## Abstract

In exploration for mineral deposits using stream sediment samples, a phenomenon known as dilution of metal content originating from mineralized sources should be taken into account. Dilution occurs when stream sediments originating from upstream mineralized and non-mineralized areas are mixed during transport and deposition. In the sample catchment basin approach, dilution correction is accomplished by employing Hawkes's equation (1976). Catchment area size is the correction factor used in the Hawkes's equation to correct geochemical residuals for dilution. However, the upstream area of each stream sediment sample is representative of the hydrological response and dilution capability of a drainage basin. In the present research, the Hawkes's equation was modified by incorporating drainage density of catchment basin to correct geochemical residuals for dilution. The existing and new equations were applied to stream sediment data from Iran. The results were compared using known occurrences of Au mineralization as validation points. This showed the superiority of the new technique using drainage density as a factor for correcting geochemical residuals against dilution.

Geochemical exploration surveys based on stream sediments are an established strategy to identify probable sources of anomalies. Stream sediments are composite materials originating from weathering and erosion of upstream rocks, sediments, and soils. Anomalously high concentrations of metals in stream sediments might be related to mineral deposits upstream of where such sediments were collected. However, element abundances in stream sediments are mainly due to geochemical background variations derived from non-mineralized units that can mask signatures derived from mineral deposits (Rose *et al.* 1970; Hawkes 1976; Bonham-Carter & Goodfellow 1984; Plant & Hale 1994; Cohen *et al.* 1999; Moon 1999). To overcome this problem, Bonham-Carter & Goodfellow (1984, 1986) and Bonham-Carter *et al.* (1987) proposed the sample catchment basin (SCB) analysis in order to estimate the background value contributed by every lithology unit. Geochemical anomalies derived by SCB analysis of stream sediment geochemical have been used as spatial evidence of mineral prospectivity (e.g. Carranza 2015; Asadi *et al.* 2016; Carranza & Laborte 2016). The SCB analysis considers an upstream contributing area that can influence the chemical composition of every stream sediment sample. Every SCB can contain *j* number of lithological units . If denotes the measured metal concentration of sample at every catchment outlet *i* in a study area , it is possible to estimate the background concentration of every element in each lithological unit as well as the background element concentration at sampling point *i* by using two numerical techniques, namely multiple regression analysis (Bonham-Carter & Goodfellow 1984, 1986; Bonham-Carter *et al.* 1987; Carranza & Hale 1997) and weighted mean method (Bonham-Carter *et al.* 1987) proposed. Bonham-Carter *et al.* (1987) and Carranza (2008) have demonstrated that employing both techniques can yield similar estimated background values however the multiple regression method is sensitive to area size of lithological units. This becomes more problematic for units with small area sizes resulting in non-robust results (Bonham-Carter *et al.* 1987; Carranza 2010). Therefore, in the present research the weighted mean technique has been used for background estimation and the related formula are presented below.

Local background content related to lithology in each SCB can be estimated by first calculating the weighted mean element concentration for the lithological unit as:
(1)where represents the area of the rock unit in SCB . The local background concentration of element related to lithology can then be assessed as:
(2)The technique is widely used by researchers to remove estimated background effect from analyzed concentration by calculating (*Y _{i}*−

*Y*) known as the residual value, which is the difference between the measured and estimated values (Bonham-Carter & Goodfellow 1984, 1986; Bonham-Carter 1994; Carranza & Hale 1997; Moon 1999; Carranza 2004, 2010; Spadoni

_{i}′*et al.*2004; Abdolmaleki

*et al.*2014; Asadi

*et al.*2015).

