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ON FINDING THE ANALYTICAL CONTINUATION OF THE MAGNETIC FIELD OF MARS FROM SATELLITE DATA USING A COMBINED APPROACH
1 Sсhmidt Institute of Physics of the Earth of the Russian Academy of Sciences
2 Trapeznikov Institute of Control Sciences of the Russian Academy of Sciences
3 Lomonosov Moscow State University,
Journal: Geophysical research
Tome: 24
Number: 2
Year: 2023
Pages: 58-83
UDK: 550.8, 523.43
DOI: 10.21455/gr2023.2-4
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Stepanova
A.M I.E. ON FINDING THE ANALYTICAL CONTINUATION OF THE MAGNETIC FIELD OF MARS FROM SATELLITE DATA USING A COMBINED APPROACH
// . 2023. Т. 24. № 2. С. 58-83. DOI: 10.21455/gr2023.2-4
@article{Stepanova
A.MON2023,
author = "Stepanova
A.M, I. E.",
title = "ON FINDING THE ANALYTICAL CONTINUATION OF THE MAGNETIC FIELD OF MARS FROM SATELLITE DATA USING A COMBINED APPROACH
",
journal = "Geophysical research",
year = 2023,
volume = "24",
number = "2",
pages = "58-83",
doi = "10.21455/gr2023.2-4",
language = "English"
}
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Keywords: regularization method, analytical continuation, time-dependent integral representation
Аnnotation: Using a combined approach, analytical models of the magnetic field of Mars are constructed based on satellite data measured by the MAG magnetometer of the American MAVEN mission in the landing area of the Zhurong rover of the Chinese Tianwen-1 mission. A new method for interpreting Mars remote sensing data is described, which includes the construction of regional modified S-approximations taking into account ellipticity (for an ellipsoid of revolution) and local (flat) approximations of a non-stationary field, which is the solution of some parabolic-type equation with constant coefficients. The main provisions of the method of linear integral representations are developed as applied to time-dependent differential operators, which is of fundamental importance in solving many inverse problems of mathematical geophysics. The time-dependent magnetic field of Mars has been studied in the Cartesian coordinate system, so far only a local version of a new technique for solving inverse problems of magnetic exploration has been developed due to the complexity of the problem of analytical description of a non-stationary field on a global scale. The results of a mathematical experiment on the analytical continuation of the magnetic field of Mars from the orbit towards the sources are presented.
The new technique is based on the construction of a modified S-approximation in the regional version for a given set of observation points in three-dimensional space and given initial approximations to unknown weight functions. According to the found distribution of sources equivalent in external magnetic field on the surface of several generalized spheres, the approximated field is analytically continued into a certain region of three- dimensional space. In this case, the value of the solution quality index is calculated, which is the ratio of the Euclidean norm of the difference between the theoretical values of the field and the values obtained as a result of the approximation, to the norm of the field itself. The weight functions are changed in accordance with the rule defined by the researcher, the process is repeated until the required accuracy is achieved. The calculated values of the magnetic field in a certain region of three-dimensional space are taken as the initial and boundary values of the time-dependent vector function, which is the solution of a three-dimensional homogeneous (or inhomogeneous) parabolic equation. For such a vector-function, a variational problem is posed, within the framework of the local version of the method of integral representations in three-dimensional space with time dependence, to find the sources of masses. The sources can be distributed either on a family of planes of three-dimensional space, if the initial-boundary value problem for the heat equation is considered, or on some discrete network of points, if it is assumed that the vector function is a solution of a parabolic type equation in the entire space.
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Martyshko P.S., Ladovskij I.V., Byzov D.D., Chernoskutov A.I., On Solving the Forward Problem of Gravim- etry in Curvilinear and Cartesian Coordinates: Krasovskii's Ellipsoid and Plane Modeling, Izvestiya, Phys- ics of the Solid Earth, 2018, vol. 54, no. 4, pp. 565-573. DOI: 10.1134/S1069351318040079
Mittelholz A., Johnson C.L., Morschhauser A., A New Magnetic Field Activity Proxy for Mars From MAVEN Data, Geophysical Research Letters, 2018, vol. 45, pp. 5899-5907.
