Introduction

Rare earth elements (REEs) include lanthanides from lanthanum (La) to lutetium (Lu) along with yttrium and scandium. These elements play a significant role in energy, technology and defense industries so have been recognized as important materials by several international agencies1. REEs are hardly formed in economic deposits of natural ore and currently they are being mined in only a few commercial deposits in the world2. Coal can be a potential resource of REEs, the average of REEs values in worldwide coal ashes have been estimated to be around 469 ppm3. The recovery processes of REEs from coal can lead to solid residues of CFA (Coal fly ash), wastewater, and secondary wastes4 which cause environmental effects. Two important issues for cost-effective recovery of REEs and environmentally friendly REEs recovery techniques include: selection of coal and coal ash containing high concentration of REEs or REYs5, and paying attention to the mineralogical composition of REEs in coal2,6.

The collected studies show that genetical factors including: source rock, magma or hydrothermal activity, faults, volcanic activity and shallow water play roles in the enrichment of elements in coal seams7. The analysis of geological structures shows that these structures play a major role in the formation of mineral deposits and alteration zones8,9,10,11,12. Investigations carried out in the last few decades show that the formation of mineral deposits and the degree of permeability are related to the processes associated with faulting13,14,15,16.

Many investigations related to the distribution pattern, concentration, origin and geochemistry of REEs in coal have been done by various researchers17,18,19,20,21,22,23,24,25,26,27 but very few of them have discussed the role of tectonics and the importance of fault types in the distribution of REEs in coal mines. Iran’s coke and thermal coal reserves are estimated to be 2 and 3 billion tons, respectively28. The Tabas coalfield is the largest coalfield in Iran, and the North Kochakali coalfield is one of the areas of this field. The coal in North Kochakali area is thermal type, sulfur and ash concentrations in the coal seams of this area are high. The operation of reverse, normal, and strike-slip faults led to severe folding and displacement of target coal seams.

Mathematical modeling is one of the best tools to understand the relationship between structures, among which fractal modeling has been widely used as a mathematical tool9,10,11,29,30. Fractal models are used to reveal association of geochemical and mineralization settings with spatial information (mineral deposit analysis)31. Geological processes such as tectonic, metamorphism, petrogenesis, and mineralization can expand the fractal dimension32. So, due to differences in fractal dimensions gained from analysis of related data different geological mechanism can be explained33. According to the relationship between mineralization and faults34, proposed Concentration-Distance (C-D) fractal model. The purpose of this research is determining the relationship between the concentration of total amount of rare earth elements (ƩREEs) with the fault types in terms of mechanism in the North Kochakali area, three types of faults have been identified in the North Kochakali area, which are: dextral faults with normal component, sinistral faults with reverse component, and thrust faults. For this purpose, Concentration-Distance (C-D) fractal models were used to find out the relationship between the concentration of ƩREEs and faults.

Geological setting

Central Iran block is a region with an area of 2300 square kilometers, which is surrounded by fold thrust fault belts35. This block consists of 3 main areas, which are known as Lut, Yazd and Tabas blocks from west to east, and are separated from each other by a series of dextral faults36. The Tabas Block is a spindle-shaped intracontinental depression, the active Nayband Fault in the east and the Kalmard-Kuhebanan Fault in the west bounded this block37. The 45,000 km2 Tabas coalfield is located 80–200 km south and southwest of Tabas city. The northern sector is divided into three coal-bearing areas, namely: Parvadeh, Nayband, and Mazino. The ten coal areas identified in the Tabas coalfield include Mazino, Kochakali (North and South), Kamar-e Mehdi, Kalshur, Kalmard, Kalshane, Dastgaran, Pirhajat, Jafaran, and Behabad. In terms of the structural divisions of Iran, the Kochakali area is located in the central Iran basin, specifically in the Tabas block and about 75 km southwest of Tabas city. Middle Jurassic coal sediments in the North Kochakali area are located in the Hojedk formation. This Middle Jurassic formation includes sequence of sandstone sediments, green shales, coaly shales and coal seams. Hojedk Formation was deposited in a back-arc basin related to Neotethys subduction38 and the normal faults of the basin floor have led to an increase the subsidence rate. During the Paleogene, due to the operation of the normal faults of the basin floor, intrusive igneous masses are injected into the thinned continental crust of the back-arc basin39. with the closure of the back-arc basin during Neogene and Quaternary due to the closure of the Neotethys ocean and the collision of the Arabian plate with the Central Iran Microcontinent (CIM) the normal fault mechanism is changed to strike-slip and reverse fault due to the change of tensile stress to compressive. This situation has caused the folding, uplift and outcropping of the Hojedk formation (Fig. 1). The faults in the North Kochakali area have acted after the formation of the coal seams because these faults caused a great displacement of the coal seams. For example, two thrust faults with slopes towards each at the location of drilled boreholes in the North Kochakali have led to the creation of a pop-up structure. The axial planes of syncline and anticline structures in the North Kochakali have been severely affected by dextral and sinistral faults and their trend changed. Syncline structures in North Kochakali area are composed of Parvadeh and Baghamshah Formations, which are younger than the Hojedk Formation, which contain coal seams. Thrust faults are the oldest faults in the North Kochakali because they have been displaced by both types of dextral faults with normal component (northeast to southwest trends) and sinistral faults with reverse component (northwest to southeast trends). Sinistral faults with a reverse component are also the youngest faults in the area because all the dextral and thrust faults in the area have been displaced by these faults’ types (Fig. 2).

