• ISSN 2097-1893
  • CN 10-1855/P

行星内部地震波及其对卫星轨道的影响

郑应才 田源

引用本文: 郑应才,田源. 2021. 行星内部地震波及其对卫星轨道的影响. 地球与行星物理论评,52(2):205-210
Zheng Y C, Tian Y. 2021. Seismic wavefields in a planet and their influence on the satellite orbit. Reviews of Geophysics and Planetary Physics, 52(2): 205-210

行星内部地震波及其对卫星轨道的影响

doi: 10.19975/j.dqyxx.2020-014
详细信息
    通讯作者:

    郑应才(1981-),男,副教授,主要从事天然、勘探和行星地震学方面的研究. E-mail:yzheng12@uh.edu

  • 中图分类号: P691

Seismic wavefields in a planet and their influence on the satellite orbit

  • 摘要: 本文指出地震学在天文和行星学科里的重要作用. 我们主要介绍最近提出的“潮汐—地震波共振”(tidal-seismic resonance)效应,并且讨论它对卫星轨道演化的作用. 当在同步轨道以下周期运动的卫星引起的引潮力的频率和行星内部自由震荡频率吻合时,就会发生潮汐—地震波共振. 此时,行星内部的地震波将被激发并引起行星表面的显著位移. 升高和下降的地面会对卫星产生一个力矩从而使得卫星轨道下降. 因为潮汐共振引起的动态地面位移可以比单纯引潮力引起的位移大两个数量级,所以潮汐共振会显著加速卫星下降速率. 我们用我们开发的三维地震波场模拟程序AstroSeis数值计算了潮汐—地震波共振对轨道的影响,进而推测这一共振效应可能对行星早期吸积速度有显著影响. 另外,因为行星内部的Q值和S波的波速对潮汐共振影响很大,未来研究微重力环境下的小行星或陨石内部地震波的速度和Q值对研究行星演化和太阳系的形成至关重要.

     

  • 图  1  潮汐—地震波共振发生条件. 假设卫星在贴近行星表面的轨道公转,在不同行星密度和半径下,能产生潮汐—地震共振的最大的横波速度VS. 纵轴是行星半径r,横轴是密度ρ,颜色代表了横波速度. 右上角白色区域没有计算,不代表没有共振.

    Figure  1.  Tidal-seismic resonance conditions for the maximum shear-wave speed of the planet for different planet densities and radii. We assume the satellite orbits on the equator. The horizontal axis is density ρ and the vertical axis is the planet radius r. The color represents the S-wave speed. We did not compute the cases in the upper right corner (white area).

    图  2  潮汐星球共振产生的影响. 数值模拟不同Q值模型和不同轨道高度下卫星的轨道下降速度. 水平轴是卫星的轨道半径. 不同的被激发的自由震荡模用黑色字体标在峰值附近. 行星半径为$ {R}_{\rm{pl}} $=2 000 km,P波速度为3 000 m/s,S波速度为1 200 m/s, 密度为2 840 kg/m3. 卫星质量为1016 kg. 在模拟中,考虑二体公转问题,但是不考虑行星自转(修改自Tian and Zheng, 2019

    Figure  2.  Modeling results of orbital decay with the influence of the tidal-seismic resonance. We compute the orbit decay rate of the satellite for different Q values and orbit radii. The horizontal axis is the orbit radius and the vertical axis is the orbital decay rate. The corresponding resonant seismic modes are labeled around the peaks. The planet radius is Rpl=2 000 km, P-wave velocity is 3 000 m/s, S wave velocity is 1 200 m/s, and the planet density is 2 840 kg/m3. The mass of the orbiting moon is 1016 kg. In our modeling, we only consider a two-body planet-moon system and neglect the planet spin (Figure reproduced from Tian and Zheng (2019) with permission from Elsevier)

    图  3  潮汐牵引力矩示意图. 当没有潮汐—地震波共振时,潮汐力使得行星变形有两个潮汐隆起. 对于同步轨道下方的卫星M1,因为它的公转角速度比行星自转的角速度快,潮汐隆起对M1的合力向后(合力矩为负)从而使其轨道下降. 对于M2,因为行星自转速度快于M2的公转速度,离得近的隆起在前面,所以M2受到的合力向前(合力矩为正),M2轨道升高. 地球和月亮与M2类似. 当潮汐—地震波共振时,行星地表形变主要由地震波引起. 地表形变的最大振幅由地震波的Q值控制,同时Q值也控制了地表形变与潮汐力的相位差,从而影响合力矩和卫星轨道

    Figure  3.  Schematic showing tidal torque. When there is no tidal-seismic resonance, tidal forces of the moon deform the planet surface to pull up tidal bulges on the planet surface. For the moon, M1, below the synchronous orbit, its orbital angular velocity is faster than the planet spin velocity. The tidal-bulge's gravitational pull exerts a negative torque on M1 so its orbit radius decays. On the other hand, for M2, above the synchronous orbit, its orbit angular velocity is lagging behind the nearest tidal bulge so that M2 will experience a forward pull hence a positive torque to raise its orbit further and further. The Earth's Moon is similar to M2. When the tidal-seismic resonance happens, the planet surface deformation is mainly due to seismic waves whose ultimate amplitudes are controlled by the dissipation factor, the seismic Q. In the meantime, Q also influences the phase lag between the tidal force and the resultant surface displacement to ultimately exert a torque on the moon to change its orbit

    图  4  AstroSeis模拟不同频率下的火卫一表面地震波场. 爆炸震源深度为4 km. 假设火卫一(Phobos)的纵波速度为3 km/s,横波速度为1.0 km/s,密度为1 880 kg/${\rm m}^{3}$. 颜色为加强对比度后的地震波场位移

    Figure  4.  Seismic wavefields in Phobos calculated by our AstroSeis modeling code. We assume Phobos has a P-wave velocity 3 km/s, S-wave velocity 1 km/s, and density 1 880 kg/m3. We put an explosion source at 4 km depth. Color shows the positive (blue) and negative (red) vertical-component displacement of the seismic field

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出版历程
  • 收稿日期:  2020-08-26
  • 录用日期:  2020-09-23
  • 网络出版日期:  2021-09-13
  • 刊出日期:  2021-03-01

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