کاربرد مدل ‌نمایی پراش- مسافت در بررسی‌ های ژئوشیمیایی کانسار روی کالامین (مجتمع معدنی مهدی آباد یزد)

معدن روی سرب کالامین (مهدی آباد، یزد، ایران مرکزی)، یک رخنمون اقتصادی غیرسولفیدی با منشا رسوبی آتشفشانی است که بر اساس سوابق اکتشافی منطقه، از ویژگی های زمین شناختی و ژئوشیمیایی متناسب با محیط های سوپرژن برخوردار است. در این پژوهش، از سه رهیافت رگرسیون خطی، توزیع پواسونی و تغییرات بعد فرکتال برای بازبینی توزیع های ژئوشیمیایی و معرفی اولویت های اکتشافی منطقه مورد بررسی استفاده‌ شده است. مقایسه ضرایب رگرسیون خطی و توزیع پواسونی عناصر مختلف، بیانگر تمایل نسبی آنها به توزیع غیرخطی است. بنابراین از مدل ‌نمایی پراش مسافت برای دستیابی به تغییرات بعد فرکتالی 13 عنصر شاخص و ردیاب ذخایر‌ برون‌دمی استفاده شده است. تعیین سطح توزیع براونی هر عنصر، ملاک هندسی جدیدی است که با فرایند خودساماندهی ژئوشیمیایی در سامانه های ماگمایی، گرمابی و آتشفشانی سازگاری دارد. در پیش بینی به روش فرکتال، از الگوی ناحیه بندی ترکیبی شامل 10 عنصر با سطوح آرمانی و 3 عنصر با سطوح نزدیک به سطح براونی برای معرفی اولویت های اکتشافی منطقه استفاده شده است. نتایج پژوهش نشان می دهند که عناصر آرسنیک، روی و آنتیموان از سطوح توزیع براونی مطلوب (fd>2 3>) برای تولید مولفه های متناظر (عیارهای متناظر) برخوردارند. تغییرات بعد فرکتالی سرب، مس، نقره و گوگرد از نوع محدود، اما قابل برازش با سطوح براونی آرسنیک، روی و آنتیموان بوده و بیانگر ناحیه بندی ژئوشیمیایی متناسب با فرایند غنی شدگی در عمق رخساره های دگرسانی است. لذا بر اساس نقشه پیش داوری مبتنی بر تحلیل های واریوفرکتالی، امکان دستیابی به ذخایر هیپوژنیک در برخی از اهداف اکتشافی منطقه کالامین وجود دارد.

Application of Variance-Distance exponential model in geochemical studies of zinc calamine ore deposit (Mehdiabad mining complex of Yazd)