A crucial part of data processing in SCB analysis is the correction of residual values for dilution effect caused by sediment transport and deposition. Downstream dilution of metal concentration originating from mineralized zones by sediment sourced from non-mineralized areas could result in masking geochemical anomalies. Rose *et al.* (1970) showed that chemical contents of stream sediments exhibited a positive correlation with area of the rock units in a catchment basin and also a negative correlation with the whole area of a catchment basin (*A _{i}*). Hawkes (1976) used such relationships for modeling the downstream dilution of chemical contents of stream sediments and proposed an idealized equation that relates element concentrations (

*Y*) in stream sediment sample

_{i}*i*and the area of the corresponding SCB (

*A*) to element concentrations in source material occupying a certain area in the SCB: (3)Equation (3) can be reorganized as: (4)Where

_{i}*Y*denotes element concentration in mineralized source material occupying an area

_{a}*A*.

_{a}In order to correct residual values for downstream dilution and enhance geochemical anomalies, Bonham-Carter & Goodfellow (1984, 1986) used Hawkes (1976) formula and assumed a unit area of 1 km^{2} (i.e. *A _{a} *= 1 km

^{2}) for exposed mineral deposits that contribute to stream sediments. Accordingly, they defined a dilution-corrected ‘mineralization rating’ variable, MR

*as: (5)The term*

_{i,}*A*in equation (4) can be ignored if

_{a}Y_{i}′*A*is much greater than

_{i}*A*(Rose

_{a}*et al.*(1979)). Carranza & Hale (1997) considered a small unit area of 1 ha (i.e.

*A*= 0.01 km

_{a}^{2}) of exposed anomalous sources, thus: (6)However, using incremental catchment area between a sample site and an adjacent upstream sample (

*A*) in the correction for downstream dilution can create problems in the interpretation of residuals. As the sizes of SCBs depend on sampling density (Spadoni 2006; Yousefi

_{i}*et al.*2013), the recognition of diluted sources could be an issue where SCBs of varying sizes have been sampled and sample density is low (Moon 1999). Using area alone as a factor for dilution correction can result in the generation of false positive or false negative anomalies. Multiplying a low residual value at the outlet of a large SCB having no mineralization may result in a false positive anomaly. Conversely, a high residual value for a SCB containing mineralization can be downgraded if multiplied by the small area of its SCB. This problem was addressed and scrutinized by Mokhtari & Garousi Nezhad (2015), who further evaluated the formulation proposed by Hawkes (1976) by considering a sedimentological parameter known as sediment delivery ratio (SDR) in their analysis of stream sediment dataset western Iran. Stream courses are hydrological pathways for sediments detached from a whole catchment, by which eroded material is transported to the basin outlet. However, not all material removed from a catchment basin surface is carried to the outlet, so the concept of sediment delivery ratio (SDR) (Wischmeier & Smith 1978; Ferro & Minacapilli 1995; Zhou & Wu 2008; Dong

*et al.*2013) is taken to be the amount of material delivered to the outlet (sediment yield) ratioed to the total amount of eroded material upstream. In this regard, SDR can be representative of the magnitude of dilution phenomenon in a SCB and therefore, it can be used to compare SCBs in regard to dilution of metal concentrations originating from a mineralized source.

Mokhtari & Garousi Nezhad (2015) incorporated SDR into Hawkes's formulation and derived a new equation depicting a nonlinear relationship between catchment area (*A _{i}*) and dilution effect (equation 7). Their equation dampened the enhancement of residual values by area as the latter is raised to a power less than 1.
(7)Although the modification of Hawkes's equation by Mokhtari & Garousi Nezhad (2015) was a novel way to correct residual values for downstream dilution and considered the sedimentological/geomorphological factors present in processing and interpreting residual values, their formula posed deficiencies and difficulties in practice. First, it contains a coefficient (

*s*, an empirical parameter obtained from physical information about sedimentation and rainfall-runoff processes within catchment basin) that should be specified empirically through field measurements that are not routine in geochemical surveys and it is almost impractical at regional geochemical surveys to measure SDR for numerous SCBs. Secondly, the calculated SDR value through field experiment only explains the sedimentation process at measuring time; however, it has been proven that SDR varies over time (Walling 1983; Duijsings 1986; Ferro & Minacapilli 1995; De Vente

*et al.*2007), which complicates interpretation of sedimentation data over the long-term. So, employing a unique value for

*s*may not give acceptable results for a study area. Therefore, to help in the precise correction of dilution of geochemical compositions of stream sediments, it is required to find an alternative parameter for SDR that accounts for the area of SCB used in Hawkes's equation (1976) without the need for field measurements.

