Erosion rate study at the Allchar deposit (Macedonia) based on radioactive and stable cosmogenic nuclides (26 Al, 36 Cl, 3 He, and 21 Ne)

Abstract This paper focuses on constraining the erosion rate in the area of the Allchar Sb‐As‐Tl‐Au deposit (Macedonia). It contains the largest known reserves of lorandite (TlAsS2), which is essential for the LORanditeEXperiment (LOREX), aimed at determining the long‐term solar neutrino flux. Because the erosion history of the Allchar area is crucial for the success of LOREX, we applied terrestrial in situ cosmogenic nuclides including both radioactive (26Al and 36Cl) and stable (3He and 21Ne) nuclides in quartz, dolomite/calcite, sanidine, and diopside. The obtained results suggest that there is accordance in the values obtained by applying 26Al, 36Cl, and 21Ne for around 85% of the entire sample collection, with resulting erosion rates varying from several tens of m/Ma to ∼165 m/Ma. The samples from four locations (L‐8 CD, L1b/R, L1c/R, and L‐4/ADR) give erosion rates between 300 and 400 m/Ma. Although these localities reveal remarkably higher values, which may be explained by burial events that occurred in part of Allchar, the erosion rate estimates mostly in the range between 50 and 100 m/Ma. This range further enables us to estimate the vertical erosion rate values for the two main ore bodies Crven Dol and Centralni Deo. We also estimate that the lower and upper limits of average paleo‐depths for the ore body Centralni Deo from 4.3 Ma to the present are 250–290 and 750–790 m, respectively, whereas the upper limit of paleo‐depth for the ore body Crven Dol over the same geological age is 860 m. The estimated paleo‐depth values allow estimating the relative contributions of 205Pb derived from pp‐neutrino and fast cosmic‐ray muons, respectively, which is an important prerequisite for the LOREX experiment.


The LOREX Project
The Allchar Sb-As-Tl-Au hydrothermal deposit is related to a Pliocene volcano-intrusive complex located at the north-western margins of the Ko zuf Mountains and close to the border between the Former Yugoslav Republic of Macedonia and Greece [Frantz et al., 1994;Janković and Jelenković, 1994]. Allchar is a world-class thallium deposit unique by its quantity of thallium reserves and by the number of thallium minerals discovered. It contains sufficient quantities of lorandite (TlAsS 2 ), and because this mineral can be used as a geochemical detector of proton-proton (pp) solar neutrinos [Freedman et al., 1976], the deposit has gained the interest of a wider community of astrophysicists, nuclear physicists, and geochemists [e.g., Frantz et al., 1994].
The main goal of the LOREX (LORanditeEXperiment) Project is to determine the average fluence of solar ppneutrinos U m for the age period of the lorandite in the Allchar deposit [Pavićević, 1994], according to the following equation:  (N 205 Pb) B is the number of 205 Pb atoms in lorandite resulting from background reactions, k is the decay constant of 205 Pb (k 5 4.68 3 10 28 a 21 ), and T 5 4.3 Ma is the age of the thallium mineralization in Allchar [Neubauer et al., 2009].
The number of 205 Pb atoms (N 205 Pb) B (see equation (1)) produced by cosmic radiation, mostly by (l,pn)reactions, and by natural nuclear reactions connected to U and Th decay, must be determined quantitatively. In this context, the knowledge of the erosion rate of the overburden rocks since the formation of lorandite, i.e., the paleo-depth as a function of time, is of utmost importance [Pavićević, 1994]. This is why at the beginning of LOREX, by the end of the eighties and the beginning of the nineties, we started with detailed studies of the erosion rate in Allchar. These studies were twofold, focusing on geomorphological analysis and on applying terrestrial in situ cosmogenic nuclides (hereafter TCN). The first TCN studies based on 36 Cl [Dockhorn et al., 1991] suggested a small erosion rate in this area, and therefore a high contribution of cosmic-ray-produced 205 Pb, which would make further investigations on the LOREX project pointless. However, the subsequent measurements of 26 Al concentrations suggested higher erosion rates [Pavićević et al., 2004], what encouraged further research.
The aim of this paper is to provide an estimate of the erosion rate in the area of the Allchar deposit by applying both radioactive ( 26 Al and 36 Cl) and stable ( 3 He and 21 Ne) cosmogenic nuclides in various minerals (quartz, dolomite/calcite, sanidine, and diopside). Although the obtained values may not reflect precise erosion rates in the studied region, they should provide a best approximation, i.e., an order of magnitude estimate of the prevailing erosion rate. Such estimates are sufficient for assessing the order of magnitude of the contribution of cosmic radiation in the 205 Pb production during the last 4.3 Ma and thereby represent an important step forward in demonstrating the feasibility of the LOREX Project. This is because, before continuing with time-consuming and expensive analytical procedures, we need to know the order of magnitude of the denudation rate.

