搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

应用模拟退火算法估算月核大小及其密度组成

文麒麟 钟振

引用本文:
Citation:

应用模拟退火算法估算月核大小及其密度组成

文麒麟, 钟振

Size and density of lunar core estimated using simulated annealing algorithm

Wen Qi-Lin, Zhong Zhen
PDF
HTML
导出引用
  • 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⋅m³, quite denser than the outer core, which is estimated at 4618 kg⋅m³. 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.
      通信作者: 钟振, zzhong@gznu.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 42030110, 41864001)资助的课题.
      Corresponding author: Zhong Zhen, zzhong@gznu.edu.cn
    • Funds: Poject supported by the National Science Foundation of China (Grant Nos. 42030110, 41864001)
    [1]

    Jiang Y, Li Y, Liao S Y, Yin Z J, Hsu W B 2022 Sci. Bull. 67 755Google Scholar

    [2]

    Mighani S, Wang H, Shuster D L, Borlina C S, Nichols C I O, Weiss B P 2020 Sci. Adv. 6 eaax0883Google Scholar

    [3]

    Tikoo S M, Weiss B P, Shuster D L, Suavet C, Wang H, Grove T L 2017 Sci. Adv. 3 1700207Google 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 331Google Scholar

    [6]

    Harada Y, Goossens S, Matsumoto K, Yan J, Ping J S, Noda H, Haruyama J 2014 Nat. Geosci. 7 569Google Scholar

    [7]

    Weber R C, Lin P, Garnero E J, Williams Q, Philippe L 2011 Science 331 309Google Scholar

    [8]

    Shimizu H, Matsushima M, Takahashi F, Shibuya H, Tsunakawa H 2013 Icarus 222 32Google Scholar

    [9]

    Yan J, Xu L, Li F, Matsumoto K, Rodriguez J A P, Miyamoto H, Dohm J M 2015 Adv. Space Res. 55 1721Google 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 671Google Scholar

    [12]

    Sakamoto S, Ozera K, Barolli A, Ikeda M, Barilli L, Takizawa M 2019 Soft Computing 23 3029Google Scholar

    [13]

    Cui Y, Zhang Z S, Shi X J, Guang C, Gao J 2020 Sep. Purif. Technol. 236 116303Google 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 3382Google Scholar

    [15]

    Park R S, Folkner W M, Williams J G, Boggs D H 2021 Astron. J. 161 105Google 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 1Google Scholar

    [17]

    Lognonné P, Gagnepain-Beyneix J, Chenet H 2003 Earth Planet. Sc. Lett. 211 27Google Scholar

    [18]

    Gagnepain-Beyneix J, Lognonné P, Chenet H, Lombardi D, Spohn T 2006 Phys. Earth. Planet. In. 159 140Google 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 96Google Scholar

    [21]

    Lorell J, Sjogren W L 1968 Science 159 625Google Scholar

    [22]

    Konopliv A S, Asmar S W, Carranza E, Yuan D N 2001 Icarus 150 1Google 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 033105Google Scholar

    [25]

    钟振, 文麒麟, 梁金福 2023 物理学报 72 029601Google Scholar

    Zhong Z, Wen Q L, Liang J F 2023 Acta Phys. Sin. 72 029601Google Scholar

    [26]

    He Y, Sun S, Kim D Y, Jang B G, Li H, Mao H 2022 Nature 602 258Google Scholar

  • 图 1  月球内部分层结构

    Fig. 1.  Lunar interior structure with various layers.

    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 1  参数取值或范围

    Table 1.  Values of fixed parameters and ranges of free parameters.

