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COMPUTATIONAL ALGORITHM FOR DETAILING MODELS OF THE INTERNAL STRUCTURE OF PLANETS BASED ON STATISTICAL INVERSION OF GEODATA
1 Sсhmidt Institute of Physics of the Earth of the Russian Academy of Sciences
2 Science Research Institute of Economics and Management in Gas Industry, LLC
Journal: Geophysical research
Tome: 25
Number: 3
Year: 2024
Pages: 48-61
UDK: 523.4, 519.688, 551.31
DOI: 10.21455/gr2024.3-3
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Boronin
T.V I.A. COMPUTATIONAL ALGORITHM FOR DETAILING MODELS OF THE INTERNAL STRUCTURE OF PLANETS BASED ON STATISTICAL INVERSION OF GEODATA // . 2024. Т. 25. № 3. С. 48-61. DOI: 10.21455/gr2024.3-3
@article{Boronin
T.VCOMPUTATIONAL2024,
author = "Boronin
T.V, I. A.",
title = "COMPUTATIONAL ALGORITHM FOR DETAILING MODELS OF THE INTERNAL STRUCTURE OF PLANETS BASED ON STATISTICAL INVERSION OF GEODATA",
journal = "Geophysical research",
year = 2024,
volume = "25",
number = "3",
pages = "48-61",
doi = "10.21455/gr2024.3-3",
language = "English"
}
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Keywords: Monte Carlo method, inverse problem, Bayesian statistics, Markov chains, internal structure of the planets.
Аnnotation: Until recently, the choice of a model of the internal structure of a planet was carried out as a result of solving the direct problem based on its gravitational field data (mass, moment of inertia, tidal Love numbers k2) and the assumed geochemical composition. To match various model parameters with observed values, solving the inverse problem became relevant. One of the goals of this research is the development and implementation of a computational algorithm that will make it possible to easily and quickly add new initial data. At the first stage, a computational algorithm is created to determine the radial distributions of parameters of the internal structure of the planet from a set of observational data. Using the Bayesian approach to statistics, an inverse problem is formulated and solved using the Monte Carlo method with Markov chains. The probabilistic approach to solving the inverse problem significantly simplifies the problem of matching model parameters that satisfy observational data and a priori data. The Bayesian approach to statistics provides the ability to take into account the correspondence between the initial information about the model and the observed data.
The verification of the implemented computational algorithm was carried out on the classical model example of the inversion of gravitational field data. The results of the numerical experiment are presented graphically. The peculiarity of the algorithm for solving the problem is the complete independence of the calculation of each Markov chain from the others. The task is easily distributed evenly across all computing cores of a computer or cluster, which allows a multiple reduction in the running time of the computational algorithm, which is important in the future when increasing the input parameters. At the second stage of the work, it is planned to use the presented computational algorithm in order to find the distributions of parameters in the interiors of planets based on known observational data.
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Shen W., Ritzwoller M., Schlute-Pelkum V., Lin F., Joint inversion of surface wave dispersion and receiver func-tions: a Bayesian Monte-Carlo approach, Geophysical Journal International, 2013, vol. 192, pp. 807-836. https://doi.org/10.1093/gji/ggs050
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Ceylan S., Clinton J., Giardini D., Stähler S., Horleston A., Kawamura T., Böse M., Charalambous C., Dah-men N., Van Driel M., Duran C., Euchner F., Khan A., Kim D., Plasman M., Scholz J.-R., Zenhäusern G., Beucler É., Garcia R., Kedar S., Knapmeyer M., Lognonne P., Panning M., Perrin C., Pike W.T., Stott A., Banerdt W.B., The marsquake catalogue from InSight, sols 0-1011, Physics of the Earth and Planetary Interiors, 2022, vol. 333, 43 p.
Drilleau M., Beucler E., Mocquet A., Verhoeven O., Moebs G., Burgos G., Montagner J.-P., Vacher P., A Bayesi-an approach to infer radial models of temperature and anisotropy in the transition zone from surface wave dispersion curves, Geophysical Journal International, 2013, vol. 195, pp. 1165-1183. https://doi.org/10.1093/gji/ggt284
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 Ph., Nakamura Y., Zhu P., Lunar Seismology: An Update on Inte-rior Structure Models, Space Science Reviews, 2019, vol. 215, 47 p. https://doi.org/10.1007/s11214-019-0613-y
Harada Y., Reconsideration of the anelasticity parameters of the martian mantle: Preliminary estimates based on the latest geodetic parameters and seismic models, Icarus, 2022, vol. 383, 114917. https://doi.org/10.1016/j.icarus.2022.114917
Khan A., Connolly J.A.D., Maclennan J., Mosegaard K., Joint inversion of seismic and gravity data for lunar composition and thermal state, Geophysical Journal International, 2007, vol. 168, pp. 243-258. https://doi.org/10.1111/j.1365-246X.2006.03200.x
Khan A., Connolly J.A.D., Pommier A., Noir J., Geophysical evidence for melt in the deep lunar interior and im-plications for lunar evolution, Journal of Geophysical Research: Planets, 2014, vol. 119, no. 10, pp. 2197-2221. https://doi.org/10.1002/2014JE004661
Khan A., Sossi P., Liebske C., Rivoldini A., Giardini D., Geophysical and cosmochemical evidence for a volatile-rich Mars, Earth and Planetary Science Letters, 2022, vol. 578, 16 p.
