Seismic wavefields in a planet and their influence on the satellite orbit
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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.Abstract: Seismology can play an important role in both astronomy and planetary science. We will mainly discuss the recently proposed Tidal-Seismic Resonance (TSR) effect and its role on the orbital evolution of the moon around a planet. For a planet-moon system, TSR is expected when a tidal force frequency matches a free-oscillation frequency of the planet. TSR can excite large-amplitude seismic waves that can change the shape of the planet, which in turn, exerts a negative torque on the moon to cause it to fall rapidly toward the planet. We have developed a 3-D seismic wavefield modeling package, AstroSeis, to numerically study the moon's orbit change. We further speculate that TSR might be an important mechanism to accelerate the planet accretion process in the early history of star formation. Because TSR significantly depends on the seismic Q value and S-wave velocity of the planet when its size was still small, future work studying the seismic wave velocity and Q of some asteroids in micro-gravity environments is important to reveal the evolution history of planets and the solar system.
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Key words:
- tides /
- tidal-seismic resonance /
- planet evolution /
- seismic wavefields in asteroids
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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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[1] Asphaug E, Moore J M, Morrison D, et al. 1996. Mechanical and geological effects of impact cratering on Ida[J]. Icarus, 120(1): 158-184. doi: 10.1006/icar.1996.0043 [2] Asphaug E. 2009. Growth and evolution of asteroids[J]. Annual Review of Earth and Planetary Sciences, 37: 413-448. doi: 10.1146/annurev.earth.36.031207.124214 [3] Asphaug E. 2020. Interiors of small bodies and moons[J]. Nature Communications, 11(1): 1-3. doi: 10.1038/s41467-019-13993-7 [4] Bills B G, Neumann G A, Smith D E, et al. 2005. Improved estimate of tidal dissipation within Mars from MOLA observations of the shadow of Phobos[J]. Journal of Geophysical Research-Planets, 110(E7): E07004. doi: 10.1029/2004JE002376 [5] Black B A, Mittal T. 2015. The demise of Phobos and development of a Martian ring system[J]. Nature Geoscience, 8(12): 913-917. doi: 10.1038/ngeo2583 [6] Chaillat S, Bonnet M, Semblat J -F. 2009. A new fast multi-domain BEM to model seismic wave propagation and amplification in 3-D geological structures[J]. Geophysical Journal International, 177(2): 509-531. doi: 10.1111/j.1365-246X.2008.04041.x [7] Courville S W, Sava P C. 2020. Speckle noise attenuation in orbital laser vibrometer seismology[J]. Acta Astronautica, 172(2): 16-32. [8] Darwin G H. 1898. The evolution of satellites[J]. The Atlantic Monthly, 81: 444-455. [9] DellaGiustina D N, Emery J P, et al. 2019. Properties of rubble-pile asteroid (101955) Bennu from OSIRIS-REx imaging and thermal analysis[J]. Nature Astronomy, 3(4): 341-351. doi: 10.1038/s41550-019-0731-1 [10] Fuller J. 2014. Saturn ring seismology: Evidence for stable stratification in the deep interior of Saturn[J]. Icarus, 242: 283-296. doi: 10.1016/j.icarus.2014.08.006 [11] Fuller J, Luan J, Quataert E. 2016. Resonance locking as the source of rapid tidal migration in the Jupiter and Saturn moon systems[J]. Monthly Notices of the Royal Astronomical Society, 458(4): 3867-3879. doi: 10.1093/mnras/stw609 [12] Ge Z, Fu L-Y, Wu R.-S. 2005. P-SV wave-field connection technique for regional wave propagation simulation[J]. Bulletin of the Seismological Society of America, 95(4): 1375-1386. doi: 10.1785/0120040173 [13] Ge Z, Chen X. 2008. An efficient approach for simulating wave propagation with the Boundary Element Method in multilayered media with irregular interfaces[J]. Bulletin of the Seismological Society of America, 98(6): 3007-3016. doi: 10.1785/0120080920 [14] Hesselbrock A J, Minton D A. 2017. An ongoing satellite–ring cycle of Mars and the origins of Phobos and Deimos[J]. Nature Geoscience, 10: 266-269. doi: 10.1038/ngeo2916 [15] Lainey V, Casajus L G, Fuller J, et al. 2020. Resonance locking in giant planets indicated by the rapid orbital expansion of Titan[J]. Nature Astronomy, https://doi.org/10.1038/s41550-020-1120-5. [16] Lognonné P, Giardini D, Banerdt B, et al. 2000. The NetLander very broad band seismometer[J]. Planetary and Space Science, 48(12-14): 1289-1302. doi: 10.1016/S0032-0633(00)00110-0 [17] Mankovich C, Marley M S, Fortney J J, et al. 2019. Cassini ring seismology as a probe of Saturn's interior I: Rigid rotation[J]. The Astrophysical Journal, 871(1): 1. doi: 10.3847/1538-4357/aaf798 [18] Murdoch N, Hempel S, Pou L, et al. 2017. Probing the internal structure of the asteriod Didymoon with a passive seismic investigation[J]. Planetary Space Science, 144: 89-105. doi: 10.1016/j.pss.2017.05.005 [19] Quillen A C, Zhao Y, Chen Y, et al. 2019. Impact excitation of a seismic pulse and vibrational normal modes on asteroid Bennu and associated slumping of regolith[J]. Icarus, 319: 312-333. doi: 10.1016/j.icarus.2018.09.032 [20] Sánchez-Sesma F J, Campillo M. 1991. Diffraction of P, SV, and Rayleigh waves by topographic features: A boundary integral formulation[J]. Bulletin of the Seismological Society of America, 81(6): 2234-2253. [21] Sava P, Asphaug E. 2019. Seismology on small planetary bodies by orbital laser Doppler vibrometry[J]. Advances in Space Research, 64(2): 527-544. doi: 10.1016/j.asr.2019.04.017 [22] Stamos A, Beskos D. 1996. 3-D seismic response analysis of long lined tunnels in half-space[J]. Soil Dynamics and Earthquake Engineering, 15(2): 111-118. doi: 10.1016/0267-7261(95)00025-9 [23] Tian Y, Zheng Y. 2019. Rapid falling of an orbiting moon to its parent planet due to tidal-seismic resonance[J]. Planetary and Space Science: 104796. [24] Tian Y, Zheng Y. 2020. AstroSeis – A 3-D Boundary element modeling code for seismic wavefields in irregular asteroids and bodies[J]. Seismological Research Letters (in press). [25] Willner K, Shi X, Oberst J. 2014. Phobos' shape and topography models[J]. Planetary and Space Science, 102: 51-59. doi: 10.1016/j.pss.2013.12.006 [26] Zheng Y, Malallah A, Fehler M, Hu H. 2016. 2D full-waveform modeling of seismic waves in layered karstic media[J]. Geophysics, 81(2): T25-T34. doi: 10.1190/geo2015-0307.1 -
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