Geological Outline of the Allchar Area
The Allchar deposit is spatially and petrogenetically related to a Pliocene volcano-intrusive complex, which is situated between the Pelagonian tectonic unit and the Vardar zone suture in the east and west, respectively [e.g., Karamata, 2006;Schmid et al., 2008]. The immediate volcanic basement consists of Triassic-Jurassic rock series, predominantly dolomite and dolomitic marble, limestone, sandstone, clayey schist, quartzite, and chert. Detailed information about the geology of Allchar can be found in Boev [1988], Frantz et al. [1994], Janković and Jelenković [1994], Karamata et al. [1994], and Amthauer et al. [2012], among others.
Three phases of magmatic activity are distinguished in the Allchar area. The first one took place in the Miocene (14.3-8.2 Ma), when numerous calc-alkaline dykes were emplaced. The second phase occurred in the Pliocene, producing latite, quartzlatite, and trachyte to subordinate andesite/dacite subvolcanic intrusions. The third phase occurred between 6.5 and 1.7 Ma [Boev, 1988], and during this event the thallium mineralization also formed. The andesite lavas and tuffs of the area Crven Dol formed 6.5-3.9 Ma, the tuffs from the localities Vitačevo and Rudina formed from 5.1 6 0.1 to 4.31 6 0.02 Ma, whereas the Kojčov Rid latites originated between 4.8 and 3.3 Ma [Neubauer et al., 2009]. Troesch and Frantz [1992] determined the geological age of a sanidine from adit Nr. 21 (Crven Dol) to be 4.22 6 0.07 Ma, which is in very good agreement with the age of the sanidine from Rudina, i.e., 4.31 6 0.02 Ma [Neubauer et al., 2009]. The Allchar volcanic rocks are overlain by volcano-sedimentary rocks mainly represented by tuffaceous dolomite that was deposited in sublacustrine basins.
The Allchar Sb-As-Tl-Au deposit is a NNW-SSE stretching, 2 km long and 300-500 m wide zone which comprises several ore bodies. The mineralization is mainly localized along unconformities between the basement rocks and the volcanic or volcaniclastic cover. The precipitation of the Sb-As-Tl-Au mineralization was dated by the Ar/Ar method at 4.31 6 0.02 Ma [Neubauer et al., 2009]. It was accompanied by intensive hydrothermal alteration predominantly represented by silicification and argilitization. The main thallium ore bodies are Crven Dol and Centralni Deo, and they are situated along the contacts between subvolcanic andesites and their volcaniclastic counterparts and hydrothermally altered dolomites .
There are no accurate data about active uplift in this part of the Balkan Peninsula. However, it is documented that from the late Miocene onward, this area underwent mainly strike-slip tectonics [Dumurdzanov et al., 2005;Hoffmann et al., 2010].
Paleoclimatic reconstructions and the timing of glacial retreat in the Allchar area are poorly constrained. Namely, the data about these events are either very limited and lack quantitative measurements [Cvijić, 1903[Cvijić, , 1913, or they mostly refer to broad regional scales, sometimes encompassing almost the entire Balkan Peninsula [Menković et al., 2004]. Nevertheless, the existing studies suggest that although a significant part of the Balkan area was covered by ice during the Quaternary, it is very likely that the Last Glacial Maximum affected only the highest altitudes.