IntroductionCalamine ZnPb deposit (Mehdiabad, Yazd, Central Iran) is a mineable nonsulfide mineralization, located in the upper part of a volcanosedimentary basin at intersection with erosion surfaces. From statistical viewpoint, geochemical distributions of trace elements due to volcanicexhalative processes, may naturally be predominated by selforganized zonation in ore mineralized regions (Cheng et al., 2000; Mehrnia, 2017). Therefore, attention is paid to nonlinear distribution of particular elements to finding their spatial relations with concealed ore mineralization for prospecting sedimentaryhosted exhalative deposit (SEDEX). In this way, calculation and analysis of statistical coefficients is a necessary stage for prospection of the interrelation of typomorphic elements. In cases where the erosion surfaces result in redistribution of supra ore elements, the approach of linear regression coefficient is not recommended, because progressive weathering usually hides the natural zonality of elements, as an expected criterion for hypogenic mineralization (HassaniPak, 2012). Our research approach which is to find a proper zonality of elements is based on nonlinear assessment of geochemical distributions for a case of epigenetic mineralization that seems to be related to deep/concealed SEDEX deposits. Material and methodCurrent research uses a variancedistance equation to modify the linear regression results as follows:                  (1)where Log (Vx) and Log (Dvx) are the logarithms of variances and distances respectively; and FD is the fractal dimension. A loglog plot is used to illustrate Vx and Dvx changes on horizontal (X) and vertical (Y) axes to obtain a distribution’s density function. By statistical concepts, FD is an independent variable from the central tendencies as well as distribution parameters. Meanwhile, a selforganizing property of geochemical distributions is geometrically dependent on fractal dimension changes on powerlaw’s loglog plots. For obtaining the natural geochemical zonation of Calamine’s pathfinder elements, a set of lithogeochemical data has been used. Consequently, a total of 180 lithosamples of Calamine region were collected and interpolated to find the anomalous populations. A GISbased software (Spatial Analyst) was used here to obtain geometric and statistical quantities which are necessary for variancedistance equation (TeymoorianMotlagh et al., 2012). This softpackage works on ArcMap with the ability to export summarized data to other supplementary software packages such as Excel which are used to complete and present VD loglog plots.At the second step, we used fractal dimension changes to identify the Brownian surfaces of elements. This surface usually contains a set of paragenetic elements which are found together within several correlated zonations with respect to their rate of activities in magmatic environments. A Brownian surfaces is formed of particular geometric locations of selfsimilar populations. When it changes between 2.5>FD>2, it represents scaleinvariant continuity of distributions (Thorarinsson and Magnusson, 1990). In other word, this surface denotes the tendency of traceelements to nonlinear distributions and it is geometrically related to a probable phase of mineralization in some epigenetic ore deposits. DiscussionBased on a variancedistance model for Calamine’s indicative and pathfinder elements, six target areas are presented in a contoured prognostic map, which contains As, Zn, Cr, Sb, S, Co, Cu, Pb, Ni and Ag in a sequent. Order of this sequent is based on geometry of their Brownian surfaces.  The largest surface belongs to As while the smallest one belongs to Ag and Cd. Among the elements which have reached the Brownian surface, As, Sb and Zn shared similar fractal parameters and extended at the background of other elements. Cr was the only element which did not follow the As, Sb and Zn backgrounds, because its geometrical location is independent of other elements. The mentioned targetareas which are marked on the prognostic map, have different scoring of mineralization potentials that is prioritized by considering zonation peculiarities of elements on fractal surfaces.   ResultsFractal relationship of elements is conceptually different from what is generally stated in statistical models. Therefore, many elements which have desirable linear correlation with each other (relatively good condition for pathfinding), are unfavorable as VD models and vice versa. From a nonlinear perspective, a Poisson distribution is the most important criterion for analyzing coherency of elements in hypogenic environments. As a final result, we have illustrated that Brownian surfaces in As, Zn and Sb are extended well in the central and southeastern parts of Calamine, marking a proper relation of the structures with the host units during exhalative activities of the region. The high amount of these elements compared to the background indicates the effect of fluid flows and the penetration of mineralizing solutions under a supergene condition of the mine as well opening the fractures and fault systems. ReferencesCheng, Q., Xu, Y. and Grunsky, E., 2000. Integrated spatial and spectrum method for geochemical anomaly separation. Natural Resources Research 9(1): 43–51. https://doi.org/10.1023/A:1010109829861HassaniPak, A.A., 2012. Principles of geochemical exploration. University of Tehran Publication, Tehran, 615 pp. (in Persian)Mehrnia, S.R., 2017. Application of Fractal Technique for Analysis of Geophysical Geochemical Databases in Tekieh PbZn Ore Deposit (SE of Arak). Journal of Economic Geology, 8(2): 325–342. (in Persian with English abstract) https://doi.org/10.22067/econg.v8i2.42454TeymoorianMotlagh, A., EbrahimzadehArdestani, 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): 1913–1923.  https://doi.org/ 10.7537/marslsj090412.290Thorarinsson, F. and Magnusson, S.G., 1990. Bouguer density determination by fractal analysis. Geophysics, 55(7): 932–935. https://doi.org/10.1190/1.1442909