explor 41:1–22CrossRefGoogle Scholar
  56. Spadoni M (2006) Geochemical mapping using a geomorphologic approach based on catchments. J Geochem Explor 90:183–196CrossRefGoogle Scholar
  57. Spadoni M, Voltaggio M, Cavarretta G (2005) Recognition of areas of anomalous concentration of potentially hazardous elements by means of a subcatchmentbased discriminant analysis of stream sediments. J Geochem Explor 87:83–91CrossRefGoogle Scholar
  58. Stanley CR, Sinclair AJ (1989) Comparison of probability plots and the gap statistic in the selection of thresholds for exploration geochemistry data. J Geochem Explor 32:355–357CrossRefGoogle Scholar
  59. Wang J, Zuo R (2015) A MATLAB-based program for processing geochemical data using fractal/multifractal modeling. Earth Sci Inf 8:937–947CrossRefGoogle Scholar
  60. Wang W, Zhao J, Cheng Q, Liu J (2012) Tectonicegeochemical exploration modeling for characterizing geo-anomalies in southeastern Yunnan district, China. J Geochem Explor 122:71–80CrossRefGoogle Scholar
  61. Webster R, Oliver MA (2007) Characterizing spatial processes: the covariance and variogram. Geostatistics for Environmental Scientists, Second Edition:47–76Google Scholar
  62. Xie S, Cheng Q, Xing X, Bao Z, Chen Z (2010) Geochemical multifractal distribution patterns in sediments from ordered streams. Geoderma 160:36–46CrossRefGoogle Scholar
  63. Yousefi M, Carranza EJM, Kamkar-Rouhani A (2013) Weighted drainage catchment basin mapping of geochemical anomalies using stream sediment data for mineral potential modeling. J Geochem Explor 128:88–96CrossRefGoogle Scholar
  64. Yousefi M, Nykänen V (2016) Data-driven logistic-based weighting of geochemical and geological evidence layers in mineral prospectivity mapping. J Geochem Explor 164:94–106CrossRefGoogle Scholar
  65. Yuan F, Li X, Zhou T, Deng Y, Zhang D, Xu C, Zhang R, Jia C, Jowitt SM (2015) Multifractal modelling-based mapping and identification of geochemical anomalies associated with Cu and Au mineralisation in the NW Junggar area of northern Xinjiang Province, China. J Geochem Explor 154:252–264CrossRefGoogle Scholar
  66. Zhang C, Tang Y, Xu X, Kiely G (2011) Towards spatial geochemical modelling: use of geographically weighted regression for mapping soil organic carbon contents in Ireland. Appl Geochem 26:1239–1248CrossRefGoogle Scholar
  67. Zhang Y, Zhou YZ, Wang LF, Wang ZH, He JG, An YF, Li HZ, Zeng CY, Liang J, Lü WC, Gao L (2013) Mineralization-related geochemical anomalies derived from stream sediment geochemical data using multifractal analysis in Pangxidong area of Qinzhou-Hangzhou tectonic joint belt, Guangdong Province, China. J Central South Univ 20:184–192CrossRefGoogle Scholar
  68. Zhong X, Kealy A, Duckham M (2016) Stream kriging: incremental and recursive ordinary kriging over spatiotemporal data streams. Comput Geosci 90:134–143CrossRefGoogle Scholar
  69. Zuo R, Wang J (2016) Fractal/multifractal modeling of geochemical data: a review. J Geochem Explor 164:33–41CrossRefGoogle Scholar
  70. Zuo R (2011a) Decomposing of mixed pattern of arsenic using fractal model in Gangdese belt, Tibet, China. Appl Geochem 26:S271–S273CrossRefGoogle Scholar
  71. Zuo R (2011b) Identifying geochemical anomalies associated with Cu and Pb–Zn skarn mineralization using principal component analysis and spectrum–area fractal modeling in the Gangdese Belt, Tibet (China). J Geochem Explor 111:13–22CrossRefGoogle Scholar
  72. Zuo R, Carranza EJM, Wang J (2016) Spatial analysis and visualization of exploration geochemical data. Earth Sci Rev 158:9–18CrossRefGoogle Scholar
  73. Zuo R, Cheng Q, Agterberg FP, Xia Q (2009) Application of singularity mapping technique to identify local anomalies using stream sediment geochemical data, a case study from Gangdese, Tibet, western China. J Geochem Explor 101:225–235CrossRefGoogle Scholar
  74. Zuo R, Wang J (2015) Fractal/multifractal modeling of geochemical data: a review. J Geochem Explor 164:33–41CrossRefGoogle Scholar
  75. Zuo R, Xia Q, Wang H (2013) Compositional data analysis in the study of integrated geochemical anomalies associated with mineralization. Appl Geochem 28:202–211CrossRefGoogle Scholar
  76. Zuo R, Zhang Z, Zhang D, Carranza EJM, Wang H (2015) Evaluation of uncertainty in mineral prospectivity mapping due to missing evidence: a case study with skarn type Fe deposits in Southwestern Fujian Province, China. Ore Geol Rev 71:502–515CrossRefGoogle Scholar

Copyright information

© Saudi Society for Geosciences 2019

Authors and Affiliations

  • Reza Ghezelbash
    • 1
  • Abbas Maghsoudi
    • 1
    Email author
  • Mehrdad Daviran
    • 2
  1. 1.Faculty of Mining and Metallurgical EngineeringAmirkabir University of TechnologyTehranIran
  2. 2.School of Mining, Petroleum and Geophysics EngineeringShahrood University of TechnologyShahroodIran

Personalised recommendations