Abstract
The aim of this paper is to delineate the different lead–zinc mineralized zones in the Zardu area of the Kushk zinc–lead stratabound SEDEX deposit, Central Iran, through concentration–volume (C–V) modeling of geological and lithogeochemical drillcore data. The geological model demonstrated that the massive sulfide and pyrite+dolomite ore types as main rock types hosting mineralization. The C–V fractal modeling used lead, zinc and iron geochemical data to outline four types of mineralized zones, which were then compared to the mineralized rock types identified in the geological model. ‘Enriched’ mineralized zones contain lead and zinc values higher than 6.93% and 19.95%, respectively, with iron values lower than 12.02%. Areas where lead and zinc values were higher than 1.58% and 5.88%, respectively, and iron grades lower than 22% are labelled “high-grade” mineralized zones, and these zones are linked to massive sulfide and pyrite+dolomite lithologies of the geological model. Weakly mineralized zones, labelled ‘low-grade’ in the C– V model have 0–0.63% lead, 0–3.16% zinc and > 30.19% iron, and are correlated to those lithological units labeled as gangue in the geological model, including shales and dolomites, pyritized dolomites. Finally, a log-ratio matrix was employed to validate the results obtained and check correlations between the geological and fractal modeling. Using this method, a high overall accuracy (OA) was confirmed for the correlation between the enriched and high-grade mineralized zones and two lithological units — the massive sulfide and pyrite+dolomite ore types.
1 Introduction
The separation of mineralized zones from the barren host rocks is important to economic geology. To aid in this purpose, detailed studies of the lithology and mineralogy of mineral deposits are important, and a number of conventional models have been proposed based on petrological and mineralogical studies including the determination of rock types, alteration zones, and minerals using thin/polished sections [1–8]. Based on this geological dataset, geological 3D models are then generated, plotting rock types, ore minerals, alteration zones, and stratigraphy [9, 10]. However, geochemical data are still essential for the identification of mineralized zones, with several methods, such as classical statistics [11–13], proposed for data interpretation in the past.
Non-Euclidian fractal geometry, as first proposed by Mandelbrot [14], is an important branch of non-linear mathematical sciences that has been applied to various fields of geoscience since the 1980s. Bolviken et al [15] and Cheng et al [16] revealed that geochemical patterns of various ore elements have fractal dimensions. Since that time, several fractal models have been developed and applied to geochemical exploration; these models work by separating geochemical populations into component mineralized zone and phase populations. Examples of fractal models include the number–size (N–S) model proposed by Mandelbrot [14], the concentration–area (C–A) model of Cheng et al [16], the concentration–perimeter (C–P) model of Cheng et al [17], the concentration–distance (C–D) model proposed by Li et al [18], and the concentration– volume (C–V) model of Afzal et al [19]. Fractal/multifractal modeling assists in identifying relationships between geological, geochemical, and mineralogical settings and linking them to spatial information obtained from mineral deposits [19–35]. Various geochemical and mineralization processes can be defined due to differences in fractal dimensions, based on analysis of relevant geochemical data. Log–log plots in fractal/multifractal modeling, being consistent with the widely accepted view that fractality always accompanies phase-changes [36], are accurate tools for delineating geological populations or geochemical zones, with breakpoints in those log–log plots representing threshold values [19, 21]. The application of fractal models to the detection of mineralized zones is based on relationships between ore grades and occupied volumes or tonnages [19, 27, 37–43].
In this paper, the C–V fractal model was used to delineate lead–zinc mineralized zones in the Zardu area of the Kushk zinc–lead deposit, Central Iran. This fractal model was built in conjunction with geological modeling based on rock types and stratigraphy, and the results from both models were correlated by use of a log ratio matrix, as proposed by Carranza [44].