In this research, total stream length in every SCB was evaluated for correcting downstream dilution of geochemical anomalies as an alternative to its area. Total stream length is a geomorphological factor that defines drainage density, as the latter is the ratio of the former to the area of a drainage basin. The results of applying both area and stream length of SCBs to correct for dilution effects were compared and contrasted using a dataset from the west part of Iran, with known gold mineralization.

## Drainage density

Drainage density (DD* _{i}*) is one of the most important and repeatedly implemented geomorphological parameters of a catchment basin and was first introduced by Horton (1933, 1945). Horton (1933) described drainage density as the ratio of cumulative length of all stream channels (

*L*) in a catchment basin to its area (

_{i}*A*): (8)The evolution of drainage density (DD

_{i}*) of a catchment basin is related to several environmental features including climate, past climate conditions, parent material and bed rock, topographic relief, catchment basin shape and slope, time and land use (Horton 1945; Hadley & Schumm 1961; Carlston 1963; Gregory & Walling 1968; Wilson 1971; Tandon 1974; Gregory & Gardiner 1975; Abrahams 1984; Kelson & Wells 1989; Di Lazzaro*

_{i}*et al.*2015). Two catchment basins with the same area but varying lithology may have unequal total stream courses (

*L*) and hence, different drainage densities (Briggs & Smithson 1986; Kelson & Wells 1989; Bloomfield

_{i}*et al.*2011).

As an important geometric parameter of catchment basins, drainage density plays a substantial role in the hydrological response of drainage system and the tendency of streams to erode landscapes (Gardiner & Gregory 1982; Bloomfield *et al.* 2011; Di Lazzaro *et al.* 2015), thereby influencing the transportation of eroded material. It has been shown that as the total lengths of stream increase the runoff volumes and peak discharges also increase (Di Lazzaro *et al.* 2015). Figure 1 displays two catchment basins with the same area, different stream length and thus different drainage densities, and having dissimilar peak discharges. A catchment basin with high drainage density has a large amount of the precipitation runoff. In contrast, a low drainage density could mean that most rainfall infiltrates the ground and thus limited channels are required to carry the runoff (Ritter *et al*. 2011).

From a geochemical point of view, dilution of stream sediment element contents can be related to the volume of runoff in a drainage system and therefore to total amount of upstream material delivered to the basin outlet (Hawkes 1976). According to Hawkes (1976), the total mass of sediment passing any catchment basin outlet is linearly related to the catchment area. In general, a positive relationship exists between drainage density and sediment yield (or SDR), channel slope, and topographic relief (Hadley & Schumm 1961; Gregory & Walling 1968; Mou & Meng 1981). The magnitude of sedimentation in a basin outlet (the concept of sediment yield) and resultant intensity of geochemical dilution can be related to some factors including drainage density and total stream length of a catchment basin (Hadley & Schumm 1961; Gregory & Walling 1968; Grauso *et al.* 2008; Di Lazzaro *et al.* 2015). This is well documented such that well drained catchment basins are considered to generate heavy storm runoff and more amount of sediments (Gregory & Walling 1968; Gardiner & Gregory 1982). Ferro (1997) considered the rule of total length of streams or the number of stream sources in sediment transport efficiency in a river network. According to the definition of geochemical dilution, when the amount of sediment delivered at the basin outlet increases, dilution of metal (originating from anomalous sources) at the basin outlet increases. The ability of well-drained catchment basins to mask or weaken the geochemical signals of anomalous (e.g. mineralized) sources in a drainage system is taken into account in this paper through the concept of drainage density. Therefore, drainage density was incorporated in correcting residual values for downstream dilution.

