Document Type : Original Research Paper

Authors

1 Department of Geology, Faculty of Earth Sciences, Kharazmi University, Tehran, Iran

2 Department of Geology, Faculty of Sciences, Payam Noor University (PNU), Tehran, Iran

3 Department of Geophysical Engineering, Faculty of Engineering, Ankara University, Ankara, Turkey

4 Zap consulting engineers, Tehran, Iran

10.22044/jme.2020.10215.1960

Abstract

In this paper, a power-law relation modeling called the vario-fractal model is introduced in order to understand the discrepancies between the linear and non-linear distribution of the elements and its application for mineral exploration in the calamine Zn-Pb ore-deposit. From a hypothetical viewpoint, since geochemical zonation of the supra- and sub-ore elements is a crucial evaluation criterion for concealed/underlying mineralization potentials, this hypothesis can be tested by delineating the fractal surfaces of elements as the geometric evidence of primary geochemical zonation of elements in the calamine mine. A comparison of the linear regression results with the Poisson distribution coefficients indicate the relative tendency of the elements towards a non-linear distribution. Therefore, a logarithmic equation derived from the variance-distance relationship (power-law) is used here for the delineation of fractal surfaces of elements as the geometric features related to proper self-organized distributions. In this research work, the vario-fractal expression of geochemical zonation has trace-element tendencies to the non-linear distribution. The results obtained show that the calamine’s fractional surfaces are mostly of self-organized types, situated at 2 < FD < 3 as "real fractal surfaces", although 3 of the elements appear in the quasi-fractal populations called "near Brownies” here. Moreover, the calamine’s fractal surfaces can be extended throughout the anomalous regions or may be distributed as limited types of the finalized model, which is a fractal-based pattern of geochemical zonation of the elements for evaluation of the hypogenic mineralization potential and has been prioritized to 6 target-areas containing 10 elements with real fractal surfaces and 3 more at near Brownies and then validated by the mineralogical evidence.

Keywords

[1]. Borg, G., 2005. Geological and economic significance of supergene non-sulfide zinc deposits in Iran and their exploration potential. In: Geological Survey of Iran (Ed.) Mining and Sustainable Development. 20th World Mining Congress, Tehran, Iran. 7-11.

[2]. Grigoryan, S.V., 1974. Primary geochemical halos in prospecting and exploration of hydrothermal deposits. International Geology Review. 16(1), 12-25. https://doi.org/10.1080/00206817409471901.

[3]. Hitzman, M.W., Reynolds, N.A., Sangster, D.F., Allen, C.R., Carmen, and C.E., 2003. Classification, genesis, and exploration guides for non-sulfide zinc deposits. Economic Geology, 98(4), 685–714. https://doi.org/10.2113/gsecongeo.98.4.685.

[4]. Emsbo, P., 2009. Geologic Criteria for the Assessment of Sedimentary Exhalative (Sedex) Zn-Pb-Ag Deposits. U.S. Geological Survey, Reston, Virginia. Open-File Report, 21 pp.

[5]. Turcotte, D.L., 2002. Fractals in petrology. Lithos, 65(3-4), 261–271. https://doi.org/10.1016/S0024-4937(02)00194-9.

[6]. Maleki, M. and Emery, X., 2020. Geostatistics in the presence of geological boundaries: Exploratory tools for contact analysis. Ore Geology Reviews. 120, 103397. https://doi.org/10.1016/j.oregeorev.2020.103397.

[7]. Mandelbrot, B.B., 1983. The Fractal Geometry of Nature. W. H. Freeman, San Fransisco, 468 pp.

[8]. Barnsley, M.F., Devaney, R.L., Mandelbrot, B.B., Peitgen, H.O., Saupe, D., and Voss, R.F., 1988. The Science of Fractal                 Images. Springer-Verlag, New York, 327 pp.

[9]. Turcotte, D.L., 1997. Fractals and Chaos in Geology and Geophysics. Cambridge University Press, 414 pp.