2 Methodology
Subsurface data from the Zardu area, Kushk deposit, was obtained from roughly 10 628 m of core in 179 boreholes. Rock samples from the boreholes were logged to construct the stratigraphy and lithological model, and 3253 lithogeochemical samples for zinc, lead were analyzed for zinc, lead and iron using A.A.S.[1]
2.1 C-V fractal model
Afzal et al [19] proposed use of the C–V fractal model to delineate different levels of mineralization in different ore deposit types. On the C-V log-log plot, it can be observed that where the slope of the curve changes, this represents an intensive change in the geochemical population, which is in turn affected by changes in geological and mineralization characteristics. In general, modeling has been defined using the following formula:
where V(ρ ≤ υ) and V(ρ ≥ υ) indicate volumes (V: m3 in this study) with ore values (ρ: % in this study) that are smaller and greater than, respectively, the threshold values (υ: % in this research) that define those volumes; a1 and a2 are characteristic exponents. In this model, threshold values represent boundaries between the various types of mineralized zones (including barren host rocks) within the different mineral deposits. To calculate V(ρ ≤ υ) and V(ρ ≥ υ), which in a 3D model represent the volumes enclosed by contour level ρ, the borehole ore-element data are interpolated or simulated by using geostatistical estimation/simulation methods [22, 41].
2.2 Geological modeling
Basic geological data — collar coordinates, azimuth and dip (orientation), lithology and mineralogy — was obtained from 179 drillcores via core logging, petrological, and mineralogical studies. Based on this data, the main rock types by depth were modeled for the study region using stratigraphic and lithoblending algorithms in the RockWorks 15 software package. This is a proper algorithm which ‘bleeds’ mapped lithology types outward from individual boreholes to form a solid model; however, this method results in lithology units extending from each borehole, which can end abruptly when the zones from neighboring boreholes do not match [41]. The ‘Triangulation’ algorithm was used for 3D modeling of mineralized strata in the Zardu area, which is an estimation environment.
3 Geological setting
3.1 Regional geology
The Bafq district, in which the Kushk deposit occurs, is located within the central part of the Kashmar–Kerman Tectonic Zone [45], also known as the Posht-e-Badam Block [46], of the Central Iranian Zone (CIZ: Fig. 1). The Posht-e-Badam Block is located between the western Yazd Block and the central Tabas Block, and together with the Lut Block further to the east, these blocks form the CIZ’s crustal domain. This major metallogenic province hosts abundant iron oxide – apatite deposits ≍2 Gt of ore distributed across 34 deposits) and an important lead–zinc SEDEX mineralized zone [47, 48].
![Figure 1. The Zarigan-Chamir basin map within zinc–lead SEDEX deposits which is taken from Ramesani and Tucker (2003) [45, 62].](/document/doi/10.1515/geo-2016-0014/asset/graphic/j_geo-2016-0014_fig_001.jpg)
The Posht-e-Badam Block is hosted by the Precambrian basement of the Iran Plate, and has later been covered by Lower Cambrian to Mesozoic rocks [49]. Although the block was originally thought to have formed during the Pan-African intra-continental extension [50–52], it has recently been redefined as a magmatic arc (Fig. 1) developed along the Proto-Tethyan margin of the Gondwanan super-continent [45, 53–55]. Some authors have reported geological features, predominantly bimodal alkaline volcanism, suggestive of an extensional back-arc regime in the eastern portion of the area [47, 48, 56].
The Bafq district is situated in a known metallogenic zone in central Iran, located alongside a containing Infra-Cambrian large ore deposits such as Choghart (iron), Esfordi (phosphate–magnetite), Kushk (lead and zinc), and Chadormalu (iron and apatite). In this district, there are also Precambrian complexes hosting uranium, thorium, vanadium, manganese, molybdenum, titanium, barium, apatite, rare-earth element (REE), stratiform lead–zinc massive sulfide, and various types of iron-ore mineralization, all of which are associated with the late- to post-rhyolite/andesite magmatism resulting from the Assyntian Orogeny [48, 49, 58–61].
3.2 Geological characteristics of the Kushk deposit
The zinc–lead SEDEX stratiform deposits at Kushk, Chahmir, and Zarigan formed in the same tectono-sedimentary environment (Posht-e-Badam Block). The opening of the Zarigan–Chahmir basin in the Posht-e-Badam Block took place during fragmentation of the Central Iranian Micro-continent in the Late Neoproterozoic - Lower Cambrian, caused by back-arc rifting of the continental margin, coeval with the convergence of the Proto-Tethys along the Gondwanan continental margin [62].