Kronrod E., Matsumoto K., Kuskov O.L., Kronrod V., Yamada R., Kamata S., Towards geochemical alterna-tives to geophysical models of the internal structure of the lunar mantle and core, Advances in Space Re-search, 2022, vol. 69, no. 7, pp. 2798-2824.
Kuskov O.L., Kronrod E.V., Matsumoto K., Kronrod V.A., Physical properties and internal structure of the cen-tral region of the Moon, Geochemistry International, 2021, vol. 59, no. 11, pp. 1018-1037. DOI: 10.1134/S0016702921110069
Matsumoto K., Yamada R., Kikuchi F., Kamata S., Ishihara Y., Iwata T., Hanada H., Sasaki S., Internal struc-ture of the Moon inferred from Apollo seismic data and selenodetic data from GRAIL and LLR, Geo-physical Research Letters, 2015, vol. 42, no. 18, pp. 7351-7358.
Metropolis N., Rosenbluth A.W., Rosenbluth M.N., Teller A.H., Teller E., Equation of state calculations by fast computing machines, Journal of Chemical Physics, 1953, vol. 21, no. 6, pp. 1087-1092.
Mosegaard K., Resolution analysis of general inverse problems through inverse Monte Carlo sampling, Inverse Problems, 1998, vol. 14, no. 3, pp. 405-426.
Mosegaard K., Tarantola A., Monte Carlo sampling of solutions to inverse problems, Journal of Geophysical Research: Solid Earth, 1995, vol. 100, no. B7, pp. 12431-12447.
Nunn C., Garcia R.F., Nakamura Y., Marusiak A.G., Kawamura T., Sun D., Margerin L., Weber R.C., Drilleau M., Wieczorek M.A., Khan A., Rivoldini A., Lognonné Ph., Zhu P., Lunar seismology: A data and instrumentation review, Space Science Reviews, 2020, vol. 216, 39 p.
Rivoldini A., Van Hoolst T., The interior structure of Mercury constrained by the low-degree gravity field and the rotation of Mercury, Earth and Planet. Science Letters, 2013, vol. 377–378, pp. 62-72.
Rivoldini A., Van Hoolst T., Verhoeven O., Mocquet A., Dehant V., Geodesy constraints on the interior structure and composition of Mars, Icarus, 2011, vol. 213, pp. 451-472.
Rosenblatt P., Dumoulin C., Marty J.-C., Genova A., Determination of Venus’ interior structure with EnVision, Remote Sensing, 2021, vol. 13, 14 p.
Shah O., Helled R., Alibert Y., Mezger K., Possible chemical composition and interior structure models of Venus inferred from numerical modeling, The Astrophysical Journal, 2022, vol. 926, 20 p.
Shapiro N.M., Ritzwoller M.H., Monte-Carlo inversion for a global shear-velocity model of the crust and upper mantle, Geophysical Journal International, 2002, vol. 151, pp. 88-105.
Shen W., Ritzwoller M., Schlute-Pelkum V., Lin F., Joint inversion of surface wave dispersion and receiver func-tions: a Bayesian Monte-Carlo approach, Geophysical Journal International, 2013, vol. 192, pp. 807-836. https://doi.org/10.1093/gji/ggs050
Tarantola A., Inverse Problem Theory: Methods for Data Fitting and Model Parameter Estimation, New York, Elsevier, 1987, 613 p.
Tarantola A., Inverse Problem Theory and Methods for Model Parameter Estimation, Philadelphia, USA, Socie-ty for Industrial and Applied Mathematics, 2005, 342 p.
Tarantola A., Valette B., Inverse problems – Quest for information, Journal of Geophysics, 1982, vol. 50, pp. 159-170.
Xiao C., Li F., Yan J.-G., Hao W.-F., Harada Y., Ye M., Barriot J.-P., Inversion of Venus internal structure based on geodetic data, Research in Astronomy and Astrophysics, 2020, vol. 20, no. 8, pp. 127-141.