    参数取值或范围
    月球平均参考半径 R/km1737.4
    月壳厚度 bc/km40
    月壳密度 ρc/(kg⋅m–3)[9]2800
    月幔密度 ρm/(kg⋅m–3)[20]3360
    月球外核半径 rco/km[50, 600]
    月球内核半径 rci/km[50, 450]
    月球外核密度 ρco/(kg⋅m–3)[3400, 6000]
    月球内核密度 ρci/(kg⋅m–3)[4000, 8500]
    下载: 导出CSV

    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 C220.3467408607293×10–4
    月球的总质量 M/kg7.3462872646575×1022
    月球的平均半径 R/km1737.4
    月球的平均密度 $ \bar{\rho } $/(kg⋅m–3)3340.642
    天平动因子 γ227.7317×10–6
    天平动因子 β631.0213×10–6
    平均惯性矩因子 I0/MR20.3930002239
    下载: 导出CSV
  • [1]

    Jiang Y, Li Y, Liao S Y, Yin Z J, Hsu W B 2022 Sci. Bull. 67 755Google Scholar

    [2]

    Mighani S, Wang H, Shuster D L, Borlina C S, Nichols C I O, Weiss B P 2020 Sci. Adv. 6 eaax0883Google Scholar

    [3]

    Tikoo S M, Weiss B P, Shuster D L, Suavet C, Wang H, Grove T L 2017 Sci. Adv. 3 1700207Google 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 331Google Scholar

    [6]

    Harada Y, Goossens S, Matsumoto K, Yan J, Ping J S, Noda H, Haruyama J 2014 Nat. Geosci. 7 569Google Scholar

    [7]

    Weber R C, Lin P, Garnero E J, Williams Q, Philippe L 2011 Science 331 309Google Scholar

    [8]

    Shimizu H, Matsushima M, Takahashi F, Shibuya H, Tsunakawa H 2013 Icarus 222 32Google Scholar

    [9]

    Yan J, Xu L, Li F, Matsumoto K, Rodriguez J A P, Miyamoto H, Dohm J M 2015 Adv. Space Res. 55 1721Google 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 671Google Scholar

    [12]

    Sakamoto S, Ozera K, Barolli A, Ikeda M, Barilli L, Takizawa M 2019 Soft Computing 23 3029Google Scholar

    [13]

    Cui Y, Zhang Z S, Shi X J, Guang C, Gao J 2020 Sep. Purif. Technol. 236 116303Google 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 3382Google Scholar

    [15]

    Park R S, Folkner W M, Williams J G, Boggs D H 2021 Astron. J. 161 105Google 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 1Google Scholar

    [17]

    Lognonné P, Gagnepain-Beyneix J, Chenet H 2003 Earth Planet. Sc. Lett. 211 27Google Scholar

    [18]

    Gagnepain-Beyneix J, Lognonné P, Chenet H, Lombardi D, Spohn T 2006 Phys. Earth. Planet. In. 159 140Google 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 96Google Scholar

    [21]

    Lorell J, Sjogren W L 1968 Science 159 625Google Scholar

    [22]

    Konopliv A S, Asmar S W, Carranza E, Yuan D N 2001 Icarus 150 1Google 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 033105Google Scholar

    [25]

    钟振, 文麒麟, 梁金福 2023 物理学报 72 029601Google Scholar

    Zhong Z, Wen Q L, Liang J F 2023 Acta Phys. Sin. 72 029601Google Scholar

    [26]

