Discrimination of Pb and Zn geochemical anomalies using classical, multifractal (C-N) and (C-A) and singularity index statistical methods in Arak 1:100000 sheet

 
1-Introduction
Separation of geochemical anomalies from background has always been a significant concern of exploration geochemistry. The search for methods that can make this analysis quantitative and objective aims not only at the reduction of subjectiveness but also at providing an automatic routine in exploration, assisting the interpretation and production of geochemical maps (Nazarpour et al., 2016). Arak 1:100000 geological sheet is located in the north of Malayer-Aligoudarz-Efsahan Pb-Zn metalogenic belt, so this sheet has been studied. In this study, we compared the methods of classical statistics (Mean+2SDEV), exploratory data analysis (MAD), concentration-number (C-N) and concentration-area (C-A) fractal models. Also, singularity index models were used to separate the Pb and Zn anomalies in Arak 1:100000 geochemical sheet. The results of mentioned methods, showed that the singularity index method has a higher accuracy. Also, indicates the higher concentration of Zn in area of study.
2-Methodology
2-1 Classical statistics
Various statistical methods have been used to process geochemical data in order to determine threshold values. Statistical quantities, such as the mean, standard deviation (SDEV) and percentiles, have been used to define threshold for separating anomalies form background. For example, geochemical anomalies have been defined as values higher than a threshold defined as the 75th or 85th percentile, and Mean+SDEV or Mean+2SDEV (Nazarpour et al., 2015).
 
2-2 EDA (Exploratory Data Analysis)
In exploratory data analysis (here after named EDA) of geochemical exploration data, the median+2MAD value was initially used to identify extreme values and act as threshold for further inspection of large data sets (Carranza, 2009). The EDA was first established by Tukey (1977), was developed further by, and then was used by many researchers in modeling of geochemical anomalies (Carranza, 2009). The MAD is the median of absolute deviations of individual dataset values (Xi) from the median of all dataset values (Tukey, 1976):
(1) MAD = median 14 [│Xi-median Xi│]">
2-3 Multifractal
Fractal and multifractal models have also been applied to separate anomalies from background values. These methods are gradually being adopted as an effective and efficient means to analyze spatial structures in metallic geochemical systems (Afzal et al., 2017). The concentration-number (C-N), concentration-area (C-A) multi-fractal methods has been used for delineation and description of relations among mineralogical, geochemical and geological features based on surface and subsurface data (Nazarpour et al., 2015). Fractal/multi-fractal models consist of the frequency distribution and the spatial self-similar or self-affine characteristics of geochemical variables and have been demonstrated to be useful tools for decomposing geological complexes and mixed geochemical populations and to recognize weak geochemical anomalies hidden within strong geochemical background (Cheng et al., 1994).
2-4 Singularity index
The singularity technique is another vital progress for fractal/multifractal modeling of geochemical data (Zuo et al., 2012). It is defined as the characterization of the anomalous behaviors of singular physical processes that often result in anomalous amounts of energy release or material accumulation within a narrow spatial–temporal interval. The singularity can be estimated from observed element concentration within small neighborhoods based on the following equation (Cheng, 2007):
(2) 14X=c·εa-E">
 
The singularity index is a powerful tool to identify weak anomalies, but it is influenced by the selection of the window size. When applying this method, one should use different window sizes to process the geochemical data and find an appropriate window size which can highlight the interesting results (Zuo et al., 2012).
 
3- Results and discussion
Threshold values obtained using mentioned methods were used to map the spatial distribution of element concentrations. These interpolated maps were produced by means of inverse distance weighted (IDW) method (Nazarpour et al., 2016). In classical statistics and MAD methods, anomalies are usually detected, regardless of the location of each instance, and only by formulating relationships (Hashemi marand et al., 2018). In these methods, it is possible that some of the proposed ranges are false anomalies (Tukey, 1977). The geochemical anomalies of the Pb and Zn elements were separated using fractal methods of concentration-number (C-N), concentration-area (C-A), and according to the fitting line of each element on the logarithmic graphs. The singularity index estimated through a small window mainly reflects the fluctuation of the element concentration (Afzal et al., 2017). The singularity index estimated through a large window mainly reflects regional changes but it does not focus on the local weak anomalies (Zuo et al., 2012). There is probably a significant effect of the contact between exposed bedrock and covered areas, or there could be other deterministic trends as well, which should be studied further (Cheng, 2007). The results of the named methods are shown in Fig. 1.
4-Conclusions
Singularity index analysis, indicated that the hidden anomalies are better coincidence with indices and mineral deposit occurrence in the study area. In general, the comparison between these methods indicate that the concentration of Pb and Zn increased toward the and southwest and south-northeast parts, respectively. In these regions there is high potential for the occurrence of promising mining areas. Moreover, the obtained Pb and Zn anomalies have a reasonable correlation with the exposure of limestone in the study area, which is a suitable host rock for the formation of MVT type Pb and Zn deposits.
 
 
 
 
 
 
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b
 
 
 
 
 
 
c
 
 
 
 
 
 
 
d
 
 
 
 
 
 
e
 
 
 
 
Figure 1. Maps of spatial distributions of Pb, Zn elements. a) Classic statistics, b) MAD, c) Multifractal (C-N), d) Multifractal (C-A), e) Singularity index
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