AG  >> Vol. 7 No. 6 (December 2017)

    宇生核素暴露测年影响因素误差分析
    Error Analysis of Influence Factors of In Situ Cosmogenic Exposure Dating Method

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作者:  

王婉颖:南京师范大学教师教育学院,江苏 南京;
张志刚:南京师范大学地理科学学院,江苏 南京

关键词:
原地生宇生核素暴露测年10Be误差In Situ Cosmogenic Nuclides Exposure Dating Method Beryllium-10 Error

摘要:

原地生宇宙成因核素暴露测年技术是20世纪80年代兴起的新的测年技术手段,目前该方法已广泛应用于地学多领域的暴露年代以及长尺度侵蚀速率的定量测定,定量研究暴露测年计算公式中不同参数误差可能引起的年代结果误差将有助于对该技术进一步的理解和更好的利用。因此,本文基于全球不同区域岩石样品的测年数据,分别对公式中宇生核素的浓度、生成速率、侵蚀速率、宇宙射线的衰减路径长度以及样品的密度等进行误差分析。研究结果表明:(1) 宇生核素生成速率和浓度的误差与所引起的年代结果误差成等比例关系;(2) 样品密度所引起的误差最大可达16%;(3) 宇宙射线衰减路径长度所引起的年代误差最大可达31%;(4) 侵蚀速率所造成的年代结果误差与样品暴露的时间尺度有关,最大可超过100%。该研究可为宇生核素暴露测年技术在地貌学中更好的应用提供参考数据。

In situ cosmogenic exposure dating method was developed in the 1980s. At present, the method has been widely used in many fields of geological hazard research and long-time erosion rate. The quantitative study of the age error made by the error of different parameters in the calculation formula, will contribute to the further understanding and better utilization of the technology. Thus, this article is based on the dating data of rock samples in different regions around the world to analyze error of the concentration, generation rate, erosion rate about in situ terrestrial cosmogenic nuclides, attenuation path length of cosmic ray and the density of the sample in the calculation formula. The results show that: (1) Errors of the concentration and the generation rate about in situ terrestrial cosmogenic nuclides are proportional to the age error. (2) The maximum time error caused by sample density can be up to 16%. (3) The error of absorption mean free path is up to 31%. (4) The result of the erosion rate is related to the exposure time scale of the sample, which can be more than 100 %. This study can be used to provide reference data for the better application of in situ cosmogenic exposure dating method in geomorphology.

2. 数据和研究方法

2.1. 数据来源

本文数据来源于2009~2012年全球不同区域宇生核素10Be暴露测年数据以及课题组实验数据 [5] (表1)。数据主要分布在亚洲 [9] - [16] 、欧洲 [10] [17] [18] [19] [20] 、北美 [21] [22] [23] 、南美 [24] [25] 以及南极洲地区 [26] [27] [28] [29] 。

2.2. 研究方法

2.2.1. 宇生核素暴露测年原理

出露于地表或地表一定深度的岩石会受到宇宙射线的轰击,岩石中的某些元素与宇宙射线粒子以一定的方式发生核反应就会生成新的核素,称为原地生宇生核素(相对大气中生成的宇生核素),主要有3He、10Be、14C、21Ne、26Al和36Cl等。原地生宇生核素浓度是岩石暴露时间与侵蚀速率的函数。因此,在相关假设条件下可以求得地表的最小暴露年代与最大侵蚀速率。其主要计算过程如下 [30] :

N ( x , t ) = N ( x , 0 ) e λ t + p ( 0 ) λ + μ ε e μ x [ 1 e ( λ + μ ε ) t ] (1)

上式在计算过程中通常假设地表岩石初始宇生核素的浓度为0;且宇宙射线通量为常数,地表宇生核素的产生速率为常数,因此,该公式可以简化为:

N = p λ + μ ε [ 1 e ( λ + μ ε ) t ] (2)

Table 1. Sources of cosmogenic nuclide 10Be datum [5]

表 1. 宇生核素10Be数据来源一览表 [5]

根据该公式可以计算出暴露年代:

t = 1 λ + μ ε ln [ 1 N ( λ + μ ε ) P ] (3)

当假设地表没有受到侵蚀,即侵蚀速率为0,此时可以计算出最小暴露年代:

t = 1 λ ln [ 1 N λ P ] (4)

