The effect of estimation methods on fractal modeling for anomalies’ detection in the Irankuh area, Central Iran

Document Type : Research Paper


1 بخش مهندسی معدن دانشگاه آزاد واحد تهران جنوب

2 Department of Mining Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran


This study aims to recognize effect of Ordinary Kriging (OK) and Inverse Distance Weighted (IDW) estimation methods for separation of geochemical anomalies based on soil samples using Concentration-Area (C-A) fractal model in Irankuh area, central Iran. Variograms and anisotropic ellipsoid were generated for the Pb and Zn distribution. Thresholds values from the C-A log-log plots based on the estimation methods revealed the presence of various geochemical anomalies within estimation variances which were compared in both methods. The comparison among the estimation variances for different geochemical anomalies based on the C-A fractal model indicated that the estimation variance is less in the OK method especially for extremely and highly Zn-Pb anomalies. The estimated variances for different Zn anomalies via OK and C-A fractal method are lower than fractal modeling obtained by IDW estimation. However, extremely and highly Pb anomalies due to OK method have estimation variances lower than IDW method. Based on the results, main Zn and Pb anomalies are situated in the NW part of the area.


Article Title [فارسی]

اثر روش های تخمین بر روی شناسایی آنومالی ها با مدلسازی فرکتالی در منطقه ایرانکوه، ایران مرکزی

Authors [فارسی]

  • پیمان افضل 1
  • مهدی رضایی 2
1 Department of Mining Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran
2 بخش مهندسی معدن دانشگاه آزاد واحد تهران جنوب
Abstract [فارسی]

هدف از این مطالعه یافتن اثر روش-های تخمین کریجینگ معمولی و عکس فاصله وزن دار بر روی جدایش آنومالی های ژئوشیمیایی حاصل از نمونه های خاک برجا با استفاده از روش فرکتالی عیار-مساحت در منطقه ایرانکوه واقع در ایران مرکزی می باشد. نخست واریوگرام ها و بیضوی ناهمسانگردی برای مدلسازی توزیع عیار سرب و روی ساخته شدند. سپس منحنی فرکتالی براساس نتایج حاصل از این روش های تخمین ترسیم شده و واریانس تخمین هر یک از جوامع آنومالی تعیین شدند. براساس مقایسه بین واریانس های تخمین جوامع و آنومالی های گوناگون مشخص شد که واریانس های تخمین برای آنومالی های حاصل از روش تخمین کریجینگ معمولی کمتر از روش عکس فاصله وزن دار است. آنومالی های شدید و بالای سرب و روی حاصل از مدلسازی فرکتالی براساس روش کریجینگ معمولی دارای واریانس کمتر از آنومالی های متناظر ناشی از روش تخمین عکس فاصله وزن دار است. براساس نتایج حاصله آنومالی های اصلی سرب و روی در شمال غربی محدوده قرار دارند.

Keywords [فارسی]