## Material and method

### Study area and geological settings

The Sanandaj–Sirjan Zone (SSZ) is considered an active structural region between the Zagros thrust in the SW and the Urumieh-Dokhtar magmatic arc in the NE, spreading from the SE to the NW of Iran (Aliyari *et al.* 2012). The SSZ hosts several major orogenic gold deposits such as Kharapeh, Alut, Qarehchar, Qabaqlujeh, Kervian, Hamzehqarenein and Qolqolah.

The study area was mapped as part of the 1:50 000 Mirdeh geological map (Fig. 2) (Geological survey of Iran 2002). The study area coordinates are 46°–46°15′ E longitude and 36°–36°15′ N latitude, covering Qolqoleh, Qarehchar, Kervian, Qabaqloujeh and Hamzeh-Gharanein gold deposits (Aliyari *et al.* 2009, 2012). This area was selected for the present research to test the applicability and effectiveness of using drainage density in correcting residual values for downstream dilution. This area was selected because of known gold occurrences and availability of high quality stream sediment geochemical data.

The dominant and oldest lithology in the region is Precambrian metamorphic rocks in the centre, west and NW of the area. The region is underlain by Permian red sandstone and thick grey limestone layers. Jurassic lithologies are composed of shale and thin layered grey-green sandstone. Further geological description of the study area can be found in Mokhtari & Garousi Nezhad (2015).

In the Qolqoleh, Qarehchar, Kervian, Qabaqloujeh and Hamzeh-Gharanein gold deposits, quartz-sulphide veins and veinlets chiefly occur along shear zones in extremely altered and deformed Upper Cretaceous, mafic to intermediate meta-volcanic and meta-sedimentary rocks. Host rocks of nearly all the gold-bearing occurrences in the Piranshahr–Sardasht–Saqqez zone are the greenschist-facies metamorphic rocks. Mineral deposits mostly consist of irregular to lenticular veins in altered rocks (Heidari *et al.* 2006; Aliyari *et al.* 2009, 2012).

### Geochemical dataset

In the study area, 299 stream sediment samples with size fraction of less than 40 mesh (0.420 mm) were collected covering a total catchment area of 617 km^{2} (Fig. 3). Gold data were obtained by fire assay (Alizadeh-Dinabad *et al.* 2013). Duplicate analyses (30 pairs) were made to control the quality of the laboratory analysis using the procedure of Thompson & Howarth (1976). The results revealed that the precision of the analysis was better than ±10%. Summary statistics of raw gold values is presented in Table 1 and a map representing spatial distribution of raw gold data amongst SCBs is presented in Figure 4.

### Dilution correction of residuals by incorporating drainage density

Subtraction of estimated local background element concentrations from the corresponding measured element contents of stream sediment samples result in geochemical residuals (*R _{i}*), which were either positive or negative. A positive residual could be taken as enrichment of element concentrations in stream sediments due to anomalous sources (e.g. mineralization) (Carranza 2008). The value of element residuals (

*R*) could be affected by downstream dilution because of mixing stream sediments from different and typically non-mineralized sources in a sample catchment basin. Equation (6) is widely used for downstream dilution correction of element residuals. Here, we have employed drainage density as a geomorphological factor and incorporated this parameter in the existing formula to obtain a new equation. The principle behind using this factor is that the residual value of a catchment basin with higher drainage density is prone to more dilution compared to a catchment basin with lower drainage density.

_{i}To incorporate drainage density in correcting for downstream dilution, equation (6) was modified by multiplying the area (*A _{i}*) by the drainage density (DD

*) of a SCB to obtain modified corrected residual values (MCR). (9)Using equations (8) in (9) results in: (10)Incorporating drainage density to correct for downstream dilution has led to the term of SLCR which stands for Stream Length Corrected Residuals. In other words, area in equation (6) was replaced by total stream length of a SCB after considering drainage density. In essence, total stream length and catchment area are correlated with each other (Horton 1932, 1945; La Barbera 1991; Talukdar 2012). However, there are exceptions that could be important if comparison is to be made among SCBs.*