Fig. 1
figure 1

Location map of Tabas city and North Kochakali coal deposit (done by ArcGIS 10.4, 1995–2016 Esri, http://www.esri.com).

Fig. 2
figure 2

 1:5000 Geological map of North Kochakali coal mine with location of samples, sampling area, faults, and boreholes (done by ArcGIS 10.4,1995–2016 Esri, http://www.esri.com).

Materials and methods

Concentration-distance to fault fractal model

In order to find out the relationship between total amount of rare earth elements (ƩREEs) and faults in the North Kochakali deposit, it is necessary to prepare a geological map along with identifying each fault types (dip- slip, and strike-slip) in the area, and analyzing the ƩREEs from the target seams in the North Kochakali mine. In this research, 28 samples (K1S1، K1S2، K1S3، K1S4، K1S5، K2، K2S1، K2S3، K2S4، K5S1، K5-3S1، K5-3S2، K5-3S3، K5-3S4، K5-3S5، K7S2، K7S3، K7S4، K7S5، K32S2، K32S3، K32S4، K32S5 K33S1، K34S1، K34S2، K34S3, K35S1) were taken to measure the amount of ƩREEs in North Kochakali mine. Currently, there are 4 extraction pits in North Kochakali mine. The samples were taken directly from different extracting seams and coal seams in depth to have the lowest moisture content, and sampling from the oxidized zone and surface coal seams have been avoided. The samples were taken from the coal, and attempts were made to prevent the entry of minerals in roof and floor of coal seam into the sample bag during sampling.

the samples were analyzed by inductively coupled plasma mass spectrometry (ICP-MS) to measure the concentrations of ƩREEs. Then, by using Concentration-Distance fractal model, the relationship between the concentration of ƩREEs and the distance from each type of faults have been investigated. Three Concentration-Distance (C-D) fractal models base on ƩREEs concentrations and the distance from dextral, sinistral and thrust faults were built. These models were named as, ƩREEC –DDF (based on the concentrations of rare earth elements and distance from dextral faults), ƩREEC-DSF (based on the concentrations of rare earth elements and distance from sinistral faults) and ƩREEC – DTF (based on the concentrations of rare earth elements and distance from thrust faults). And finally, based on these fractal models, 3D and 2D modeling of ƩREEs concentrations base on ƩREEC –DDF, ƩREEC-DSF and ƩREEC – DTF fractal models in sampling area were drawn by Rockworks software (Fig. 2). Concentration-Distance fractal model was first proposed by34 and developed by12. The basis of this model is based on the inverse relationship between the occupied space and variables such as the grade or concentration of the elements40,41 this model as follow.

$${\rm DBF} (\ge \uprho ) \infty{\rm F} \uprho - {\rm D}$$
(1)

ρ is the concentration of the elements, DBF represents the cumulative distance from the samples with concentration values equal to or greater than ρ, F is a constant and D represents the fractal dimension. In the fractal logarithmic diagram, the threshold values indicate different geochemical groups or populations which represent different mineralization zones. According to the Concentration-Distance fractal diagrams, each geochemical group or population (the lines drawn between the threshold values) show the concentrations distribution of elements in the distances of each faults types, these geochemical groups are marked with different colors in the tables as well as the Concentration-Distance fractal diagrams.