Mikhailov V.O., Timoshkina E.P., Kiseleva E.A., Khairetdinov S.A., Dmitriev P.N., Kartashov I.M., Smir- nov V.B., Problems of the Joint Inversion of Temporal Gravity Variations with the Data on Land and Sea- floor Displacements: a Case Study of the Tohoku-Oki Earthquake of March 11, 2011, Izvestiya, Physics of the Solid Earth, 2019, vol. 55, no. 5, pp. 746-752. DOI: 10.1134/S1069351319050070
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Pan L., Quantin-Nataf C., Tauzin B., Michaut C., Golombek M., Lognonné P., Grindrod P., Langlais B., Gudko- va T., Stepanova I., Rodriguez S., Lucas A., Crust heterogeneities and structure at the dichotomy boundary in western Elysium Planitia and Implications for InSight lander, Icarus, 2020, vol. 338, 113511, 19 p. DOI: 10.1016/j.icarus.2019.113511
Portniaguine O., Zhdanov M., Focusing geophysical inversion images, Geophysics, 1999, vol. 64, pp. 874-887. Portniaguine O., Zhdanov M., 3-D magnetic inversion with data compression and image focusing, Geophysics,
2002, vol. 67, pp. 1532-1541.
Reshetnyak M.Yu., Spatial spectra of the geomagnetic field in the observations and geodynamo models, Izves- tiya, Physics of the Solid Earth, 2015, vol. 51, no. 3, pp. 354-361.
Salnikov А.M., Batov A.V., Gudkova T.V., Stepanova I.E., Analysis of the magnetic field data of Mars, in The Eleventh Moscow Solar System Symposium (11M-S3). 5–9 October 2020, Moscow, Space Research Insti- tute of the Russian Academy of Sciences (IKI), 2020, pp. 73-74. DOI: 0.21046/11MS3-2020
Salnikov A., Stepanova I., Gudkova T., Batov A., Analytical modeling of the magnetic field of Mars from satel- lite data using modified S-approximations, Doklady Earth Sciences, 2021, vol. 499, pp. 575-579. https://doi.org/10.1134/S1028334X21070096
Schattner U., Segev A., Mikhailov V., Rybakov M., Lyakhovsky V., Magnetic Signature of the Kinneret– Kinarot Tectonic Basin Along the Dead Sea Transform, Northern Israel, Pure and Applied Geophysics, 2019, vol. 176, pp. 4383-4399.
Shimbirev B.P., Teorija figury Zemli (Theory of the figure of the Earth), Moscow, Nedra, 1975, 432 p. [In Russian].
Stepanova I.E., On the S-approximation of the Earth’s gravity field: Regional version, Inverse Problems in Sci- ence and Engineering, 2009, vol. 17, pp. 1095-1111.
Stepanova I.E., Shchepetilov A.V., Mikhailov P.S., Analytical Models of the Physical Fields of the Earth in Re- gional Version with Ellipticity, Izvestiya, Physics of the Solid Earth, 2022, vol. 58, no. 3, pp. 406-419. DOI: 10.1134/S1069351322030089
Stepanova I.E., Shchepetilov A.V., Pogorelov V.V., Mikhailov P.S., Parametric Structural Approach to Con- structing Digital Models of the Relief and Gravitational Field of the Earth Using Analytical S- Approximations, Izvestiya, Atmospheric and Oceanic Physics, 2020, vol. 56, no. 8, pp. 859-868. https:// doi.org/10.1134/S0001433820080083
Stepanova I., Kerimov I., Raevskiy D., Shchepetilov A., Improving the methods for processing large data in geophysics and geomorphology based on the modified S- and F-approximations, Izvestiya, Physics of the Solid Earth, 2020, vol. 56, no. 3, pp. 364-378.
Strakhov V.N., Stepanova I.E., Method of S-approximations and its use in solving problems of gravimetry (re- gional version), Fizika Zemli (Izvestiya, Physics of the Solid Earth), 2002, no. 7, pp. 3-12. [In Russian].
Strakhov V.N., Stepanova I.E., Solution of gravity problems by the S-approximation method (regional version),
Izvestiya, Physics of the Solid Earth, 2002, vol. 38, no. 7, pp. 535-544.
Titov V.V., Stepanov R.A., Sokoloff D.D., Transient Regimes of the Screw Dynamo, Journal of Experimental and Theoretical Physics, 2020, vol. 130, pp. 287-292. https://doi.org/10.1134/S1063776120010100
Uieda L., Barbosa V.C.F., Braitenberg C., Tesseroids: Forward-modeling gravitational fields in spherical coor- dinates, Geophysics, 2016, vol. 81, no. 5, pp. F41-F48. DOI: 10.1190/geo2015-0204.1
Vladimirov V.V., Uravnenija matematicheskoj fiziki (Equations of mathematical physics), Moscow, Nauka, 1981, 512 p. [In Russian].