_{i}Manual delineation of drainage networks (Jarvis 1977; Marcus & Fonstad 2008; Smith & Pain 2009) (from conventional topographic maps and imagery) is extremely dependent on map reading, interpolation and measurement methods. In this regard, the procedure is subjected to many errors due to scanning, digitizing, scale, and the quality of data acquisition procedures (Zhou *et al.* 2008). Traditional techniques for calculation of drainage basin characteristics (area size, stream length, slope, stream order and so on) are field-inspection method (Zavoianu 1984), the blue-line method (Horton 1932, 1945), the contour crenulation method (Strahler 1953), Horton-Strahler ordering method (Miller 1953), slope-criterion method (Smart 1978), calculation of distances along paths extracted from topographic maps (Mueller 1979). However, the advantageous of digital terrain modelling (DTM) (Miller & Laflamme 1958; Quinn *et al.* 1991; Tucker *et al.* 2001) in depicting relief properties of any area under investigation compared to topographic maps including multi-scale characteristic, no quality loss over time and capability of automation have been oriented the drainage network delineation procedures to use digital elevation models as a basis to derive geomorphological features (O'Callaghan & Mark 1984; Moore *et al.* 1991; Evans *et al.* 2003; Li *et al.* 2005; Passalacqua *et al.* 2010; Pirotti & Tarolli 2010; Sofia *et al.* 2013; Persendt & Gomez 2016).

In order to extract drainage patterns from digital elevation models, a number of flow routing algorithms which determine the pathways of water, sediments from a cell to adjacent cells have been proposed by various researches. A number of such algorithms including D8 (deterministic eight-node) (O'Callaghan & Mark 1984), Rho8 (random eight-node) (Fairfield & Leymarie 1991), The FD8 multiple flow direction (MFD) (Quinn *et al.* 1991), Lea (1992), DEMON (Digital Elevation Model Network) (Costa-Cabral & Burges 1994), ANSWERS (Areal Nonpoint Source Watershed Environment Response Simulation (Beasley & Huggins 1978), flux decomposition (Desmet & Govers 1996), D (Tarboton 1997), MFD-md (Qin *et al.* 2007). In the present paper, the D8 (deterministic eight-node) single-flow-direction (SFD) algorithm which supports by geographic information system software packages was used to delineate drainage systems. In this method, the flow from each cell to eight nearest neighbors is identified through a slope gradient (O'Callaghan & Mark 1984). The slope gradient is the measure for estimating the steepest fall for each cell in a catchment basin (Wilson & Gallant 2000; Zhou *et al.* 2008).

Practical procedure of automated delineating the drainage networks of a catchment basin involves identifying sinks, extracting the flow direction and flow accumulation and, finally, delineation of catchment basins and drainage networks. The procedure starts with fill rule, which identifies the cells with undefined directions and then replaces their values with compatibles values. Then the flow direction (the output direction of water from each cell within a SCB) is determined. The flow direction raster map is the basis for flow accumulation, which is a raster map containing accumulated flow into each cell in a SCB. To distinguish between the cells labeled and those unlabeled as drainage pathways, a threshold values is used. To calculate the total stream length of each SCB, such raster map is conditioned using the threshold value and then is converted to a vector map of drainage networks. Ultimately, the total length of each drainage segment inside each SCB is the measure for total stream length of a SCB. It is important to emphasize that estimates of stream length depend on the spatial resolution of DEM (in this study, 10 m) and on threshold value selected for delineation of stream channels. However, if stream length of different SCBs (resulting from changes in the threshold value) vary linearly with each other, any value within this range can be selected as a threshold value, as long it is constant for all basins. Table 2 comprises summary statistics of drainage density and incremental area upstream of each stream sediment sample. Figure 5 shows the distribution of drainage density of each SCBs Figure 5. The relationship between drainage density and basin area has been demonstrated by Gregory & Walling (1968). Their work has shown that drainage density is independent of basin area. This finding is consistent with this study as it was found that there was no significant statistical correlation between drainage density and the corresponding SCB area.