Locations of Samples
The Allchar area is mostly covered by vegetation, therefore only a few locations were suitable for sampling. All samples were ranging in weight from 2 to 5 kg and were taken from the surface to a depth of 10 cm, except for three calcite/dolomite samples from depths of 1.3 m (Do 50L/13), 2.5 m (Do 1/13), and 5 m (Do 8/13).Over more than 10 years, we have been collecting samples that would primarily contain quartz that is commonly used for studies of the cosmogenic radionuclides 10 Be and 26 Al. Figure 1 shows a map of 11 sampling locations, which are either near or above the lorandite ore bodies of Crven Dol and Centralni Deo. This ensures that the erosion rate estimates are significant for the determination of the paleo-depth of the thallium mineralization.
All the samples were studied petrologically and mineralogically, by applying optical microscopy, X-ray diffraction, and, in some cases, Scanning Electron Microscopy and Energy Dispersive X-ray Spectroscopy (SEM-EDX). Information about the sampling locations and the petrography of samples is summarized in Table 1.

Mineral Separation Procedures 2.2.1. Preparation of Quartz Concentrates
Total quartz concentrates (60-70% pure silica) were produced from pristine rock samples (about 3-5 kg each), applying standard mineral separation techniques [Pavićević et al., 2006]: (I) crushing and grinding, (II) sieving to selected grain sizes <0.5 mm, and (III) separation of quartz concentrates on the shaking table with water. From the quartz concentrates, two samples of 80-100 g each were taken and were etched following the procedure described in Pavićević et al. [2004]. The etching was performed repeatedly (3-5 times) with 30% H 2 SiF 6 and ''aqua regia'' (HCl:HNO 3 5 3:1) at room temperature over a time period of 3-4 days, under constant shaking. After each step, the sample was washed with bidistilled water and dried at 808C, along with a control of weight loss. The quality of each treatment was checked with X-ray diffraction. At the end of the treatment, we obtained pure stoichiometric quartz with >99% SiO 2 [Pavićević et al., 2006].
The preparation procedure for hydrothermal quartz was similar to the one applied for total stoichiometric quartz. Relatively big ($5-15 mm) crystals of hydrothermal quartz were sampled at three locations (cf. Tables 4 and 5). 2-3 g of crystals of hydrothermal quartz were etched with 30% H 2 SiF 6 and ''aqua regia'' (HCl:HNO 3 5 3:1). The quality of each treatment was checked with X-ray diffraction and SEM-EDX techniques.

Preparation of Calcite/Dolomite Concentrates
Samples of calcite/dolomite were taken at the localities L-1c/R, L-3c/RML, and L-8/CD (sample numbers: Do 50L/13, Do 1/13, and Do 8/13) in quantities from 3 to 4 kg (Table 1). For producing calcite/dolomite concentrates, a standard procedure of mineral separation was carried out. It involved crushing, sieving, and grinding to a fraction of <0.5 mm, then, separation on a shaking table and magnetic separation for reducing quartz concentrations. Because they contain both minerals, we labeled these samples calcite/dolomite concentrates.

Preparation of Sanidine and Diopside
Sanidine (K 0.75 Na 0.25 AlSi 3 O 8 ) was separated from a hydrothermally altered and mineralized volcaniclastic rock (3-4 kg of a sample from the locality L-1a/R; Table 1). The classical procedure comprised grinding, crushing, and sieving (<125 mm to <2 mm), and the obtained fraction 400-630 mm was used for further treatment. Pure sanidine crystals ($500 mg) were separated by hand-picking using a binocular microscope. X-ray diffraction data (performed in duplicate) confirmed a sanidine crystal structure.

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A similar procedure was applied for diopside (MgCaSi 2 O 6 ) separation. One sample of 2 kg from the locality L-7/KR (Table 1) underwent grinding, crushing, and sieving (<125 to <355 mm). The fraction 250-355 mm was further separated using a shaking table. After that, pure diopside crystals ($370 mg) were separated using magnetic separation and hand-picking. X-ray diffraction and SEM-EDX analyses confirmed that the obtained separates consisted of >96% pure diopside. Geochemistry, Geophysics, Geosystems