  • : عکس فاصله وزن دار
  • کریجینگ معمولی
  • واریانس تخمین
  • روش فرکتالی عیار-مساحت
  • ایرانکوه
Afzal, P., Fadakar Alghalandis, Y., Khakzad, A., Moarefvand, P., Rashidnejad Omran, N., 2011. Delineation of mineralization zones in porphyry Cu deposits by fractal concentration–volume modeling. J Geochem Explor. 108: 220–232.
Afzal, P., FadakarAlghalandis, Y., Moarefvand, P., RashidnejadOmran, N., AsadiHaroni, H., 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: 131-138.
Afzal, P., Khakzad, A., Moarefvand, P., Rashidnejad Omran, N., Esfandiari, B., Fadakar Alghalandis, Y., 2010. Geochemical anomaly separation by multifractal modeling in Kahang (GorGor) porphyry system, Central Iran. J Geochem Explor . 104: 34–46.
Afzal, P., Harati, H., Fadakar Alghalandis, Y., Yasrebi, A.B., 2013. Application of spectrum–area fractal model to identify of geochemical anomalies based on soil data in Kahang porphyry-type Cu deposit, Iran. Chemie der Erde. 73: 533– 543.
Agterberg, F.P., 1995.Multifractal modeling of the sizes and grades of giant and supergiant deposits. Int Geol Rev. 37: 1–8.
Aramesh Asl, R., Afzal, P., Adib, A., Yasrebi, A.B., 2015. Application of multifractal modelling for the identification of alteration zones and major faults based on ETM+ multispectral data. Arab J Geosci. 8: 2997–3006.
Bayraktar, H., Turalioglu, F.S., 2005. Kriging-based approaches for locating a sampling site-in the assessment of air quality. SERRA. 19: 301-305.
Brus, D. J., de Gruijter, J. J., Marsman, B. A., Visschers, R., Bregt, A. K., and Breeuwsma, A. 1996.The performance of spatial interpolation methods and choropleth maps to estimate propertiesatpoints:A soil survey case study: Environmetrics. 7: 1–16.
Calder, C.A., Cressie, N., 2009. Kriging and Variogram Models. Elsevier Ltd. All rights reserved, pp. 49-55.
Cheng, Q, Agterberg, F. P., Ballantyne, S. B., 1994. The separartion of geochemical anomalies from background by fractal methods. Journal of Geochemical Exploration. 51: 109–130.
Chile's, J.P., Delfiner, P., 1999. Geostatistics: Modeling Spatial Uncertainty. Wiley, New York.695pp.
Cressie, N., 1993.Statistics for spatial data. John Wiley & Sons, New York, 900 pp.
David, M., 1970. Geostatistical Ore Reserve Estimation, Amsterdam, Elsevier, 283 pp.
Delavar, S. T., Afzal, P., Borg, G., Rasa, I., Lotfi, M., RashidnejadOmran, N., 2012. Delineation of mineralization zones using concentration–volume fractal method in Pb–Zn carbonate hosted deposits. J Geochem Explor. 118: 98-110.
Declercq, F. A. N., 1996. Interpolation methods for scattered sample data: Accuracy, spatial patterns, processing time: Cartography and Geog Inf Sys. 23: 128–144.
Dimitrakopoulos, R., Martinez, L., Ramazan, S., 2007.A maximum upside/minimum downside approach to the traditional optimization of open pit mine design. J Min Sci. 43: 73-82.
Emery, X., 2005. Simple and Ordinary Kriging Multigaussian Kriging for Estimating recoverable Reserves. Math Geol. 37: 295-319.
Englund, E.J., Weber, D.D., Leviant, N., 1992.The effects of sampling design parameters on block selection. Math. Geol. 24: 29–343.
Gallichand, J., and Marcotte, D., 1993. Mapping clay content for subsurface drainage in the Niledelta: Geoderma. 58: 165–179.
Ghazban, F.R., McNutt, H., Schwarcz, H.P., 1994. Genesis of sediment-hosted Zn–Pb–Ba deposits in the Irankuh district, Esfahan area, west-central Iran. Econ. Geol. 89: 1262–1278.
Goncalves, M.A., Mateus, A., Oliveira, V., 2001. Geochemical anomaly separation by multifractal modeling. Journal of Geochemical Exploration. 72: 91-114.
Goovaerts, P. 1997. Geostatistics for Natural Resources Evaluation. Oxford University Press, New York. 496 pp.
Heidari, M., Ghaderi, M., Afzal, P., 2013.Delineating mineralized phases based on lithogeochemical data using multifractal model in Touzlar epithermal Au-Ag (Cu) deposit, NW Iran. Appl Geochem. 31: 119-132.
Hormozi, H., Hormozi, E., Rahimi Nohooji N., 2012. The Classification of the Applicable Machine Learning Methods in Robot Manipulators. Int J of Mach Learning and Computing. 2: 560-563.
Journel, A., 1983. Geostatistics: roadblocks and challenges, in A. Soares, ed., Geostatistics-Troia 1, Kluwer, pp. 213-224.
Journel, A., Huijbregts, Ch.J., 1978.Mining Geostatistics. The Blackburn Press. 600 pp.
Juan, P., Mateu, J., Jordan, M.M., Mataix-Solera, J., Meléndez-Pastor, I., Navarro-Pedreño, J., 2011.Geostatistical methods to identify and map spatial variations of soil salinity. J Geochem Explor. 108: 62-72.