The SEDEX type Kushk zinc–lead deposit is the biggest zinc–lead deposit of Bafq area. Related to a caldera structure [55, 63], the area contains outcrop of various rock types including volcanic and sub-volcanic rocks (rhyolites, rhyodacites, dacites, and rhyolitic tuffs) and sedimentary rocks (shale, limestones, and dolomites). Mineralization at the deposit is hosted by Neoproterozoic black shales (Figs 1 and 2), and sedimentary breccias exist in the lower sandstone and silty limestone lithologies recorded in the northeastern part of the deposit [64]. The paragenetic sequence of minerals indicates two stages of lead ore (galena) mineralization and one stage of zinc ore formation [65]. Overall, the Kushk deposit is a fine-grained stratiform-banded deposit, with sphalerite, galena and pyrite the main sulfides developed [64]. The deposit forms conformably in tuff, shale, carbonate and ash beds within the larger black shale package [57]. The Kushk deposit consists of four geographic areas, known as, from south to north, old Kushk, Zardu, South Pahnu and North Pahnu.
![Figure 2. Geological map of Kushk deposit [48].](/document/doi/10.1515/geo-2016-0014/asset/graphic/j_geo-2016-0014_fig_002.jpg)
Geological map of Kushk deposit [48].
The ore-bearing sequence of footwall limestones and hanging-wall dolomites within black shales outcrops in the Zardu Syncline and is truncated by the northwest– southeast trending Kushk Fault. A rhyolitic dome intrudes the ore-bearing sequence in the southeastern part of the deposit, and several diabasic dykes are observed as cross-cutting the volcanosedimentary sequence [62].
3.3 Geology of Zardu area
The Zardu area is one of the main parts of Kushk deposit, and like the larger deposit consists of a series of sedimentary and volcanosedimentary rocks. Lithological sequences in the area include rhyolite, gray to brown dolomite, pyritic black shale, micro-diorite, massive sulfide ore (pyrite–galena–sphalerite–shale), massive pyrite+dolomite ore (pyrite–galena–sphalerite– dolomite–shale), gray to green tuff, gray to brown limestone, and dolomite (Fig. 3). The stockwork zone consists of an irregular network of sulfide-bearing dolomite veins cutting the footwall sedimentary rocks, and which extend into the massive ore as large veins greater than 7 cm thick; the sedimentary host rocks are also hydrothermally altered and intensely brecciated near the stockwork zone. The sulfide content of the stockwork zone is generally low, but included pyrite, sphalerite, and minor galena in some veins. The massive ore forms a high-grade ore body, the thickness part of the Zardu deposit [62].
![Figure 3. Zardu geological map [48].](/document/doi/10.1515/geo-2016-0014/asset/graphic/j_geo-2016-0014_fig_003.jpg)
Zardu geological map [48].
In the Zardu area, ore mineral paragenesis has been interpreted as follows: (Fig. 4):
A) Massive sulfide ore including galena (ga), sphalerite (sp), and pyrite (py); B) Massive, highly pyritic ore consisting of pyrite (py), sphalerite (sp), and dolomite (dl); C) Bedded ore containing pyrite (py), galena (ga), sphalerite (sp), and organic-rich shale (sh).
Massive sulfide ore (pyrite, sphalerite, galena), and organic-rich black shale.
Massive, highly pyritic ore (minerals pyrite, sphalerite, galena, dolomite) and minor organic-rich black shale.
Bedded ore consisting of alternating beds of shale and ore minerals (galena, sphalerite, and pyrite).
Massive, bedded, and spherulitic and spheroidal mineral textures have been identified (Fig. 5).
Microphotographs of ore minerals and textures in polished sections (Zand, 2013): A) massive texture, including galena (Ga), sphalerite (Sp), and pyrite (Py); B) bedded texture, including pyrite (Py), sphalerite (Sp), galena (Ga), and organic matter (Om); C) spheroidal texture, consisting of pyrite (Py), sphalerite (Sp), and organic matter (Om); D) spheroidal and spherulitic texture, consisting of pyrite (Py), sphalerite (Sp), galena (Ga) and organic matter (Om).