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suggests that the contribution of 36 Cl from thermal neutron capture of 35 Cl is only about 0.1% of that produced from Ca [Phillips et al., 2001], and can therefore be neglected as well.
The concentrates of calcite/dolomite samples (ca. 150 g each) were sent to the PRIME Lab, where the final sample preparation and the AMS measurements of 36 Cl were carried out. 2.3.3. Determinations of Cosmogenic 3 He and 21 Ne in Diopside, Quartz, and Sanidine Cosmogenic 21 Ne concentrations were determined at GFZ Potsdam in one sanidine and six quartz separates, whereas the cosmogenic 3 He concentration was assessed in one diopside separate. The samples were wrapped in Al foil and loaded in the sample carrousel above the extraction furnace, which was then baked at 1008C for about one week. The noble gases were extracted by stepwise heating (400, 600, 800, and 12008C for quartz; 600, 800, and 17508C for sanidine; 900 and 17508C for diopside) for at least 20 min each. Chemically active gases were removed by two Ti sponge getters and two SAES (ZrAl) getters, and He, Ne, and Ar-Kr-Xe were separated from each other by trapping in a cryogenic adsorber and subsequent sequential release. Noble gas concentrations and isotopic compositions were determined in a VG5400 sector field mass spectrometer. Results were corrected for isobaric interferences, instrumental mass fractionation, and analytical blanks. Further details about the analytical procedures can be found in Niedermann et al. [1997].

Cosmogenic and Stable Nuclides
The results of 26 Al measurements of 15 samples are shown in Table 2, those of 36 Cl measurements are reported in Table 3. Stable Al concentrations in quartz from Allchar are uncommonly high, ranging from 2520 to 3014 mg/g [Pavićević et al., 2006]. This caused a decrease in the precision of 26 Al/ 27 Al measurements, which have a detection limit of $10 215 for a stable Al concentration range of 100-200 mg/g.
The same sample set was analyzed for 10 Be as well. However, compared to both 26 Al and 21 Ne, the 10 Be concentrations were apparently an order of magnitude higher, and consequently the nominal erosion rates calculated on the basis of these 10 Be AMS measurements were considerably smaller than those obtained on the basis of 21 Ne, 26 Al, and 36 Cl concentrations. Because, in particular, a 10 Be/ 21 Ne ratio higher than the production ratio is physically impossible, such discrepancy suggests that our quartz purification procedure did not successfully remove all meteoric 10 Be from the grain surfaces, and therefore the 10 Be results are not reported here.
Results of He and Ne analyses are shown in Tables 4 and 5, respectively. The 21 Ne/ 20 Ne ratios are only slightly above the atmospheric value (0.002959) in most heating steps of all quartz and sanidine samples. When plotted in a three-isotope diagram (Figures 2 and 3), all 400-8008C quartz data overlap with the ''spallation line'' [Niedermann et al., 1993] within error limits, indicating two-component mixing between atmospheric and cosmogenic Ne. Above 8008C, no cosmogenic Ne is released from quartz [Niedermann, 2002]. Therefore, cosmogenic Ne in the quartz samples was calculated from the excesses over atmospheric composition in the 400-8008C heating steps (Table 5); the small excesses observed in the 12008C steps are interpreted to be nucleogenic Ne produced by the reaction 18 O(a,n) 21 Ne, with a particles derived from U or Th decay. In the sanidine sample, the 21 Ne excess is barely significant at the 1r level (not significant at the 2r level), thus the total concentration of cosmogenic 21 Ne based on the 6008C and 8008C steps [Kober et al., 2005] should be considered as an upper limit rather than a robust figure (Table 5). Similarly, cosmogenic 3 He in the diopside sample can only be reported as an upper limit, assuming that all 3 He measured in this sample (87.3 6 3.9 3 10 5 at/g) is cosmogenic. Prior to the stepwise heating extraction, this sample had been crushed in vacuo in order to characterize the composition of trapped noble gases. However, the He released by this method was very small, <1% of that extracted by heating (Table 4), and showed an imprecise 3 He/ 4 He ratio of (0.18 6 0.11) 3 10 26 . This indicates that the major 4 He fraction in this sample is radiogenic and represents a component which resides in the crystal lattice and is thus not released by crushing. This interpretation is further supported by the isotopic composition of Ne (Table 4) and the ratio of excess 21 Ne to 4 He of (4.22 6 0.19) 3 10 28 . The latter value is almost identical to the production ratio of nucleogenic 21 Ne to radiogenic 4 He (4.5 3 10 28 ) [Yatsevich and Honda, 1997]. Since the 3 He/ 4 He ratio of radiogenic He is on the order of 10 28 , while the measured 3 He/ 4 He ratio was about 1.5 3 10 27 , it is reasonable to assume that the major fraction of 3 He is cosmogenic. Nevertheless, we can only report cosmogenic 3 He as an upper limit.