上式中: N ( x , t ) 指经过t时间后在x深度处样品的宇生核素浓度(atom/g); N ( x , 0 ) 为暴露前深度x处样品的残留宇生核素浓度(atom/g); λ 为放射性宇宙核素的衰变系数(1/Ma);t为暴露时间(a); p ( 0 ) 为地表宇宙核素的产生率(atoms/g·a); μ = ρ / Λ 为目标的吸收系数(cm1); ρ 为目标岩石的平均密度( g / cm 3 ), Λ 为目标岩石中原子核相互作用粒子的衰减路径长度(160 g/cm2) [10] ; ε 为侵蚀速率( cm / a )。

由此关系式可得N、P、ε、Λ以及ρ共同影响着年代结果,因此对这些影响因素进行误差分析,有助于进一步了解宇生核素暴露测年原理,从而可以在野外采样和实验过程中注意控制误差,从而提高测年的精度。

2.2.2. 宇生核素浓度和生成速率所造成的年代误差计算方法

根据公式(4)本文研究宇生核素浓度(N)的变化以及宇生核素生成速率(P)的变化对年代结果的影响。具体思路是:不改变N (原始数据),分别取(1 − 50)%P、(1 − 40)%P、(1 − 30)%P、(1 − 20)%P、(1 − 10)%P、(1 + 10)%P、(1 + 20)%P、(1 + 30)%P、(1 + 40)%P、(1 + 50)%P十组实验值并通过公式(4)计算出t实验p的值。将得到的t实验p与t标准p作比较,得出生成速率对宇生核素暴露测年结果的影响率Pi = |((t实验p − t标准p)/t标准p)|*100%。

不改变P (原始数据),分别取(1 − 50)%N、(1 − 40)%N、(1 − 30)%N、(1 − 20)%N、(1 − 10)%N、(1 + 10)%N、(1 + 20)%N、(1 + 30)%N、(1 + 40)%N、(1 + 50)%N十组实验值并通过公式计算出t实验p的值。将得到的t实验N与t标准N作比较,得出浓度对宇生核素暴露测年的影响率Ni (i = 1, 2, ∙∙∙, 10)——Ni (i = 1, 2, ∙∙∙, 10) = |((t实验N − t标准N)/t标准N)|*100%。

2.2.3. 样品密度和宇宙射线衰减路径长度所造成的年代误差计算方法

要想探讨样品密度和衰减路径长度误差所造成的年代结果误差,就需要根据公式(4)进行分析。保持N、P、Λ不变,对ρ进行年代误差分析。尽管在年代测定时选择的是石英颗粒,但是样品采集时这些含有石英的岩石密度会有所差异,多数学者在计算暴露年代时通常将岩石密度估计为2.7g/cm3 [31] [32] ,有的学者采用岩石的密度为2.6 g/cm3 [33] [34] ,2.65 g/cm3 [34] [35] 和2.8 g/cm3 [36] [37] ,也有学者在年代计算时对不同的样品采用的不同的岩石密度进行计算,但其密度范围也在2.6~2.8 g/cm3。因此,为了讨论岩石密度误差对年代结果误差的影响,本文选择2.5和2.8 g/cm3作为岩石的密度阈值,以此探讨其对应的年代结果与通常采用的岩石密度为2.7 g/cm3(标准密度)所对应的年代结果之间的差异。而在探讨密度误差所引起的年代误差时,必须考虑到侵蚀速率的影响,本文岩石表面侵蚀速率(ε)取0.5,1,2 mm/ka三组值。最后,样本密度ρ对宇生核素暴露测年的影响率ρi = |((t实验ρ − t标准ρ)|/t标准ρ) * 100%。

在考虑衰减路径长度误差对年代结果影响时,与考虑岩石密度影响的方法一样,保持N、P、ρ不变,对Λ进行年代误差分析。宇宙射线随着岩石样品深度的增加能量衰减也增加,衰减路径长度通常为121 到>170 g/cm2,对于大多数样品而言,衰减路径长度为150~190 g/cm2,通常情况下采用160 g/cm2 [7] [38] 。因此,本文选择衰减路径长度150和190 g/cm2作为宇宙射线在岩石中的衰减路径范围,以此探讨其对应的年代结果与通常采用的衰减路径长度为160 g/cm2所对应年代结果之间的差异。同样在讨论时考虑侵蚀速率的影响,取岩石表面侵蚀速率(ε)为0.5,1,2 mm/ka三组值。最后,样品衰减路径长度对宇生核素暴露测年的影响率Λi = |(t实验Λ − t标准Λ)|/t标准Λ*100%。

