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提出结合高阶月球重力场模型GL990D的2阶位系数和月球天平动参数, 以及月球的平均密度和平均惯性矩因子, 来解决月核大小及其密度组成的问题. 基于不同分层结构模型, 推导了不同分层结构情况下的平均密度和平均惯性矩因子, 并以它们理论值和观测值的残差平方和作为目标函数, 应用模拟退火算法对多参数进行估算. 考虑三层模型的月球内部结构模型, 估算的月核大小约为470 km, 月核密度约为5486 kg/m3, 反演的月核大小及其密度组成与其他研究相近, 验证了本文算法的可靠性. 考虑月核分成外核和内核的情况, 反演的外核大小约为385 km, 内核大小约为350 km, 对应的外核密度约为4618 kg/m³, 内核密度约为7879 kg/m3. 表明月球至35.6亿年前发电机效应约束时, 形成了以硫化亚铁为主的外核, 月核内部则形成了纯铁为主包含部分镍铁合金的内核.This study focuses on the size of composition of lunar core. In this study, we consider the lunar mean density and mean moment of inertia factor in our inversion. We use the degree-2 coefficients of lunar gravity field model GL990D and the lunar physical liberation parameters to compute mean moment of inertia factor, which is treated as an observed value. We also compute the observed value of the mean density according to the total mass of the Moon. Based on the interior structure with various layers, we deduce the modeled expressions for the lunar mean density and mean moment of inertia factor. Summing the squares of the difference between the observed value and modeled value as an inversion criterion, we estimate the multi-parameters based on the simulated annealing algorithm. By considering the lunar interior structure with three layers, the estimated size of the lunar core is around 470 km, and the density of the core is close to 5486 kg·m–3. The computed size and density of the lunar core are close to other reported values, thereby validating our algorithm. We then consider the scenarios that the lunar core differentiates between a solid inner core and a liquid outer core. The good-inversed outer core is close to 385 km, while the inner core approaches to 350 km. By using the good-inversed sizes as fixed parameters, it is found that the inner core reaches 7879 kg⋅m–³, quite denser than the outer core, which is estimated at 4618 kg⋅m–³. Our result indicates that the outer core is composed of ferrous sulfide (FeS), while the inner core is comprised of ferrous or ferro-nickel, formed 3.56 billion years ago when the lunar core dynamo ended.
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Keywords:
- gravity field /
- physical liberation /
- simulated annealing /
- size of lunar core /
- density of lunar core
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图 2 三层模型下月核半径和密度的频率分布图 (a)月核半径频率分布图; (b)月核密度频率分布图
Fig. 2. Histograms of frequency distributions of the estimated radius (a) and density (b) of the core, considering the lunar interior structure with three layers.
图 3 四层模型的月核半径频率分布图 (a) 外核半径频率分布图; (b) 内核半径频率分布图
Fig. 3. Histograms of frequency distributions of the estimated outer (a) and inner core (b), considering the lunar interior structure with four layers.
图 4 四层模型的月核密度频率分布图 (a) 外核密度频率分布图; (b) 内核密度频率分布图
Fig. 4. Histograms of frequency distributions of the density of outer core (a) and the density of inner core (b), considering the lunar interior structure with four layers.
表 2 月球相关参数
Table 2. Values of lunar parameters.