. Maximum Erosion Rates Based on Individual Cosmogenic Nuclides
In a first step, we have calculated maximum erosion rates for the 10 sampling locations in Allchar based on individual cosmogenic nuclides. Table 6 presents the values of oblique and vertical erosion rates (see below) estimated by four individual cosmogenic nuclides in various monitoring minerals (total stoichiometric and hydrothermal quartz, dolomite/calcite, sanidine, and diopside).
Production rates (resulting from spallation, slow muon capture, and fast muon-induced reactions) were calculated on the basis of geographical position of the sample locations (Table 1) using scaling factors according to Dunai [2001] for 26 Al and 36 Cl and Dunai [2000] for 3 He and 21 Ne. We assumed sea level and high latitude (SLHL) production rates for spallation of 29.9 at/g SiO 2 /a for 26 Al [Balco et al., 2008], 48.8 at/g Ca/a for 36 Cl [Stone et al., 1996], 19.86 at/g SiO 2 /a for 21 Ne [Goethals et al., 2009], and 124 at/g diopside/a for 3 He [Goehring et al., 2010] (combined olivine and pyroxene production rate). The 21 Ne production rate in sanidine was assumed to be $1.5 times that in quartz [Kober et al., 2005]. This rough value is accurate enough considering the large uncertainty of the cosmogenic 21 Ne concentration in our sanidine sample Sa/08 (Table 5). The contribution of muon-induced reactions to the total production was assumed to be zero for 3 He and 21 Ne [Schoenbohm et al., 2004].
Two additional corrections have been applied to the acquired data for the calculation of erosion rates on sloped surfaces. First, we considered the dip angles of the sampled surfaces, i.e., we calculated shielding factors for sloped surfaces as given in equations (10) and (11) of Niedermann [2002] to account for the shielded fraction of cosmic rays. We then calculated erosion rates e using the relation  Geochemistry, Geophysics, Geosystems 10.1002/2015GC006054 where K sp 5 160 g/cm 2 , K m 5 1510 g/cm 2 , and K f 5 4320 g/cm 2 are the attenuation lengths for spallation, muon capture, and production induced by fast muons, respectively, q 5 2.71 g/cm 3 is adopted for the density of the studied rocks, P sp , P m , and P f are the (local) production rates on the sloped surface (see above) through spallation, muon capture, and production by fast muons, respectively, C is the cosmogenic nuclide concentration, h is the present depth of the samples, and k is the decay constant of radionuclides (k 5 0 for 3 He and 21 Ne). Second, we applied an additional correction to the erosion rates according to equation (1) of Hermanns et al. [2004], which takes into account the reduced attenuation length beneath sloped surfaces and is based on earlier work of Dunne et al. [1999].
The resulting values determined in this way for 26 Al in quartz agreed very well with those obtained by the CRONUS Earth online calculator (http://hess.ess.washington.edu/) [Xiuzeng et al., 2007;Balco et al., 2008] when the above corrections are included; the latter values are reported in Table 6. Finally, vertical erosion rates, i.e., downwearing rates of the overall horizontal landscape, were estimated by dividing those acting on inclined surfaces by the cosine of the dip angle (Table 6). We did not include any corrections for vegetation or snow cover, because they are difficult to assess over geological timescales, but most probably insignificant. For example, Plug et al.
[2007] estimate a 2.3% effect for temperate (Acadian) forest. Figure 4 shows the ''erosion island plot'' for 21 Ne/ 26 Al versus 26 Al. All data either overlap with the steady state erosion island or lie above it in the complex exposure history field. Therefore, the combined 21 Ne and 26 Al data can be explained by scenarios involving one or more periods of exposure (with or without erosion) Figure 2. Neon three-isotope plot showing the stepwise heating extractions of three stoichiometric quartz samples from Allchar. Colors in symbols indicate heating steps: white-4008C, gray-6008C, red-8008C, and black-12008C. All 400-8008C data are consistent within 2r error limits with the spallation line [Niedermann et al., 1993], i.e., with two-component mixtures of atmospheric and cosmogenic Ne. Contributions of 12008C steps, where no cosmogenic Ne is released any more [Niedermann, 2002], are small as reflected by large error bars. The mass fractionation line (mfl) is shown for reference. Note that unlike the data in Table 4, those plotted here do not include blank corrections, which would only increase the relative deviations from atmospheric composition as well as the uncertainties without changing the general picture.