2.2.4. 侵蚀速率所造成的年代误差计算方法

岩石表面的侵蚀速率(尤其是万年尺度及以上时间尺度的侵蚀速率)难以估计,因此,通常情况下假设岩石表面的侵蚀速率为0,来获得最小暴露年代。自然环境下岩石的侵蚀速率不可能为0,相关研究表明,侵蚀速率对暴露测年结果影响比较大,暴露尺度越大影响越严重 [39] 。当侵蚀速率为0时(不考虑侵蚀速率的影响)与侵蚀速率为0.5,1,2 mm/ka时对同一样品暴露年代计算结果,并估算了侵蚀速率为0时对年代结果的低估程度 [5] 。本文基于侵蚀速率的影响分析便直接引用文献 [5] 的研究方法和数据。

3. 结果与讨论

3.1. 宇生核素10Be的生成速率和浓度所造成的年代误差分析

利用原地生宇生核素测定暴露年代时,通常会假设地貌体侵蚀速率为0。研究表明,该假设会低估地貌体的真实暴露年代 [5] 。

经实验,影响率Pi(i = 1, 2, ∙∙∙, 10)与P的实验值基本呈线性关系,(1 + 10)%P、(1 + 20)%P、(1 + 30)%P、(1 + 40)%P、(1 + 50)%P五组实验值的影响率总是不小于(1 − 50)%P、(1 − 40)%P、(1 − 30)%P、(1 − 20)%P、(1 − 10)%P五组实验值的影响率。P的十组实验值对Queen Maud Land (Antarctica)研究点中PK68样本的影响Pi最大,分别为−59%,−49%,−38%,−26%,−14%,15%,33%,52%,75%,102%。10Be的生成速率和10Be的浓度对宇生核素测年技术的影响情况一致。

3.2. 样品密度ρ所造成的年代误差分析

经实验,总体上可见样本密度ρ对宇生核素测年技术的影响较小,在−2%~1%,ρ取2.5 g/cm3时,影响率为负,取2.8 g/cm3时,影响率为正;对样本Na84,Ron-46,KF-0218-2,BC06-103,Da12,MAR-04-MJB的影响率偏大,其中,ρ取2.5 g/cm3、ε取2 mm/ka时,对样本Ron-46的影响率最大,为16%。且对于同一样本,ε取值越大,影响率Pi越大(图1)。(样本Na21,K15,Ron-50,MUST-48,MANLY-1,Da19,PK62,PK68,CF-08-08在侵蚀速率存在或过大时,无法计算其暴露时间。)

3.3. 宇宙射线衰减路径长度Λ所造成的年代误差分析

经实验,总体上可见10Be的衰减路径长度Λ对宇生核素测年技术的影响较小,在−5%~2%,Λ取150 g/cm−2时,影响率为正,取190 g/cm−2时,影响率为负;对样本Na84,Ron-46,KF-0218-2,BC06-103,Da12,MAR-04-MJB的影响率偏大,其中,Λ取150 g/cm2、ε取2 mm/ka时,对样本Ron-46的影响率最大,为31%。且对于同一样本,ε取值越大,影响率Pi越大(图2)。(样本Na21,K15,Ron-50,MUST-48,MANLY-1,Da19,PK62,PK68,CF-08-08在侵蚀速率存在或过大时,无法计算其暴露时间。)

3.4. 侵蚀速率对年代结果影响的误差分析

研究表明 [5] :样品侵蚀速率为0对于侵蚀速率为0.5 mm/ka,在1 × 104 a尺度上可能低估约0.5%,在10 × 104 a尺度上可能低估约5%,在50 × 104 a尺度上可能低估约40%;对于侵蚀速率为1 mm/k a,在1 × 104 a尺度上可能低估约为1%,在10 × 104 a尺度上可能低估约为7%,在50 × 104 a尺度上可能低估70%;对于侵蚀速率为2 mm/ka,在1 × 104 a尺度上可能低估约2%,在10 × 104 a尺度上可能低估20%,在20 × 104 a尺度上可能低估60%,在50 × 104 a尺度上,校正结果趋于饱和无法计算(图3)。

Figure 1. The influence of the sample density error for the age results (Unit:ρ (g/cm3),ε (mm/ka))