4 Discussion
When the geochemical data from this deposit is plotted, zinc and lead values illustrate an L-shape distribution, whereas iron distribution has multi-modal nature; the mean values for lead, zinc and iron are 1.47%, 7.28% and 22.48%, respectively (Fig. 6). The experimental semi-variograms for lead, zinc and iron, generated using Datamine Studio software (Fig. 7), demonstrate data ranges of 25 m, 100 m, and 100 m, respectively. Of the three variograms, only the zinc and iron plots are structural, and can separate the different types of mineralized zones within the study area. On the other hand, all three variograms have two ranges, which can show variations in geological characteristics, particualrly mineralization.
Histograms plotting zinc, lead, and iron data from the Zardu area, Kushk deposit.
Variograms plotting lead (a), iron (b) and zinc (c) data from the Zardu area, Kushk deposit.
4.1 Geological modeling
Construction of a geological model began with stratigraphic modeling based on logging data and mineralogical studies of zinc–lead ore strata. As part of this lithological model, 179 exploratory boreholes were analysed, and 16 rock types were selected and identified (Fig. 8). Most of the strata-ore zone consists of massive sulfide and pyrite+dolomite ore lithologies in the Zardu area, as depicted in Fig. 7. Therefore, all other lithological units identified in the gological modeling, such as pyritized dolomites, shales, and tuffs, are herein termed gangue units.
Lithological model of mineralized strata for the Zardu area: A) all mapped lithologies; B) massive sulfide ore type distribution; C) pyrite+dolomite ore type distribution; and D) gangue distribution (d).
4.2 C–V fractal modeling
The Zardu area of the Kushk deposit was modeled using 89 173 voxels, with each voxel 10 m×10 m×0.5 m in the X, Y and Z directions, respectively; voxel dimensions were based on the geometrical shape of the deposit and dimensions of the drilling grid [66]. The zinc, lead and iron distribution models were generated using the inverse distance squared (IDS) method in the Rockworks 15 software package, as the variography results for V(ρ ≥ υ) indicated volumes enclosure within an ore value in the 3D models. Based on the estimated models, elemental thresholds values were then identified from zinc, lead and iron log–log plots (Fig. 9). This work demonstrates a power–law relationship between zinc, lead and iron values and their volumes occupied. These power–law relationships reveal changes in the geological, mineralization and geochemical characteristics within the deposit. Geochemical populations for these elements were separated into straight-line segments in the log–log plots. All elemental log–log plots for this area show four distinct geochemical populations based on sudden changes in the rate of volume decrease, as depicted in Fig. 8 and Table 1; in the “enriched” population, the slope of the segments is close to 90° [16, 67].
C–V log–log plots for lead (a), iron (b), and zinc (c).
Elemental thresholds and ranges for mineralization zones identified using the C–V model.
| Elements | Low-grade zone and barren host rock | Medium-grade zone | High-grade zone | Enriched zone |
|---|---|---|---|---|
| Pb | <0.63% | 0.63%–1.58% | 1.58%–6.3% | > 6.3% |
| Zn | <3.16% | 3.16%–5.88% | 5.88%–19.95% | > 19.95%– |
| Fe | >30.19% | 22.9%–30.19% | 12.02%–22.9% | < 12.02% |
Using the log–log plots, the furthermost element populations are interpreted as “enriched” zinc–lead zones, having lead and zinc concentrations higher than 19.95% and 6.3%, respectively. Iron values in this enriched zinc– lead zone, where it is obstensibly a waste element, are lower than 12.02% (Table 1). In the mineralogy, this corresponds to an increase in zinc and lead minerals, specifically sphalerite and galena, in the enriched zone, with simultaneous decrease in the volume of pyrite corresponding to the lower iron values.
The “high-grade” mineralized zone has a zinc concentration between 5.88% and 19.95%, lead values between 1.58% and 6.3%, and iron values between 12.02% and 22.9%. Both the enriched and high-grade zones are concentrated in the northeastern, central and western parts of the study area (Fig. 10).
3D models of mineralized zones deliniated using C–V fractal modeling, including a) the enriched and high-grade zones; b) the medium-grade zone and c) the low-grade zone and barren host rocks.