[10]. Mehrnia, S.R., 2009. Using Fractal Filtering Technique for Processing ETM Data as Main Criteria for Evaluating Gold Indices in North West of Iran. International Conference on Computer Technology and Development, Kota Kinabalu, Malaysia, 379–393. https://doi.org/10.1109/ICCTD.2009.29.

[11]. Cheng, Q., 2012. Singularity theory and methods for mapping geochemical anomalies caused by buried sources and for predicting undiscovered mineral deposits in covered areas. Journal of Geochemical Exploration. 122, 55-70. https://doi.org/10.1016/j.gexplo.2012.07.007.

[12]. Nazarpour, A., 2018. Application of C-A fractal model and exploratory data analysis (EDA) to delineate geochemical anomalies in the: Takab 1:25,000 geochemical sheet, NW Iran. Iranian Journal of Earth Sciences. 10, 173–180.

[13]. Parsa, M., Maghsoudi, A., Yousefi, M., and Carranza, E.J.M., 2017. Multifractal interpolation and spectrum-area fractal modeling of stream sediment geochemical data: Implications for mapping exploration targets. Journal of African Earth Sciences. 128, 5-15. https://doi.org/10.1016/j.jafrearsci.2016.11.021.

[14]. Behera, S., Panigrahi, M.K., and Pradhan, A., 2019. Identification of geochemical anomaly and gold potential mapping in the Sonakhan Greenstone belt, Central India: An integrated concentration-area fractal and fuzzy AHP approach. Applied Geochemistry. 107, 45-57. https://doi.org/10.1016/j.apgeochem.2019.05.015.

[15]. Ghezelbash, R., Maghsoudi, A., and Carranza, E.J.M., 2019. Mapping of single- and multi-element geochemical indicators based on catchment basin analysis: Application of fractal method and unsupervised clustering models. Journal of Geochemical Exploration. 199, 90-104. https://doi.org/10.1016/j.gexplo.2019.01.017.

[16]. Liu, Y., Zhu, L., Ma, Sh., Guo, F., Gong, Q., Tang, Sh., Gopalakrishnan, G., and Zhou, Y., 2019. Constraining the distribution of elements and their controlling factors in the Zhaojikou Pb–Zn ore deposit, SE China, via fractal and compositional data analysis. Applied Geochemistry. 108, 104379. https://doi.org/10.1016/j.apgeochem.2019.104379.

[17]. Pourgholam, M.M., Afzal, P., Yasrebi, A.B., Gholinejad, M., and Wetherelt, A., 2021. Detection of geochemical anomalies using a fractal-wavelet model in Ipack area, Central Iran. Journal of Geochemical Exploration 220, 106675. https://doi.org/10.1016/j.gexplo.2020.106675.

[18]. Zuo, R., Xia, Q., Wang, H., 2013. Compositional data analysis in the study of integrated geochemical anomalies associated with mineralization. Applied Geochemistry. 28, 202-211. https://doi.org/10.1016/j.apgeochem.2012.10.031

[19]. Afzal, P., Heidari, S.M., Ghaderi, M., and Yasrebi, A.B., 2017. Determination of mineralization stages using correlation between geochemical fractal modeling and geological data in Arabshah sedimentary rock-hosted epithermal gold deposit, NW Iran. Ore Geology Reviews. 91, 278-295. https://doi.org/10.1016/j.oregeorev.2017.09.021.

[20]. Li, Ch., Ma, T., and Shi, J., 2003. Application of a fractal method relating concentrations and distances for separation of geochemical anomalies from background. Journal of Geochemical Exploration, 77(2-3), 167-175. https://doi.org/10.1016/S0375-6742(02)00276-5.

[21]. Hassanpour, Sh. and Afzal, P., 2013. Application of concentration–number (C–N) multifractal modeling for geochemical anomaly separation in Haftcheshmeh porphyry system, NW Iran. Arabian Journal of Geosciences. 6(3), 957-970. https://doi.org/10.1007/s12517-011-0396-2.