Results

By using the HREEs and LREEs, the total concentration of rare earth elements (ƩREEs) was obtained, and according to this, the highest concentrations belong to K2 and K5-3S3 samples with 627 and 528 ppm concentrations, respectively. Three fractal diagrams ƩREEC –DDF, ƩREEC-DSF and ƩREEC – DTF were drawn According to distance of each fault types and ƩREEs concentrations. Based on ƩREEs concentration and ƩREEC –DDF, ƩREEC-DSF and ƩREEC – DTF fractal diagrams four different geochemical populations (Low, Moderate, high and very high) were obtained. Different geochemical populations are marked in fractal diagrams with different colors (blue color for low geochemical populations, green color for moderate geochemical populations, yellow color for high geochemical populations, and red color for very high geochemical populations). The breaking points in the Concentration-Distance fractal diagram represent the threshold values ​​that separate different geochemical populations from each other. In ƩREEC –DDF fractal model, the low geochemical population includes concentrations lower than 229 ppm, and the moderate and high geochemical populations include concentrations between 229 and 346 ppm and 346–489 ppm, respectively (Table 1, and Fig. 3a). Concentrations lower 251 ppm represent the low geochemical population in ƩREEC-DSF fractal model, while concentrations between 251 and 398 ppm and 398–489 ppm, respectively belong to the moderate and high geochemical populations (Table 2; Fig. 3b). The low geochemical population in ƩREEC – DTF fractal model includes higher concentrations (263 ppm> ) compared to the other two fractal models (ƩREEC- DDF and ƩREEC-DSF fractal models). In ƩREEC – DTF fractal model, similar to the ƩREEC-DSF fractal model, concentrations between 398 and 489 ppm indicate the high geochemical population (Table 3; Fig. 3c). Threshold values that separate the very high geochemical populations are same in all three diagrams (ƩREEC- DDF, ƩREEC-DSF, and ƩREEC – DTF fractal diagrams) and in all three fractal models concentrations higher than 489 ppm indicate the very high geochemical population (Fig. 3) (Tables 1 and 2, and 3).

Fig. 3
figure 3

ƩREEs concentration-distance (C-D) fractal diagram (a) ƩREEC- DDF (b) ƩREEC-DSF (c) ƩREEC – DTF.

Table 1 Different geochemical populations base on ƩREEC –DDF diagram.
Table 2 Different geochemical populations base on ƩREEC –DSF diagram.
Table 3 Different geochemical populations base on ƩREEC –DTF diagram.

Table 4 shows the ƩREEs concentration related to each sample, and the distance of samples from each fault types in North Kochakali. In this table, different geochemical groups are separated from each other with different color names, for example, red color indicates the very high geochemical populations and blue color indicates the low geochemical populations. ƩREEC –DDF fractal model show that very high ƩREEs population (concentrations higher than 489 ppm) is located at a distance of 36–76 m from dextral faults (K2 and K5-3S3 samples in the very high geochemical population are located at the closest and the farthest distance from these faults, respectively). Base on ƩREEC –DSF fractal model in very high geochemical population K5-3S3 sample is the closest sample and K35S1sample is the farthest sample from sinistral faults which are located at a distance of 2 m and 360 m from these faults, respectively. In ƩREEC –DTF fractal model very high geochemical population is located at a distance of 55–800 m from thrust faults (Table 4).

Table 4 ƩREEC –DDF, ƩREEC-DSF and ƩREEC – DTF fractal models.

2D and 3D models of sampling area were created based on fractal diagrams (ƩREEC –DDF, ƩREEC-DSF and ƩREEC – DTF) and by using RockWorks software. In the 2D models, different geochemical populations which include a specific concentration range, show the distribution pattern of ƩREEs in the sampling area. But in the 3D models, the concentrations of ƩREEs and different geochemical populations are determined based on the elevation levels. In this way, the areas that have higher elevation levels include a higher concentration range. In 3D and 2D model of sampling area base on ƩREEC –DSF fractal model high geochemical population (398–489 ppm ƩREEs concentrations) is located at west part of sampling area and most parts of sampling area are surrounded by the moderate geochemical population, in this model low geochemical population (229 ppm> ) is present in a small part of sampling area, these concentrations are only seen in a small part of the southeast of the sampling area (Fig. 4). In ƩREEC –DDF fractal model high geochemical population (346–489 ppm ƩREEs concentrations) is located at west, center and southeast parts of sampling area (Fig. 5). In 3D and 2D model of sampling area base on ƩREEC –DTF fractal model same as ƩREEC –DSF fractal model most parts of the sampling area are surrounded by the moderate geochemical population. But in this model, in addition to the southeast of the sampling area, the low geochemical population can also be seen in parts of the southwest of the sampled area (Fig. 6).

Fig. 4
figure 4

Modeling sampling area based on ƩREEC –DSF fractal model a-2D model b-3D model.

Fig. 5
figure 5

Modeling sampling area based on ƩREEC –DDF fractal model a-2D model b-3D model.

Fig. 6
figure 6

Modeling sampling area based on ƩREEC –DTF fractal model a-2D model b-3D model.

