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宇宙射线缪子吸收成像技术是一种无损成像技术, 适用于对大尺度的成像目标进行无损探测. 考古学中现有的无损探测方法均存在一定的局限性, 若将缪子吸收成像技术应用于考古领域, 可以作为对传统无损探测方法的重要补充. 本文使用蒙特卡罗GEANT4程序, 对秦始皇陵地宫缪子吸收成像进行研究, 基于已有的秦始皇陵考古数据构建秦始皇陵地宫模型, 根据Reyna提出的海平面缪子能谱公式抽样产生缪子源的信息, 模拟了宇宙射线缪子在秦始皇陵地宫中的输运过程, 并利用图像重建算法实现墓室大小和位置的重构. 模拟结果表明, 利用单视角获得的缪子通量投影数据可以给出地宫中墓室边界的二维角坐标, 利用两个视角的投影数据可以重建墓室大小和三维位置, 重建得到的墓室边长和墓室中心位置相对于理论值的差异在7%左右.Muon radiography is a nondestructive imaging technology based on the naturally existing cosmic ray muons. Because cosmic ray muons have the strong ability to penetrate, muon radiography in which the absorption of muons through matter is utilized, is especially suitable for the imaging of large-scale objects. While the traditional geophysical technologies used in archeology have some limitations, muon radiography is expected to become a powerful supplement in the nondestructive detection of large-scale cultural relics. Based on Monte Carlo simulation method Geant4, the muon radiography of the underground palace of Qinshihuang Mausoleum is studied in this work. A model of the underground palace of Qinshihuang Mausoleum is set up with GEANT4 program according to the data acquired by the previous archaeological study of Qinshihuang Mausoleum’s inner structure, as well as a reference model without these inner structure. By investigating the differences between the muon fluxes obtained from the two models, the muon radiography image of the inner structure of the model can be obtained. During the simulation, the cosmic ray muon source is generated by sampling according to an empirical formula summarized by Reyna, which can accurately describe the energy spectrum and angular distribution of cosmic ray muons at sea level. In addition, two viewpoints are selected in order to determine the three-dimensional position of the chamber. The simulation data are processed by using an image reconstruction algorithm which can be described as the following three steps. Firstly, the counts of muons in different directions are converted into muon flux. Secondly, the muon flux of the reference model is deducted from that of the Qinshihuang Mausoleum model, and the angular coordinates of the chamber walls are determined. Finally, combined with the wall’s angular coordinates obtained from the two viewpoints and the relative position between the two viewpoints, the chamber size and its position are reconstructed according to the geometric relationship. The errors of the reconstructed chamber center position and the length of chamber walls are both approximately 7%. In this article, we conduct only a preliminary study of muon radiography applied to the nondestructive detection of Qinshihuang Mausoleum, but the results show that muon radiography can be a promising tool for the archeological study of Qinshihuang Mausoleum. In the follow-up study, more factors will be taken into consideration, including the details of Qinshihuang Mausoleum model, and the improvement of image reconstruction algorithm.
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Keywords:
- muon radiography /
- cosmic ray muon /
- Monte Carlo simulation
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图 3 秦始皇陵模型示意图 (a) 模型1内部结构示意图; (a1) 模型1俯视图; (a2) 模型1正视图; (a3) 模型1剖面3示意图; (a4) 模型1剖面1示意图; (b) 模型2示意图(无内部结构);
Fig. 3. Model of Qinshihuang Mausoleum: (a) Inner structure of Model 1; (a1) top view of Model 1; (a2) front view of Model 1; (a3) profile 3 of Model 1; (a4) profile 1 of Model 1; (b) Model 2 (no inner structure).
图 4 根据Reyna公式抽样产生的1000万个μ子的动量和天顶角分布 (a) μ子数量随μ子动量变化分布; (b) μ子数量随μ子速度方向的天顶角变化分布
Fig. 4. Momentum spectrum and zenith angle distribution of the 10 million muons sampled by Reyna formula: (a) Momentum spectrum of the sampled muons; (b) zenith angle distribution of the sampled muons.
图 5 两个测量点得到的
$ f(\theta, \varphi ) $ 的二维投影图 (a)测量点1的$ f(\theta, \varphi ) $ 投影图, 其中,$ {\rm{t}\rm{a}\rm{n}}{\theta }_{x}={\rm{t}\rm{a}\rm{n}}\theta {\rm{c}}{\rm{o}}{\rm{s}} \varphi $ ,${\rm{t}\rm{a}\rm{n}}{\theta }_{y}= $ $ {\rm{t}\rm{a}\rm{n}}\theta {\rm{s}}\rm{i}\rm{n} \varphi$ ; (b)测量点2的$ f(\theta, \varphi ) $ 投影图Fig. 5. Two-dimensional projection of
$ f\left(\theta, \varphi \right) $ obtained at viewpoint 1 and 2: (a) Distribution of$ f\left(\theta, \varphi \right) $ obtained at viewpoint 1, where the$ {\rm{t}\rm{a}\rm{n}}{\theta }_{x}={\rm{t}\rm{a}\rm{n}}\theta {\rm{c}}{\rm{o}}{\rm{s}} \varphi $ ,$ {\rm{t}\rm{a}\rm{n}}{\theta }_{y}={\rm{t}\rm{a}\rm{n}}\theta {\rm{s}}\rm{i}\rm{n} \varphi $ ; (b) distribution of$ f\left(\theta, \varphi \right) $ obtained at viewpoint 2.