[22]. Farahmandfar, Z., Jafari, M.R., Afzal, P., and Ashja Ardalan, A., 2020. Description of gold and copper anomalies using fractal and stepwise factor analysis according to stream sediments in NW Iran. Geopersia. 10(1), 135-148. Doi: 10.22059/geope.2019.265535.648413.

[23]. Daneshvar Saein, L., 2017. Delineation of enriched zones of Mo, Cu and Re by concentration-volume fractal model in Nowchun Mo-Cu porphyry deposit, SE Iran. Iranian Journal of Earth Sciences. 9(1), 64–72.

[24]. Mirzaei, M., Afzal, P., Adib, A., Rahimi, E., and Mohammadi, Gh., 2020. Detection of zones based on ore and gangue using fractal and multivariate analysis in Chah Gaz iron ore deposit, Central Iran. Journal of Mining and Environment. 11(2), 453-466. Doi: 10.22044/jme.2020.9111.1801.

[25]. Aliyari, F., Afzal, P., Lotfi, M., Shokri, S., and Feizi, H., 2020. Delineation of geochemical haloes using the developed zonality index model by multivariate and fractal analysis in the Cu–Mo porphyry deposits. Applied Geochemistry. 121, 104694. https://doi.org/10.1016/j.apgeochem.2020.104694.   

[26]. Mark, D.M. and Aronson, P.B., 1984. Scale-Dependent Fractal Dimensions of Topographic Surfaces: An Empirical Investigation, with Applications in Geomorphology and Computer Mapping. Mathematical Geology, 16(7), 671-683. https://doi.org/10.1007/BF01033029.

[27]. Thorarinsson, F. and Magnusson, S.G., 1990, Bouguer density determination by fractal analysis: Geophysics, 55(7), 932-935. https://doi.org/10.1190/1.1442909.

[28]. Mehrnia, S.R., Ebrahimzadeh Ardestani, V., and Teymoorian, A., 2013. Application of fractal method to determine the Bouguer density of Charak Region (South of Iran). Iranian Journal of Geophysics, 7(1), 34-50 (in Persian).

[29]. Holland, H.D., 2005. Sedimentary Mineral Deposits and the Evolution of Earth’s Near-Surface Environments. Society of Economic Geologists, Inc. Economic Geology, 100(8), 1489-1509. http://dx.doi.org/10.2113/gsecongeo.100.8.1489.

[30]. Haldar, S.K., 2017. Mineral Exploration Principles and Applications. Elsevier, 378 PP.

[31]. Russ, J.C., 1994. Fractal Surfaces. Springer Science & Business Media, Plenum Press, New York (313 pp.).

[32]. Agterberg, F.P., 2012. Multifractals and geostatistics. Journal of Geochemical Exploration. 122, 113-122. https://doi.org/10.1016/j.gexplo.2012.04.001.

[33]. Mehrnia, S.R., 2017. Application of Fractal Technique for Analysis of Geophysical- Geochemical Databases in Tekieh Pb-Zn Ore Deposit (SE of Arak). Journal of Economic Geology (ISSN 2008-7306). 8(2).

[34]. Mehrnia, R., 2013. Application of fractal geometry for recognizing the pattern of textural zoning in epithermal deposits (case study: Sheikh-Darabad Cu-Au indices, East-Azarbaijan province). Journal of Economic Geology (in Persian), 5(1), 23-36.

[35]. Pourfaraj, H., 2016. Structural analysis of fault systems in Mehdiabad Zn-Pb mine area, SE Yazd. [Unpublished MSc Thesis], Tarbiat Modares University, Iran, 192 pp.

[36]. G.S.I., 1988. Geological studies on the Mehdiabad Lead and Zinc Project (Unpubl. internal report).