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and one or more intermittent periods of burial. In case of samples 5/9 and 6/9 from locations L-3b/RML and L-3a/RML, respectively, the data would even allow for a simple exposure history with no erosion and no burial. However, this is not reasonable in the geological context (see the next section). More likely, the positions of the data points indicate a combination of erosion rates in the range from about 100 to 500 m/Ma and burial periods lasting for $0.5-3.5 Ma.

Geological Considerations
Geological data indicate that during and particularly after volcanic activity, the rocks in Allchar underwent erosion and redeposition in adjacent terrain depressions. Because parts of the terrain, which were sampled for this cosmogenic nuclide study, have likely undergone multiphase periods of burial by variably thick volcaniclastic material, their exposure time must have been different as well.
The following geological and geochronological information should be taken into consideration before interpreting the erosion rates in the area of Allchar: 1. The time span of volcanic activity was between 6.5 and 1.7 Ma [Boev, 1988]. 2. Alteration of the wall-rocks in the surroundings of the ore bodies Crven Dol and Centralni Deo, as well as formation of thallium mineralization, commenced at 4.3 Ma. 3. The maximal thickness of volcaniclastic material may have been up to several hundreds of meters. 4. After the termination of volcanic activity, the volcaniclastic material was redeposited and accumulated in the low level surroundings (depressions and river valleys). 5. There is no solid evidence about the existence of glaciers in the area of Allchar. 6. The relevant erosion period lasted from the time of formation of the ore bodies until present day, and was constantly influenced by exogenous processes.

Episodes of Exposure and Burial
Any stable geological surface that is exposed to cosmic rays accumulates cosmogenic nuclides. In principle, two major cases can be elaborated, namely, eroded and noneroded surfaces. In the Allchar case, we consider an eroded surface at various locations that are characterized by variable lithology. We may assume that for a comparably short time s e (up to a few thousand years), the erosion rate e was constant [e.g., Lal, 1991;Niedermann, 2002]. If we calculate apparent exposure ages s e 5 C 21 /P 21 (where C 21 is the 21 Ne concentration and P 21 its production rate) for different Allchar locations on the basis of 21 Ne concentrations, postulating that during the last 100 ka the area of Allchar was neither covered by glaciers nor influenced by any volcanic activity (see section 4.1), then 9 ka s e 93 ka. The high value of 93 ka is an exception; most values being around 20 ka or less. For surfaces undergoing erosion, s e corresponds to the characteristic erosion timescale, i.e., the time it takes to erode the thickness of rock equivalent to one attenuation length. This is the timescale over which our measurements integrate. As noted earlier, the ''individual-nuclide'' erosion rate values given in Table 6 must be regarded as upper limits, because any deviation from the assumed ''simple exposure history'' will cause an overestimate of the mean erosion rate over the relevant time period. However, in exposure scenarios involving burial the true erosion rate during sufficiently short periods when the surface was not covered may nevertheless have been higher than the calculated ''maximum erosion rate'' for the whole period, because burial (or sedimentation) is equivalent to ''negative erosion'' and thus reduces the mean. As it is clearly not possible to apply a linear erosion model (i.e., a steady state irradiation history) for the whole period between the Pliocene (5.33-2.58 Ma) and Holocene (the last 11.5 ka) at Allchar, more complex scenarios of the exposure to cosmic rays must be considered.
Given that volcanic activity in the Allchar region lasted from 6.5 to $1.7 Ma, it can be supposed that it could have caused fast deposition of primary pyroclastic or volcaniclastic (redeposited) material. Such rapid burial of the surface rocks could have stopped the neutron-controlled production of cosmogenic nuclides for as long as 4 Ma. This time period corresponds to almost six half-lives of 26 Al. In other words, during the time of burial, the ratio 21 Ne/ 26 Al would have increased $60 times. However, in the last Pleistocene/Holocene epochs, from 200 to 300 ka to present, new phases of erosion and redeposition into adjacent depressions and river valleys may have occurred. During that time surface rocks would have been again exposed to cosmic radiation and this would have decreased the 21 Ne/ 26 Al ratio again. The erosion island plot for 21 Ne and 26 Al (Figure 4) is in agreement with such a supposed geological history of Allchar. The high 21 Ne/ 26 Al ratios imply a relatively long time of sedimentation (high duration of burial), some 2-3 Ma at the locations L-1b/R Geochemistry, Geophysics, Geosystems 10.1002/2015GC006054 and L-4/ADR and probably several hundreds of ka at L-3a/RML and L-3b/RML. A smaller burial duration at the latter locations is reasonable because they are closer to the mountains and may thus have been uncovered earlier.
In a model scenario involving a single burial episode, the stable cosmogenic nuclides 21 Ne and 3 He from the analyzed samples originate from two periods: a preburial time, which lasted from the quartz crystallization to the moment when accumulation of volcaniclastic material occurred, and a postburial time, which started when the cover was removed and lasted until present time. In contrast to 21 Ne and 3 He, the major fractions of 26 Al and 36 Cl would have been produced during the last period of exposure, because 26 Al and 36 Cl that was present before burial decayed almost completely during the long duration of burial. This is why the ratio 21 Ne/ 26 Al is higher than in case of a ''simple exposure history,'' i.e., when assuming a steady state erosion model. Therefore, 26 Al and 36 Cl may yield reasonable estimates of the erosion rate prevailing in the postburial episode, i.e., over the last few tens of ka. Of course, the data do not allow us to infer an exposure history involving just one burial period. There may have been several successions of exposure and burial, but nevertheless, it is likely that the 26 Al and 36 Cl concentrations are most closely representing the erosion rate during the most recent exposure period.