Laslett, G.M., 1994.Kriging and splines: An empirical comparison of their predictive performance in some applications. Jour. Am. Stat. Assoc. 89: 391–409.
Laslett, G.M., and Mc Bratney, A.B., 1990.Further comparison of spatial methods for predicting soil pH. Soil Sci Soc America J. 54: 1553–1558.
Laslett, G. M., Mc Bratney, A. B., Pahl, P. J., Hutchinson, M. F., 1987.Comparison of several spatial prediction methods for soil pH: Jour. of Soil Sci. 38: 325–341.
Li, J., Heap, A.D., 2008. A Review of Spatial Interpolation Methods for Environmental Scientists. Geoscience Australia, GPO Box 378, Canberra, ACT 2601, Australia.
Marechal, A., Serra, J., 1971. Random Kriging. Geostatistics, D.F. Merriam Editor, Plenum Press, New York.
Matheron, G., 1967. Kriging or polynomial interpolation procedures. C.I.M. Bulletin. 60: 1041-1045.
Mokhtari, A.R., Roshani Rodsari, P., Cohen, D.R., Emami, A., Dehghanzadeh Bafghi, A.A., Khodaian Ghegeni, Z., 2015. Metal speciation in agricultural soils adjacent to the Irankuh Pb–Zn mining area, central Iran. Journal of African Earth Sciences. 101: 186–193.
Parhizkar, A., Ataei, M., Moarefvand, P., and Rasouli, V., 2011. Grade Uncertainty and Its Impact on Ore Grade Reconciliation between the Resource Model and the Mine. Arch. Min. Sci. 56: 119–134.
Phillips, D.L., Lee, E.H., Herstrom, A.A., Hogsett, W.E., and Tingey, D.T., 1997.Use of auxiliary data for spatial interpolation of ozone exposure in southeastern forests. Environmetrics. 8: 43–61.
Rahmati, A., Afzal, P., Abrishamifar, S.A., Sedeghi, B., 2015. Application of Concentration -Number and Concentration-Volume fractal models to delineate mineralized zones in the Sheytoor iron deposit, Central Iran. Arab J Geosci. 8: 2953–2965.
Reichert, J., 2007. A metallogenic model for carbonate-hosted non-sulphide zinc deposits based on observations of Mehdi Abad and Irankuh, Central and Southwestern Iran, Ph.D thesis, Martin Luther University, Halle Wittenberg, 152 pp.
Reichert, J., Borg, G., 2008. Numerical simulation and a geochemical model of supergene carbonate-hosted non-sulphide zinc deposits. Ore Geology Reviews. 33: 134-151.
Shademan Khakestar, M., Madani, H., Hassani, H., Moarefvand, P., 2013. Determining the best search neighbourhood in reserve estimation, using geostatistical method: A case study anomaly No 12A iron deposit in central Iran. J Geol. Soci.. India. 81: 581-585.
Shahbeik, Sh., Afzal, P., Moarefvand, P., Qumarsy, M., 2014. Comparison between Ordinary Kriging (OK) and Inverse Distance Weighted (IDW) based on estimation error Case study: in Dardevey iron ore deposit, NE Iran. Arabian Journal of Geosciences, Arab J Geosci. 7: 3693–3704.
Shamseddin Meigoony, M., Afzal, P., Gholinejad, M., Yasrebi, A.B., Sadeghi, B., 2014. Delineation of geochemical anomalies using factor analysis and multifractal modeling based on stream sediments data in Sarajeh 1:100,000 sheet, Central Iran. Arab J Geosci. 7: 5333–5343.
Soltani Mohammadi, S., Hezarkhani, A., Tercan, A.E., 2012.Optimally locating additional drill holes in three dimensions using grade and simulated annealing. J Geol. Soci. India. 80: 700-706.
Tahmasebi, P, Hezarkhani, A., 2010. Application of Adaptive Neuro-Fuzzy Inference System for Grade Estimation; Case Study, Sarcheshmeh Porphyry Copper Deposit, Kerman, Iran. Aust J of Basic and Appl Sci. 4: 408-420.
VerHoef, J.M., Cressie, N. (1993) Multivariable spatial prediction. Math Geol. 252: 219-239.
Wang, G., Carranza, E. J. M., Zuo, R., Hao, Y., Du, Y., Pang, Zh., Sun, Y., Qu, J., 2012.Mapping of district-scale potential targets using fractal models. J Geochem Explor. 122: 34-46.
Wang, Q.F., Deng, J., Liu, H.,Wang, Y., Sun, X.,Wan, L., 2011.Fractal models for estimating local reserves with different mineralization qualities and spatial variations. J Geochem Explor. 108: 196–208.
Weber, D.D., Englund, E.J., 1992.Evaluation and comparison of spatial interpolators. Math. Geol. 24: 381–391.
Weber, D.D., Englund, E.J., 1994.Evaluation and comparison of spatial interpolators, II. Math. Geol. 26: 589–603.
Yasrebi, A.B., Wetherelt, A., Foster, P., Coggan, J., Afzal, P., Agterberg, F.P., Kaveh Ahangaran, D., 2014. Application of a density-volume (D-V) fractal model for rock characterisation and correlation of RQD and lithological units with density model in the Kahang porphyry deposit, Central Iran. International Journal of Rock Mechanics and Mining Sciences. 66:188–193.
Zimmerman, D., Pavlik, C., Ruggles, A., Armstrong, M.P., 1999.An Experimental comparison of ordinary and universal kriging and inverse distance weighting. Math Geol. 31: 375–390.