Development of a new more precise algorithm for computing tidal Love numbers

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Abstract

Tidal Love numbers are often used for studying the interior structure of planets and satellites of the Solar System. Measuring the deformation in response to tidal loading belongs to the methods for probing the interiors. The algorithm for computing tidal deformation depends on a series of assumptions and approximations and, therefore, can differ according to different authors. In this paper we compare the existing methods and, based on them, we propose a new and more precise algorithm for computing the tidal Love numbers of the Earth and other bodies with a similar interior structure.

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About the authors

D. O. Amorim

Moscow Institute of Physics and Technology

Author for correspondence.
Email: amorim.dargilan@gmail.com
Russian Federation, Dolgoprudny, Moscow Region

T. V. Gudkova

Sсhmidt Institute of Physics of the Earth of the Russian Academy of Sciences

Email: gudkova@ifz.ru
Russian Federation, Moscow

References

  1. Love A.E.H. The yielding of the Earth to disturbing forces // Proc. Тhe Royal Society of London. Series A. Containing Papers of a Mathematical and Physical Character. 1909. 82.551. P. 73–88.
  2. Amorim D.O., Гудкова Т.В. Внутреннее строение Венеры на основе модели PREM // Астрон. вестн. 2023. Т. 57(5). С. 403–414.
  3. Dumoulin C., Tobie G., Verhoeven O., et al.Tidal constraints on the interior of Venus // J. Geophysical Research: Planets. 2017. V. 122(6). P. 1338–1352.
  4. Steinbrugge G., Padovan S., Hussmann H., et al. Viscoelastic tides of Mercury and the determination of its inner core size // J. Geophysical Research: Planets. 2018. V. 123(10). P. 2760–2772.
  5. Bagheri A., Khan A., Al-Attar D., et al. Tidal response of mars constrained from laboratory-based viscoelastic dissipation models and geophysical data // J. Geophysical Research: Planets. 2019. V. 124(11). P. 2703–2727.
  6. Alterman Z., Hans Jarosch, Pekeris C.L. Oscillations of the Earth. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences. 1959. 252.1268. P. 80–95.
  7. Chinnery M.A. The static deformation of an earth with a fluid core: a physical approach // Geophysical J. Intern. 1975. V. 42. № 2. P. 461–475.
  8. Longman I.M. A Green’s function for determining the deformation of the Earth under surface mass loads: 2. Computations and numerical results // J. Geophysical Research. 1963. V. 68. № 2. P. 485–496.
  9. Saito M. Some problems of static deformation of the Earth // J. Physics of the Earth. 1974. V. 22(1). P. 123–140.
  10. Helffrich G., Satoshi Kaneshima. Outer-core compositional stratification from observed core wave speed profiles // Nature. 2010. № 468. P. 807–810.
  11. Michel A., Jean-Paul Boy. Viscoelastic Love numbers and long-period geophysical effects // Geophysical J. International. 2022. V. 228. № 2. P. 1191–1212.
  12. Virtanen P. et al. SciPy 1.0: fundamental algorithms for scientific computing in Python // Nature methods. 2020. V. 17. № 3. P. 261–272.
  13. Petit Gerard, Brian Luzum. IERS technical note No. 36, IERS conventions (2010) / International Earth Rotation and Reference Systems Service: Frankfurt, Germany, 2010.

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2. Fig. 1. Comparison of values in the external core. The Adams–Williamson condition does not hold at the boundary of the inner core and at the boundary of the mantle.

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