Vertical Erosion Rates in Allchar Based on TCN
As already mentioned above, the main purpose of this study is to determine vertical erosion rates in a 1.5 km long and 0.3 km wide, north-south elongated area of the Allchar deposit (see Figure 1). Because this area underwent a complex geological history, we applied different nuclides (both radioactive-26 Al and 36 Cl and stable-3 He and 21 Ne) on different monitoring minerals (magmatic and hydrothermal quartz, dolomite/calcite, diopside, and sanidine) in order to acquire relevant information about prevailing erosion rates. The results are summarized in Table 6, where vertical erosion rate estimates are given in m/Ma for all the applied cosmogenic nuclides.
The results show accordance in the values obtained by applying 26 Al, 36 Cl, 3 He, and 21 Ne. Hence, at sample locations L-2/RT, L-3a/RML, L-3b/RML, and L-4/ADR (except for 26 Al) the obtained erosion rate values vary between several tens of m/Ma to hundreds of m/Ma. These values are similar to those from earlier AMS measurements, albeit on a considerably smaller number of samples. The erosion rates determined earlier based on 26 Al at the locations L-3a/RML and L-3b/RML are 49 and 59 m/Ma, respectively, whereas based on Most data lie in the burial field, indicating a combination of cosmic-ray exposure and erosion with intermittent burial periods. See text for discussion. Graph was drawn in CosmoCalc version 1.8 [Vermeesch, 2007].
Geochemistry, Geophysics, Geosystems 10.1002/2015GC006054 53 Mn a rate of !40 m/Ma at the location closest to L-1a/R was estimated [Pavićević et al., 2010]. However, the 26 Al data from the localities L-1b/R, L-1c/R, L-4/ADR, and L-8/CD imply remarkably higher erosion rate values, which may potentially be explained by abrupt exhumations (sudden exposure to cosmic radiation), which must have occurred in the recent geological past in this part of Allchar. In spite of the mentioned differences, it can be postulated that a conservative lower limit to the prevailing erosion rates in the Allchar area is between 50 and 100 m/Ma. This range enables us to estimate vertical erosion rate values for the immediate locations of the ore bodies of Crven Dol and Centralni Deo.