Discussion

Both North Kochakali and Parvadeh coal mines are located in Central Iran Microcontinent but North Kochakali coal sediments are placed in Hojedk Formation with Middle Jurassic age, while coal sediments of Parvadeh are placed in Nayband Formation with Late Triassic age. The comparison of REEs values in these two coal mine shows that the average value of ƩREEs in the North Kochakali area is 118.8 ppm more than the Parvadeh area. The comparison of ƩREEs values in North Kochakali mine with coal deposits of the Erlian basin in China shows that the average values of ƩREEs (except Yttrium and Ho concentrations) in the North Kochakali mine are very similar to the average values of these elements in the Jurassic coal deposits in the Erlian basin. It is important to note that Scandium is not considered as a REEs in Chinese coal deposits. The average value of ƩREEs in North Kochakali mine is 89.4 ppm higher than the average abundance of these elements in the continental crust, shows that the ƩREEs in North Kochakali coal are higher than the continental crust, but average value of ƩREEs in this mine is about 137.8 ppm lower than the average value of these elements in world coal ash, however, the average values of HREEs (except Ho concentration) are very similar to the average values of these elements in world coal ash. (Table 5). Geological factors and different deposition pathways are the most important factors in the distribution and chemistry of REEs in coal642. proposed, the multi-stage hydrothermal process as the main factor in the enrichment of REEs in Sichuan, China43. considered the enrichment of REEs in coal fly ash as a result of alkaline hydrothermal processes. So, geological processes such as faulting, which control the movement of hydrothermal fluids and igneous masses, play a fundamental role in the enrichment of REEs12,30. The Concentration-Distance fractal model have been used by various researchers to determine the role of geological structures in the enrichment of elements in different deposits12] and [30. used the Concentration-Distance fractal models for determining the relationship between REEs and faults and achieved acceptable results. A series of processes may lead to the enrichment of REEs in coal seams in study area. But in this research considering the role of faults in enrichment of REEs, for the first time, the Concentration-Distance fractal models were applied to determine the relationship between the REEs concentrations and fault types in the coal deposit.

Table 5 Comparison table of the average concentrations of ƩREEs (ppm) in North Kochakali coal mine with Parvadeh coal mine44, China jurassic coal (Erlian Basin)45, continental crust46, and world coal ash47.

Conclusion

The results of the Concentration-Distance (C-D) fractal models show a significant relationship between mineralization and faults. Base on ƩREEC –DDF fractal model, very high ƩREEs concentrations are located at a distance of 36–76 m from dextral faults. Very high ƩREEs concentrations are located at a distance of 2–360 m from sinistral faults. However, the maximum distance of very high ƩREEs concentrations from thrust faults have reached 800 m. These results show a significant relationship between the concentrations of these elements and the distance from dextral faults with normal component. So, this fractal model can be used as a useful tool in exploration. Dextral and sinistral faults have caused displacement of syncline structures. These structures composed of Formations younger than the Hojedk Formation, which contains coal seams in North Kochakali coal deposit. According to the displacement of thrust faults by dextral and sinistral faults, it can be concluded that thrust faults are the oldest faults and sinistral and dextral faults are young faults. However, the displacement of dextral faults by sinistral faults shows that sinistral faults are the youngest faults in the study area. Thrust faults have caused the complete displacement of coal seams. Therefore, faults in North Kochakali worked after the formation of coal seams, and also young dextral faults show a very good relationship with REEs concentration. So, the mineralization of ƩREEs in North Kochakali coal deposit is epigenetic.

Due to the thermal nature of North Kochakali coal and its high ash content, the concentration of HREEs in this mine are comparable to the World coal ash average HREEs concentration, which could be the result of normal and strike slip faulting in this mine. 3D and 2D models of sampling area base on fractal models for ƩREEs are showing northeast-southwest trend so that the concentration of ƩREEs increases towards the southwest. This trend is the same as the trend of dextral faults with normal component in study area. Also, these models show that high concentrations of ƩREEs are located in the place of the dextral faults with normal component.

Identifying the source of enrichment of REEs in coal besides being the key to the exploration of these elements can also help to identify the mineralogical composition of these elements as well as using the appropriate recovery method. In this research, the Concentration-Distance fractal models were used to determine the role of faults in the enrichment of ƩREEs in North Kochakali coal deposit. But there is always a factor or factors such as: misdiagnosis of faults in the study area, incorrect sampling, laboratory and human errors, which cause mistake in the results of the Concentration-Distance fractal model. For example, minerals in floor and roof of coal seam may have different concentration ranges of REEs in study area. Therefore, samples taken from different parts of the coal seam better analyzed separately by Concentration-Distance fractal model.