The medium-grade zone has zinc, lead, and iron values of 3.16% – 5.88%, 0.63% – 1.58% and 12.02% – 22.9% respectively; this zone is located around the margins of the enriched and high-grade zones (Fig. 10). The barren host rocks and low-grade zone are identified as containing zinc and lead concentrations lower than 3.16% and 0.63%, respectively, and iron values higher than 30.19%; this zone is concentrated in the western and southern parts of the study area (Fig. 10).
5 Correlation of geological and fractal modeling results
Carranza [68] previously presented a calculation of the spatial correlations between two binary models, especially geological and mathematical models, which was first applied to gold exploration within stream sediments in the Philippines. Through this method, the results of the C– V fractal and geological models are compared with each other in a matrix in order to assess the overall agreement of results obtained from each model. Using the total number of voxels on which the fractal model was based, Type I errors (T1E), Type II errors (T2E), and the overall accuracy (OA) of the fractal model were calculated with respect to various units plotted in the geological ore model (Table 2: Carranza [68]). Finally, for each of the mineralized zone types identified, OA values for comparison to the massive sulfide and pyrite+dolomite lithologies were compared (Table 3).
Matrix comparing performance of fractal modeling against the geological model. A, B, C, and D represent numbers of voxels overlapping between classes in the binary geological model and the binary fractal model, respectively [59].
| Geological Model | |||
|---|---|---|---|
| Inside Zone | Outside Zone | ||
| Fractal model | Inside Zone | True Positive(A) | False Positive(B) |
| Outside Zone | False Negative (C) | True Negative(D) | |
| Type I Error = C/(A+C) | Type II Error = B/(B+D) | ||
| Overall Accuracy = (A+D)/(A+B+C+D) | |||
Calculated overall accuracies between mineralized and lithological zones identified by the geological and fractal models.
| Mineralized rock types obtained by geological modeling | ||||
|---|---|---|---|---|
| Mineralized zones obtained by fractal modeling | Overall Accuracy (OA) | Gangue zone | Pyrite+dolomite | Massive sulfide zone |
| Low-grade zone | 0.86 | 0.29 | 0.77 | |
| Medium-grade zone | 0.23 | 0.91 | 0.82 | |
| High-grade zone | 0.24 | 0.92 | 0.83 | |
| Enriched zone | 0.22 | 0.93 | 0.93 | |
Comparison of the distribution of massive sulfides, pyrite+dolomites and gangue (derived form the 3D geological modeling) to the distribution of zinc–lead enriched mineralized zones (from the C–V fractal modeling) indicate that both the massive sulfide and pyrite+dolomite lithologies are strongly correlated due to this zone, based on their high, similar OA values. Overall accuracies between the pyrite+dolomite and massive sulfide lithologies when compared to the high-grade zone are 0.92 and 0.83, respectively, which shows that the pyrite+dolomite lithology distribution provides the better indicator to the distribution of zinc–lead high-grade mineralized zones within the deposit (Table 3). Similarly, the medium-grade zone from the C–V fractal modeling correlates better with the pyrite+dolomite lithology from the geologica model, as illustrated by the higher OA value.
6 Conclusions
In this paper, geological and C–V fractal models were used to identify different sets zinc–lead mineralized zones in the Zardu area of the Kushk zinc–lead SEDEX deposit, Central Iran. The elemental log–log plots indicated four mineralization zones in the deposit, consisting of enriched, high-grade, medium-grade, and low-grade with barren host-rock zones. The enriched and high-grade zones were located in the northeastern and western parts of the study area. Using a log-ratio matrix to compare between the mineralized zones and related rock types showed the following results:
The low-grade zone derived via the C–V fractal modeling correlated well with gangue lithologies identified in the geological modeling, such as pyritized dolomites, shales, and tuffs.
The pyrite+dolomite ore type (Pd) from the geological model has best OA when correlated with the enriched, high-grade, and medium-grade zones obtained by C–V fractal modeling.
The massive sulfide ore type (Ms) from the geological model has a good correlation with enriched zone; the OAs between this rock type and the high-grade and medium-grade fractal zones are lower than those seen in the pyrite+dolomite ore type.
Results obtained from this study show that C–V fractal modeling is an effective tool for the delineation and separation of mineralized zones, and can be used to improve geological modeling in different ore-deposit types.
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