Paleo-Depth Estimates of the Crven Dol and Centralni Deo Ore Bodies
A principle factor for the success of the LOREX Project is relevant information about the erosion rate of the rock in the Allchar area for the last 4.3 Ma, which is the geological age of the Allchar deposit. Namely, in case of very low erosion rates, a small ratio of the experimentally determined total concentration of 205 Pb in lorandite, i.e., (N 205 Pb) exp in equation (1), and the concentration of 205 Pb produced by cosmic irradiation and other background processes, i.e., (N 205 Pb) B in equation (1), could potentially harm the project feasibility [Jelenković and Pavićević, 1990]. The ratio (N 205 Pb) exp /(N 205 Pb) B in lorandite is predominantly depthdependent, which means that it depends on the average depth of the lorandite from the time when the mineralization precipitated to the present day [Pavićević et al., 2010]: where d today is the present-day depth of the lorandite ore and e is the average erosion rate for the time period T 5 4.3 Ma. Although this is a simplified relation, neither taking into account the complex depth dependence of cosmogenic nuclide production by spallation and muon interactions nor the very probable variations of the erosion rate in the past, it is sufficient for a first-order estimate. Pavićević et al. [2012] reported an estimate of the present amount of 205 Pb produced in lorandite due to solar neutrinos and background reactions in the last 4.3 Ma as a function of the paleo-depth of the lorandite [Pavićević et al., 2012, Figure 2]. Furthermore, it is straightforward to estimate the present-day depth of the lorandite, taking into account the available information about mining horizons and geological boreholes in the ore bodies Crven Dol and Centralni Deo. However, assessing the depth of the eroded layer (equation (3)) by applying TCN is a delicate task, especially bearing in mind that the Allchar area underwent a complex geological evolution (see sections 4.1 and 4.2).
As argued above, the erosion rate values that we obtained by applying the radioactive nuclides 26 Al and 36 Cl (Table 6) are valid only for the last geological past-essentially the Holocene. On the other hand, the concentrations of cosmogenic 21 Ne and 3 He (Table 6) reflect a combination of erosion and burial during the total geological history of the Allchar area, from the Lower Pliocene to the present day. Therefore, the estimates of erosion rate obtained from the stable nuclides 21 Ne and 3 He can be considered as closer to ''long-term average values'' than those that are calculated on the basis of the radioactive nuclides 26 Al and 36 Cl. Consequently, the erosion rate estimates based on stable nuclides and those obtained by radioactive nuclides are considered minimal and maximal erosion rates in the Allchar area, respectively.
On the basis of the erosion rate values reported in Table 6, equation (3) and the values of d today (28 m for the ore body Crven Dol 1, 103 m for the shallower part of the ore body Centralni Deo 3, and 140 m for the deeper part of the ore body Centralni Deo 4)   These values should be multiplied by a factor of 2.71 to obtain paleo-depths in units of meter water equivalent (mwe).

10.1002/2015GC006054
At the Crven Dol locality, we did not have samples in which the stable nuclides 3 He or 21 Ne could be measured, and this is the reason why we do not have a lower limit estimate of the paleo-depth there. In spite of this, these data provide a reasonable basis for estimating the pp-neutrino and fast muon contributions to 205 Pb production.

Conclusions
Based on the combined analysis of 26 Al and 21 Ne in a subset of our samples (Figure 4), it can be concluded that the Allchar area underwent a complicated geological history and that cosmic irradiation of the surface rocks reflects erosion rates ranging from $100 to 500 m/Ma and burial ages between $500 ka and 3 Ma.
By estimating the maximum erosion rates at 10 different localities of Allchar (within an area of around 0.3 km 3 1.5 km), applying two radioactive ( 26 Al and 36 Cl) and two stable ( 3 He and 21 Ne) nuclides in quartz, calcite/dolomite, sanidine, and diopside as monitoring minerals, we established that 85% of the values range from several tens of m/Ma to 350 m/Ma, depending on the location.
The obtained range of erosion rates based on stable and radioactive nuclides enables us to estimate reasonable limits for the vertical erosion rate values at the locations of the main lorandite ore bodies Crven Dol and Centralni Deo. On this basis, we estimate that the minimum and maximum paleo-depths of the ore body Centralni Deo (averaged from 4.3 Ma to present) are 250-290 and 750-790 m, respectively. In relation with this, we further estimate a maximum paleo-depth for the ore body Crven Dol (over the same geological age) of around 860 m. The original data used in this study can be made available by the corresponding author, up on request. This study is directly supported by the FWF-Wien grant P 25084 N27. We also appreciate the continuous support of PRIME Lab, Purdue University for their work in the chemical preparation of target samples from quartz, AMS measurements of 26 Al and 36 Cl and for their very helpful information about erosion rate calculations. We are very much indebted to G. Tippelt (University of Salzburg) for the X-ray diffraction measurement of rock samples and quartz separates and to E. Schnabel (GFZ Potsdam) for performing the noble gas analyses. M.K.P. is very thankful to the University of Salzburg for its hospitality and financial support. V.C. thanks the project 176016 of the Serbian Ministry of Education, Science, and Technological Development.