### Anomaly separation

In order to delineate anomalous SCBs, dilution corrected residual values of gold obtained by equation (6) and the new equation (equation 10) were analyzed by exploratory data analysis. A common non-parametric statistics called median absolute deviation (MAD) which is robust to the outliers in the dataset were calculated (equation 11) and the values corresponding to median + 2MAD (Tukey 1977) were threshold values to define anomalies (Ali *et al.* 2007; Carranza 2008, 2010; Nazarpour *et al.* 2014; Darwish 2016; Reimann & de Caritat 2017).
(11)where denotes dilution correction factor (*100A _{i}* or

*100L*) and is geochemical residual value of each SCB. It should be mentioned that only samples with positive dilution corrected residual values were taken into account. The threshold values, according to this method, were 539.6 and 907.3 for gold area corrected residuals and SLCR, respectively.

_{i}## Discussion and conclusion

Figure 6 portrays anomalous basins resulting from the above procedure after applying equations (6) and (10) on the residual values. There was a general consistency between the two maps; however, there were also some discrepancies. Some SCB IDs were shown on Figure 6 for reference to the discussion of differences between the two methods of analysis. The values related to these SCBs listed in Table 3, which were the ones considered anomalous when stream length was used to correct residual values for downstream dilution, aside from using area. In order to see the effect of stream length on dilution correction, the corresponding values of and , (Fig. 7) and the cutoff values corresponding to each method were displayed as straight line perpendicular to corresponding axes. The large residuals values for gold is due to the multiplication of residuals (, ppb) by a constant 100 and area size of each SCB (equations 6 and 10).

The SCBs in Table 3 are marked by red symbols in Figure 7 (please refer to the online version for colour references). It is evident that these basins are anomalous (above the green line) based on dilution corrections using stream length but not using area. The Ksl unit (altered of grey shale, shaly limestone, limestone and metamorphosed) was found to be a promising lithological unit in the study area after calculation of weighted mean concentrations which has a relatively high background value . SCB number 122 has a significantly high residual value and Qabaqloujeh mineralization is present in this SCB. This SCB was not classified as anomalous when applying the original Hawkes's equation to correct residuals for downstream dilution, however, the new formula using stream length resulted in its successfully classification as anomalous. Thus, part of downstream dilution is accounted by stream length, which was not considered in Hawkes's formula. Ignoring this factor could lead to false negative anomalies. Although it could not be confirmed that all newly recognized anomalous SCBs contain mineralization, the new proposed formula produced more realistic results, thereby preventing the elimination of some potentially favourable SCBs from further detailed exploration.

It can be concluded that, drainage density or stream length play a more significant role in downstream dilution of sediments originating from mineralized areas than catchment area does. The area upstream of each stream sediment sample is not representative of the hydrological response of a channel network and the diluting capability of a catchment basin. Using catchment area to correct geochemical residuals for downstream dilution could lead to discarding for further exploration small catchment basins with mineralization, and with high dilution capacity due to high drainage density. So, drainage density or stream length of sample catchment basins should be taken into account for more robust dilution corrected residuals.

Many other factors such as runoff intensity, erodibility, slope gradient, relief, kinematic viscosity of runoff and acceleration of gravity control sediment transportation in a basin. These are important parameters that can be used to modify Hawkes' calculation in consideration of the sediment transportation process in a catchment basin; however, it is not always possible to measure them during stream sediment geochemical exploration surveys, considering the geological timeframe and the cost of such field measurements. Stream length can be used as a proxy at least for some of these factors to improve the correction for downstream dilution compared to using catchment area. This study has been confirmed that stream length corrected residuals are capable of showing all main Au-bearing occurrences in the study area.

## Acknowledgement

Special thanks are extended to Dr. R. Bagherpour and Eng. P. Roshani from the Isfahan University of Technology (Iran) and Geological Survey of Iran. Also, we are greatly thankful to all reviewers who reviewed the earlier and final versions of the manuscripts and appreciate their valuable comments resulting in significant improvements of the paper.

- © 2017 The Author(s)