    He Y, Sun S, Kim D Y, Jang B G, Li H, Mao H 2022 Nature 602 258Google Scholar

  • [1] 焦宝宝. 基于原子核密度的核电荷半径新关系. 物理学报, 2023, 72(11): 112101. doi: 10.7498/aps.72.20230126
    [2] 钟振, 文麒麟, 梁金福. 应用重力场模型二阶位系数及新近岁差率约束火星内核大小及密度组成. 物理学报, 2023, 72(2): 029601. doi: 10.7498/aps.72.20221170
    [3] 穆萌, 张海燕, 王晓, 李存惠, 张小平, 王明智, 朱应敏, 高立波, 赵呈选, 陆洋, 王卫东. 月尘被动防护技术的最新研究进展. 物理学报, 2021, 70(6): 060501. doi: 10.7498/aps.70.20201517
    [4] 臧益鹏, 许振宇, 黄安, 艾苏曼, 夏晖晖, 阚瑞峰. 基于改进模拟退火算法的非均匀燃烧场分布重建. 物理学报, 2021, 70(13): 134205. doi: 10.7498/aps.70.20202124
    [5] 苏勇, 范东明, 游为. 利用GOCE卫星数据确定全球重力场模型. 物理学报, 2014, 63(9): 099101. doi: 10.7498/aps.63.099101
    [6] 孟云鹤, 陈琪锋. 地月平动点导航星座的概要设计与性能分析. 物理学报, 2014, 63(24): 248402. doi: 10.7498/aps.63.248402
    [7] 胡健, 邱锡钧. 重力场作用下微管自组装过程中向列相取向的空间模式的形成. 物理学报, 2014, 63(7): 078201. doi: 10.7498/aps.63.078201
    [8] 刘思思, 张朝辉, 刘俊铭. 微平面接触分离中弯月面力的计算. 物理学报, 2010, 59(10): 6902-6907. doi: 10.7498/aps.59.6902
    [9] 万仕全, 顾承华, 康建鹏, 邹建新, 胡玉玲, 徐莎莎. 中国月极端高温对大气涛动的响应. 物理学报, 2010, 59(1): 676-682. doi: 10.7498/aps.59.676
    [10] 高永华, 赵志恒, 侯召宇, 曹鹤飞, 段春贵, 何祯民. 改进的核密度模型与强子-核Drell-Yan过程中的核效应. 物理学报, 2006, 55(11): 5760-5763. doi: 10.7498/aps.55.5760
    [11] 娄太平. 具有广义协变的包含重力场贡献的重力场方程. 物理学报, 2006, 55(4): 1602-1606. doi: 10.7498/aps.55.1602
    [12] 娄太平. 含物质纯重力场部分贡献的静态和稳态重力场研究. 物理学报, 2005, 54(1): 18-23. doi: 10.7498/aps.54.18
    [13] 娄太平. 物质纯重力场部分的能量-动量张量研究. 物理学报, 2004, 53(6): 1657-1661. doi: 10.7498/aps.53.1657
    [14] 刘玉真, 罗成林. 硅团簇的结构及生长模式——紧束缚分子动力学:Si11—Si32. 物理学报, 2004, 53(2): 592-595. doi: 10.7498/aps.53.592
    [15] 郭立平, 成之绪, 韩甫田, 柳 义, 赵志祥. 粉末衍射谱图分解的模拟退火法. 物理学报, 2003, 52(11): 2842-2848. doi: 10.7498/aps.52.2842
    [16] 李树有, 都志辉, 吴梦月, 朱静, 李三立. 模拟退火算法的并行实现及其应用. 物理学报, 2001, 50(7): 1260-1263. doi: 10.7498/aps.50.1260
    [17] 刘日平, 赵建华, 张湘义, 贺端威, 许应凡, 王文魁. Zr65Cu17.5Ni10Al7.5合金定向凝固组织特征及其与重力场取向的关系. 物理学报, 1998, 47(9): 1571-1578. doi: 10.7498/aps.47.1571
    [18] 胡深洋, 折晓黎, 李玉兰. 不同应力场中马氏体形核的择优取向. 物理学报, 1996, 45(2): 339-344. doi: 10.7498/aps.45.339
    [19] 于工, 郝茂盛, 张仿清, 陈光华. 用模拟退火模型研究非晶硅的结构和振动性质. 物理学报, 1993, 42(2): 314-319. doi: 10.7498/aps.42.314
    [20] 时永澄. 一种高阶重力场方程及其静态球对称解. 物理学报, 1979, 28(5): 143-149. doi: 10.7498/aps.28.143
计量
  • 文章访问数:  3764
  • PDF下载量:  67
  • 被引次数: 0
出版历程
  • 收稿日期:  2022-11-30
  • 修回日期:  2023-01-21
  • 上网日期:  2023-03-03
  • 刊出日期:  2023-04-20

/

返回文章
返回