图1. 样本密度误差对测年结果的影响(单位:ρ (g/cm3),ε (mm/ka))

Figure 2. The effect of the absorption mean free path for the age results (Unit:Λ (g/cm2),ε (mm/ka))

图2. 衰减路径长度对测年结果的影响(单位:Λ (g/cm2),ε (mm/ka))

Figure 3. Effects of different erosion rates on samples of different exposures

图3. 不同侵蚀速率对不同暴露时间样品的影响 [5]

4. 结论

1) 假设地貌体侵蚀速率为0时,10Be的生成速率、10Be的浓度对年代结果的影响呈正相关关系。

2) 样本密度ρ、衰变系数Λ的误差对年代结果的影响较小。随侵蚀速率ε增大,影响率增大;随误差值增大,影响率增大。

3) 实际侵蚀速率越大,对年代结果影响越大;且相同的侵蚀速率,暴露时间越长,对年代结果的影响率越高。

基金项目

国家自然科学基金资助项目(41503054);中国博士后科学基金面上资助(2015M582728);江苏省高校优势学科建设工程资助项目资助(PAPD)

NOTES

*通讯作者。

文章引用:
王婉颖, 张志刚. 宇生核素暴露测年影响因素误差分析[J]. 地球科学前沿, 2017, 7(6): 803-811. https://doi.org/10.12677/AG.2017.76082