[37]. Ankomah, A.B., 1992. Magnesium and pH Effect on Zinc Sorption by Goethite. Soil Science. 154(3), 206-213.

[38]. Reichert, J., Borg, G., and Rashidi, B., 2003. Mineralogy of calamine ore from the Mehdi Abad zinc-lead deposit, Central Iran. Conference 7th Biennial Meeting, Society for Geology Applied to Mineral Deposits; Mineral exploration and sustainable development, Athens. 97-102.

[39]. Ghasemi, M., 2006. Formation Mechanism of the Mehdiabad Zn–Pb Deposit and its Comparison with Other Near Lead and Zinc Deposits [Unpublished MSc Thesis], Research Institute of Earth Sciences, Geological Survey and Mineral Exploration of Iran, Iran, 238 pp.

[40]. Reichert, J., 2007. A Metallogenetic Model for Carbonate hosted Non-sulfide Zinc Deposits based on Observations of Mehdiabad and Iran Kouh, Central and Southwestern Iran [Unpublished PhD Thesis], University of Martin Luther, Shillong, 129 pp.

[41]. Ebrahim-Mohseni, M., 2011. Study of genesis of Mehdiabad deposit using fluid inclusion and stable isotope [Unpublished MSc Thesis], Damghan University, Damghan, Iran, 166 pp.

[42]. Maghfouri, S., 2017. Geology, Geochemistry, Ore Controlling Parameters and Genesis of Early Cretaceous Carbonate-clastic Hosted Zn-Pb Deposits in Southern Yazd Basin, with Emphasis on Mehdiabad Deposit [Unpublished PhD Thesis], Tabriz University, Iran, 475 PP.

[43]. Teymoorian-Motlagh, A., Ebrahimzadeh-Ardestani, V., and Mehrnia, R., 2012. Fractal method for determining the density                 of the stone tablet in Charak region (southern Iran). Life Science Journal. 9(4).

[44]. Bonham-Carter, G.F., 1994. Geographic Information Systems for Geoscientists: Modelling with GIS. Pergamon (402 pp).

[45]. Cheng, Q., 2006. Multifractal modelling and spectrum analysis: method and applications to gamma ray spectrometer data from southwestern Nova Scotia, Canada. Science China Earth Sciences. 49(3), 283-294. https://doi.org/10.1007/s11430-006-0283-y.

[46]. Tan, Q. and Xu, X., 2014. Comparative Analysis of Spatial Interpolation Methods: an Experimental Study. Sensors & Transducers Journal. 165(2), 155-163.

[47]. Xie, Sh., Cheng, Q., Ke, X., Bao, Zh., Wang, Ch., and Quan, H., 2008. Identification of Geochemical Anomaly by Multifractal Analysis. Journal of China University of Geosciences. 19(4), 334-342. https://doi.org/10.1016/S1002-0705(08)60066-7.

[48]. Morison, G., 2003. AMIRA Project, Revised version: Evaluating of Gold Mineralization Potentials in Queensland Epithermal Systems, Queensland J.C Univ. press, Queensland, Australia, 249 pp.

[49]. Akbari, E. and Mehrnia, R., 2013. Association of Silica Fractal Distribution with Gold Mineralization: a case study from the Takmeh-Dash Region, NW of Iran. Journal of Tethys. 1(4), 241-253.

[50]. Cheng, Q., 2007. Mapping singularities with stream sediment geochemical data for prediction of undiscovered mineral                 deposits in Gejiu, Yunnan Province, China. Ore Geology Reviews. 32(1-2), 314-324. https://doi.org/10.1016/j.oregeorev.2006.10.002.

[51]. Khaled, A., Cheng, Q., and Chen, Zh., 2007. Multifractal power spectrum and singularity analysis for modelling stream sediment geochemical distribution patterns to identify anomalies related to gold mineralization in Yunnan Province, South China. Geochemistry: Exploration, Environment, Analysis. 7(4), 293-301. https://doi.org/10.1144/1467-7873/06-116.