参数 取值 二阶重力位系数 C20 –0.9088124807048×10–4 二阶重力位系数 C22 0.3467408607293×10–4 月球的总质量 M/kg 7.3462872646575×1022 月球的平均半径 R/km 1737.4 月球的平均密度 $ \bar{\rho } $/(kg⋅m–3) 3340.642 天平动因子 γ 227.7317×10–6 天平动因子 β 631.0213×10–6 平均惯性矩因子 I0/MR2 0.3930002239 
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[1] Jiang Y, Li Y, Liao S Y, Yin Z J, Hsu W B 2022 Sci. Bull. 67 755
Google Scholar
[2] Mighani S, Wang H, Shuster D L, Borlina C S, Nichols C I O, Weiss B P 2020 Sci. Adv. 6 eaax0883
Google Scholar
[3] Tikoo S M, Weiss B P, Shuster D L, Suavet C, Wang H, Grove T L 2017 Sci. Adv. 3 1700207
Google Scholar
[4] Williams J G, Konopoliv A S, Boggs D H, Park R S, Yuan D, Lemoine F G, Goossens S, Mazarico E, Nimmo F, Weber R C, Asmar S W, Melosh H J, Neumann G A, Phillips R J, Smith D E, Solomon S C, Watkins M M, Wieczorek M A, Andrews-hanna J C, Head J W, Kiefer W S, Matsuyama I, Mcgovern P J, Taylor G J, Zuber M T 2014 J. Geophys. Res. Planet. 119 1546
[5] Khan A, Pommier A, Neumann G A, Mosegaard K 2013 Tectonophysics 609 331
Google Scholar
[6] Harada Y, Goossens S, Matsumoto K, Yan J, Ping J S, Noda H, Haruyama J 2014 Nat. Geosci. 7 569
Google Scholar
[7] Weber R C, Lin P, Garnero E J, Williams Q, Philippe L 2011 Science 331 309
Google Scholar
[8] Shimizu H, Matsushima M, Takahashi F, Shibuya H, Tsunakawa H 2013 Icarus 222 32
Google Scholar
[9] Yan J, Xu L, Li F, Matsumoto K, Rodriguez J A P, Miyamoto H, Dohm J M 2015 Adv. Space Res. 55 1721
Google Scholar
[10] 钟振, 张腾, 段炼, 李毅, 朱化强 2021 武汉大学学报-信息科学版 46 238
Zhong Z, Zhang T, Duan L, Li Y, Zhu H Q 2021 Geomat. Inform. Sci. Wuhan Univ. 46 238
[11] Kirkpatrick S, Gelatt C D, Vecchi M P 1983 Science. 220 671
Google Scholar
[12] Sakamoto S, Ozera K, Barolli A, Ikeda M, Barilli L, Takizawa M 2019 Soft Computing 23 3029
Google Scholar
[13] Cui Y, Zhang Z S, Shi X J, Guang C, Gao J 2020 Sep. Purif. Technol. 236 116303
Google Scholar
[14] Lemoine F G, Goossens S, Sabaka T J, Nicholas J B, Mazarico E, Rowlands D D, Loomis B D, Chinn D S, Neumann G A, Smith D E, Zuber M T 2014 Geophys. Res. Lett. 41 3382
Google Scholar
[15] Park R S, Folkner W M, Williams J G, Boggs D H 2021 Astron. J. 161 105
Google Scholar
[16] Garcia R F, Khan A, Drilleau M, Margerin L, Kawamura T, Sun D, Wieczorek M A, Rivoldini A, Nunn C, Weber R C, Marusiak A G, Lognonné P, Nakamura Y, Zhu P 2019 Space. Sci. Rev. 215 1
Google Scholar
[17] Lognonné P, Gagnepain-Beyneix J, Chenet H 2003 Earth Planet. Sc. Lett. 211 27
Google Scholar
[18] Gagnepain-Beyneix J, Lognonné P, Chenet H, Lombardi D, Spohn T 2006 Phys. Earth. Planet. In. 159 140
Google Scholar
[19] Khan A, Mosegaard K 2002 J. Geophys. Res. Planet 107 3
[20] Garcia R F, Gagnepain-Beyneix J, Chevrot S, Lognobnné P 2011 Phys. Earth Planet. In. 188 96
Google Scholar
[21] Lorell J, Sjogren W L 1968 Science 159 625
Google Scholar
[22] Konopliv A S, Asmar S W, Carranza E, Yuan D N 2001 Icarus 150 1
Google Scholar
[23] Matsumoto K, Goossens S, Ishihara Y, Liu Q, Kikuchi T, Namiki I N, Noda H, Hanada H, Kawano N, Lemoine F G, Rowlands D D 2010 J. Geophys. Res. Planet 115 003499
[24] Tiesinga E, Mohr P J, Newell D B, Taylor B N 2021 J. Phys. Chem. Ref. Data 50 033105
Google Scholar
[25] 钟振, 文麒麟, 梁金福 2023 物理学报 72 029601
Google Scholar
Zhong Z, Wen Q L, Liang J F 2023 Acta Phys. Sin. 72 029601
Google Scholar
[26] He Y, Sun S, Kim D Y, Jang B G, Li H, Mao H 2022 Nature 602 258
Google Scholar
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