图 6 墓室三维重建结果 (a) 剖面1处重建结果; (b)剖面2处重建结果
Fig. 6. Three-dimensional reconstruction results of the chamber: (a) Reconstruction result at Profile 1; (b) reconstruction result at Profile 2
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[1] Amenomori M, Bao Y W, Bi X J, et al. 2019 Phys. Rev. Lett. 123 51101
Google Scholar
[2] Cao Z, Aharonian F A, An Q, et al. 2021 Nature 594 33
Google Scholar
[3] Liu Y Y, Chen Z Q, Zhao Z R, Zhang L, Wang Z T 2009 Tsinghua Sci. Technol. 14 313
Google Scholar
[4] Tanaka H K M, Nakano T, Takahashi S, et al. 2007 Earth Planet. Sci. Lett. 263 104
Google Scholar
[5] George E P 1955 Commonw. Eng. 1955 455
[6] Alvarez L W, Anderson J A, Bedwei F E, et al. 1970 Science 167 832
Google Scholar
[7] Nagamine, K, Iwasaki, M, Shimomura K, Ishida K 1995 Nucl. Instrum. Methods Phys. Res., Sect. A 356 585
Google Scholar
[8] Caffau E, Coren F, Giannini G 1997 Nucl. Instrum. Methods Phys. Res., Sect. A 385 480
Google Scholar
[9] Malmqvist L, Jonsson G, Kristiansson K, Jacobsson L 1979 Geophysics 44 1549
Google Scholar
[10] Carbone D, Gibert D, Marteau J, Diament M, Zuccarello L, Galichet E 2014 Geophys. J. Int. 196 633
Google Scholar
[11] Tanaka H K M 2016 Sci. Rep. 6 39741
Google Scholar
[12] Rosas-Carbajal M, Jourde K, Marteau J, Deroussi S, Komorowski J C, Gibert D 2017 Geophys. Res. Lett. 44 6743
Google Scholar
[13] Schouten D, Ledru P 2018 J. Geophys. Res. Solid Earth 123 8637
Google Scholar
[14] Morishima K, Kuno M, Nishio A, et al. 2017 Nature 552 386
Google Scholar
[15] Saracino G, Amato L, Ambrosino F, et al. 2017 Sci. Rep. 7 1181
Google Scholar
[16] 蒋宏耀, 张立敏 1997 地球物理学报 40 383
Jiang H Y, Zhang L M 1997 Chin. J. Geophys. 40 383
[17] 宗鑫, 王心源, 刘传胜, 骆磊 2016 地球信息科学学报 18 273
Zong X, Wang X Y, Liu C S, Luo L 2016 J. Geo-Information Science 18 273
[18] 林金鑫 2011 博士学位论文 (杭州: 浙江大学)
Lin X J 2011 Ph. D. Dissertation (Hangzhou: Zhejiang University) (in Chinese)
[19] Beringer J, Arguin J F, Barnett R M, et al. 2012 Phys. Rev. D 86 010001
Google Scholar
[20] Tsuji S, Katayama T, Okei K, Wada T, Yamamoto I, Yamashita Y 1998 J. Phys. G:Nucl. Part. Phys. 24 1805
Google Scholar
[21] Agostinelli S, Allison J, Amako K, et al. 2003 Nucl. Instrum. Methods Phys. Res., Sect. A 506 250
Google Scholar
[22] 于国明, 王书民, 王帮兵, 等 2005 秦始皇陵地宫地球物理探测成果与技术 (北京: 地质出版社) 第17—58页
Yu G M, Wang S M, Wang B B, et al. 2005 Geophysical Exploration for the Underground Palace of Emperor Qinshihuang Mausoleum (Beijing: Geological Publishing House) pp17–58 (in Chinese)
[23] 吴明清, 文启忠, 潘景瑜, 刁桂仪 1996 自然科学进展 01 82
Wu M Q, Wen Q Z, Pan J Y, Diao G Y 1996 Prog. Nat. Sci. 01 82
[24] Gaisser T K 1990 Cosmic Rays and Particle Physics (New York: Cambridge University Press) p71
[25] Reyna D 2006 arXiv: 0604145v2 [hep-ph]
[26] Smith J A, Duller N M 1959 J. Geophys. Res. 64 2297
Google Scholar
[27] Su N, Liu Y Y, Wang L, Wu B, Cheng J P 2021 Front. Energy Res. 9 640
Google Scholar
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