参考文献

[1] 张志刚, 徐孝彬, 王建, 等. 青藏高原地区宇生核素暴露年代数据存在问题探讨[J]. 地质论评, 2014, 60(6): 1359-1369.
[2] Raisbeck, G.M., Yiou, F., Klein, J., et al. (1983) Accelerator Mass Spectrometer Measurement of Cosmogenic 26Al in Terrestrial and Extraterrestrial Matter. Nature, 301, 690-692.
https://doi.org/10.1038/301690a0
[3] Elmore, D. and Phillips, F. (1987) Accelerator Mass Spectrometry for Measurement of Long-Lived Radioisotopes. Science, 236, 543-550.
https://doi.org/10.1126/science.236.4801.543
[4] Balco, G., Stone, J.O., Lifton, N.A., et al. (2008) A Complete and Easily Accessible Means of Calculating Surface Exposure Ages or Erosion Rates from Be-10 and Al-26 Measurements. Quaternary Geochronology, 3, 174-195.
https://doi.org/10.1016/j.quageo.2007.12.001
[5] 张志刚, 王建, 白世彪, 等. 地表岩石侵蚀速率对宇生核素暴露测年影响的研究[J]. 地理科学, 2014(1): 116-121.
[6] Balco, G. (2011) Contributions and Unrealized Potential Contributions of Cosmo-genic-Nuclide Exposure Dating to Glacier Chronology, 1990-2010. Quaternary Science Reviews, 30, 3-27.
https://doi.org/10.1016/j.quascirev.2010.11.003
[7] Gosse, J.C. and Phillips, F.M. (2001) Terrestrial In Situ Cosmogenic Nuc-lides: Theory and Application. Quaternary Science Reviews, 20, 1475-1560.
https://doi.org/10.1016/S0277-3791(00)00171-2
[8] Ballantyne, C.K. (2010) Extent and Deglacial Chronology of the Last British-Irish Ice Sheet: Implications of Exposure Dating Using Cosmogenic Isotopes. Journal of Quaternary Science, 25, 515-534.
https://doi.org/10.1002/jqs.1310
[9] Owen, L.A., Yi, C.L., Finkel, R.C., et al. (2010) Quaternary Glaciation of Gurla Mandhata (Naimon’anyi). Quaternary Science Reviews, 29, 1817-1830.
https://doi.org/10.1016/j.quascirev.2010.03.017
[10] Arzhannikov, S.G., Braucher, R., Jolivet, M., et al. (2012) History of Late Pleistocene Glaciations in the Central Sayan-Tuva Upland (Southern Siberia). Quaternary Science Reviews, 49, 16-32.
https://doi.org/10.1016/j.quascirev.2012.06.005
[11] Zhang, Z.G., Xu, X.B., Wang, J., Jian, et al. (2014) Last Deglaciation Climatic Fluctuation Record by the Palaeo-Daocheng Ice Cap, Southeastern Qinghai-Tibetan Plateau. Acta Geologica Sinica (English Edition), 88, 1863-1874.
https://doi.org/10.1111/1755-6724.12352
[12] 王建, 张志刚, 徐孝彬, 等. 青藏高原东南部稻城古冰帽南缘第四纪冰川活动的宇生核素年代研究[J]. 第四纪研究, 2012, 32(3): 394-402.
[13] Owen, L.A., Robinson, R., Benn, D.I., et al. (2009) Quaternary Glaciation of Mount Everest. Quaternary Science Reviews, 28, 1412-1433.
https://doi.org/10.1016/j.quascirev.2009.02.010
[14] Seong, B.A., Owen, L.A., Yi, C.L., et al. (2009) Quaternary Glaciation of Muztag Ata and Kongur Shan: Evidence for Glacier Response to Rapid Climate Changes throughout the Late Glacial and Holocene in Westernmost Tibet. Geological Society of America Bulletin, 121, 348-365.
https://doi.org/10.1130/B26339.1
[15] Zech, R., Zech, M., Kubik, P.W., et al. (2009) Deglaciation and Landscape History around Annapurna, Nepal, Based on 10Be Surface Exposure Dating. Quaternary Science Reviews, 28, 1106-1118.
https://doi.org/10.1016/j.quascirev.2008.11.013
[16] Heyman, J., Stroeven, A.P., Caffee, M.W., et al. (2011) Palaeoglaciology of Bayan Har Shan, NE Tibetan Plateau: Exposure Ages Reveal a Missing LGM Expansion. Quaternary Science Reviews, 30, 1988-2001.
https://doi.org/10.1016/j.quascirev.2011.05.002
[17] Zahno, C., Akcar, N., Yavuz, V., et al. (2010) Chronology of Late Pleis-tocene Glacier Variations at the Uludag Mountain, NW Turkey. Quaternary Science Reviews, 29, 1173-1187.
https://doi.org/10.1016/j.quascirev.2010.01.012
[18] Darnault, R., Rolland, Y., Braucher, R., et al. (2012) Timing of the Last Deglaciation Revealed by Receding Glaciers at the Alpine-Scale: Impact on Mountain Geomorphology. Quaternary Science Reviews, 31, 127-142.
https://doi.org/10.1016/j.quascirev.2011.10.019
[19] Larsen, N.K., Linge, H., Hakansson, L., et al. (2012) Investigating the Last Deglaciation of the Scandinavian Ice Sheet in Southwest Sweden with 10Be Exposure Dating. Journal of Quaternary Science, 27, 211-220.
https://doi.org/10.1002/jqs.1536
[20] Rinterknecht, V., Braucher, R., Bose, M., et al. (2012) Late Quaternary Ice Sheet Extents in Northeastern Germany Inferred from Surface Exposure Dating. Quaternary Science Reviews, 44, 89-95.
https://doi.org/10.1016/j.quascirev.2010.07.026
[21] Owen, L.A., Frankel, K.L., Knott, J.R., et al. (2011) Beryllium-10 Terrestrial Cosmogenic Nuclide Surface Exposure Dating of Quaternary Landforms in Death Valley. Geomorphology, 125, 541-577.
https://doi.org/10.1016/j.geomorph.2010.10.024
[22] Roberts, D.H., Long, A.J., Schnabel, C., et al. (2009) Ice Sheet Extent and Early Deglacial History of the Southwestern Sector of the Greenland Ice Sheet. Quaternary Science Reviews, 28, 2760-2773.
https://doi.org/10.1016/j.quascirev.2009.07.002
[23] Stroeven, A.P., Fabel, D., Codilean, A.T., et al. (2010) Investigating the Glacial History of the Northern Sector of the Cordilleran Ice Sheet with Cosmogenic 10Be Concentrations in Quartz. Quaternary Science Reviews, 29, 3630-3643.
https://doi.org/10.1016/j.quascirev.2010.07.010
[24] Hein, A.S., Hulton, N.R.J., Dunai, T.J., et al. (2009) Middle Pleistocene Glaciation in Patagonia Dated by Cosmogenic-Nuclide Measurements on Outwash Gravels. Earth and Planetary Science Letters, 286, 184-197.
https://doi.org/10.1016/j.epsl.2009.06.026
[25] Hein, A.S., Hulton, N.R.J., Dunai, T.J., et al. (2010) The Chronology of the Last Glacial Maximum and Deglacial Events in Central Argentine Patagonia. Quaternary Science Reviews, 29, 1212-1227.
https://doi.org/10.1016/j.quascirev.2010.01.020
[26] Todd, C., Stone, J., Conway, H., et al. (2010) Late Quaternary Evolution of Reedy Glacier, Antarctica. Quaternary Science Reviews, 29, 1328-1341.
https://doi.org/10.1016/j.quascirev.2010.02.001
[27] Altmaier, M., Herpers, U., Delisle, G., et al. (2010) Glaciation History of Queen Maud Land (Antarctica) Reconstructed from in Situ Produced Cosmogenic 10Be, 26Al and 21Ne. Polar Science, 4, 42-61.
https://doi.org/10.1016/j.polar.2010.01.001
[28] Johnson, J.S., Bentley, M.J., Roberts, S.J., et al. (2011) Holocene Deglacial History of the Northeast Antarctic Peninsula—A Review and New Chronological Constraints. Quaternary Science Reviews, 30, 3791-3802.
https://doi.org/10.1016/j.quascirev.2011.10.011
[29] Fogwill, C.J., Hein, A.S., Bentley, M.J., et al. (2012) Do Blue-Ice Moraines in the Heritage Range Show the West Antarctic Ice Sheet Survived the Last Interglacial? Palaeogeography, Palaeoclimatology, Palaeoecology, 335-336, 61-70.
https://doi.org/10.1016/j.palaeo.2011.01.027
[30] Lal, D. (1991) Cosmicray Labeling of Erosion Surfaces: In Situ Nuclide Pro-duction Rates and Ersion Models. Earth and Planetary Science Letters, 104, 424-439.
https://doi.org/10.1016/0012-821X(91)90220-C
[31] Dong, G.C., Yi, C.L. and Marc, C. (2014) 10Be Dating of Boulders on Moraines from the Last Glacial Period in the Nyainqentanglha Mountains, Tibet. Science China: Earth Sciences, 57, 221-231.
https://doi.org/10.1007/s11430-013-4794-z
[32] Chen, Y.X., Li, Y.K., Wang, Y.Y., et al. (2015) Late Quaternary Glacial History of the Karlik Range, Easternmost Tian Shan, Derived from 10Be Surface Exposure and Optically Stimulated Luminescence Datings. Quaternary Science Reviews, 115, 17-27.
https://doi.org/10.1016/j.quascirev.2015.02.010
[33] Balco, G. and Schaefer, J.M. (2016) Cosmogenic-Nuclide and Varve Chronologies for the Deglaciation of Southern New England. Quaternary Geochronology, 1, 15-28.
https://doi.org/10.1016/j.quageo.2006.06.014
[34] Ballantyne, C.K., McCarroll, D. and Stone, J.O. (2011) Periglacial Trimlines and the Extent of the Kerry-Cork Ice Cap, SW Ireland. Quaternary Science Reviews, 30, 3834-3845.
https://doi.org/10.1016/j.quascirev.2011.10.006
[35] Balco, G., Schaefer, J.M. and LARISSA Group (2013) Exposure-Age Record of Holocene Ice Sheet and Ice Shelf Change in the Northeast Antarctic Peninsula. Quaternary Science Reviews, 59, 101-111.
https://doi.org/10.1016/j.quascirev.2012.10.022
[36] Fabel, D., Stroeven, A.P., Harbor, J., et al. (2002) Landscape Preservation under Fennoscandian Ice Sheets Determined from in Situ Produced 10Be and 26Al. Earth and Planetary Science Letters, 201, 397-406.
https://doi.org/10.1016/S0012-821X(02)00714-8
[37] Barrows, T.T., Stone, J.O., Fifield, L.K., et al. (2002) The Timing of the Last Glacial Maximum in Australia. Quaternary Science Reviews, 21, 159-173.
https://doi.org/10.1016/S0277-3791(01)00109-3
[38] Dunai, T.J. (2010) Cosmogenic Nuclides: Principles, Concepts, and Ap-plications in the Earth Surface Sciences. Cambridge University Press, Cambridge.
https://doi.org/10.1017/CBO9780511804519
[39] Gillespie, A.R. and Bierman, P.R. (1995) Precision of Terrestrial Exposure Ages and Erosion Rates Estimated from Analysis of Cosmogenic Isotopes Produced in Situ. Journal of Geophysical Research-Solid Earth, 100, 24637-24649.
https://doi.org/10.1029/95JB02911