Wang Y., Kolotov I., Lukyanenko D., Yagola A., Reconstruction of magnetic susceptibility using full magnetic gradient data, Computational Mathematics and Mathematical Physics, 2020a, vol. 60, pp. 1000-1007. https://doi.org/10.1134/S096554252006010X
Wang Y., Leonov A., Lukyanenko D., Yagola A., General Tikhonov regularization with applications in geo- science, CSIAM Transaction on Applied Mathematics, 2020b, vol. 1, pp. 53-85. doi: 10.4208/csiam-am. 2020-0004
Wang Y., Lukyanenko D., Yagola A., Magnetic parameters inversion method with full tensor gradient data, In- verse Problems and Imaging, 2019, vol. 13, pp. 745-754.
Whaler K.A., Purucker M.E., A spatially continuous magnetization model for Mars, Journal of Geophysical Re- search: Planets, 2005, vol. 110, E09001, 11 p. doi: 10.1029/2004JE002393
Yagola A.G., Stepanova I.E., Titarenko V.N., Wang Y., Obratnye zadachi i metody ih reshenija. Prilozhenija k geofizike (Inverse problems and methods for their solution. Applications to geophysics), Moscow, Binom, 2014, 216 p. [In Russian].
Arkani-Hamed J., An improved 50-degree spherical harmonic model of the magnetic field of Mars derived from both high-altitude and low-altitude data, Journal of Geophysical Research: Planets, 2002, vol. 107, pp. 13.1-13.8. DOI: 10.1029/2001JE001835
Arnold V.I., Khesin B.A., Topological Methods in Hydrodynamics, New York, Springer-Verlag, 1998, 391 p. Budak B.M., Samarsky A.A., Tikhonov A.N., Sbornik zadach po uravnenijam matematicheskoj fiziki (Collec-
tion of problems on the equations of mathematical physics), Moscow, Nauka, 1980, 687 p. [In Russian].
Frick P.G., Sokoloff D.D., Stepanov R.A., Wavelets for the space-time structure analysis of physical fields,
Physics–Uspekhi, 2022, vol. 65, pp. 62-89. DOI: 10.3367/UFNe.2020.10.038859
Gudkova T., Stepanova I., Batov A., Density anomalies in subsurface layers of mars: model estimates for the Site of the InSight Mission Seismometer, Solar System Research, 2020, vol. 54, pp. 15-19. DOI: 10.1134/ S0038094620010037
Gudkova T., Stepanova I., Batov A., Shchepetilov A., Modified method S- and R-approximations in solving the problems of Mars’s morphology, Inverse Problems in Science and Engineering, 2021, vol. 29, pp. 790- 804. DOI: 10.1080/17415977.2020.1813125
Kazantsev S.G., Kardakov V.B., Poloidal-Toroidal Decomposition of Solenoidal Vector Fields in the Ball, Jour- nal of Applied and Industrial Mathematics, 2019, vol. 13, pp. 480-499. https://doi.org/10.1134/ S1990478919030098
Ladovskiy I.V., Byzov D.D., Chernoskutov A.I., On the Problem of Construction of Medium-Scale Density Models for the Spheroidal Earth, Ural'skiyGeofizicheskiyVestnik (Ural Geophysical Bulletin), 2017, no. 1, pp. 73-97. [In Russian]. DOI: 10.25698/UGV.2017.1.12031
Langlais B., Thébault E., Houliez A., Purucker M.E., Lillis R.J., A New Model of the Crustal Magnetic Field of Mars Using MGS and MAVEN, Journal of Geophysical Research: Planets, 2019, vol. 124, pp. 1542-1569.
Langlais B., Purucker M.E., Mandea M., Crustal magnetic field of Mars, Journal of Geophysical Research: Pla- nets, 2004, vol. 109, E02008, 16 p.
Liu J., Li Ch., Zhang R., Rao W., Cui X., Geng Y., Jia Y., Huang H., Ren X., Yan W., Zeng X., Wen W.,
Wang X., Gao X., Fu Q., Zhu Y., Dong J., Li H., Wang X., Zuo W., Su Y., Kong D., Zhang H., Geomorphic contexts and science focus of the Zhurong landing site on Mars, Nature Astronomy, 2022, vol. 6, pp. 65-71. https://doi.org/10.1038/s41550-021-01519-5
Malkin Z.A., New Equal-area Isolatitudinal Grid on a Spherical Surface, The Astronomical Journal, 2019, vol. 158, no. 4, pp. 1-4. doi:10.3847/1538-3881/ab3a44
Martyshko P.S., Fedorova N.V., Rublev A.L., Numerical algorithms for structural magnetometry inverse problem solving, Russian Journal of Earth Sciences, 2021, vol. 21, ES3002, 9 p. doi: 10.2205/2021ES000766
Martyshko P.S., Ladovskij I.V., Byzov D.D., Chernoskutov A.I., On Solving the Forward Problem of Gravim- etry in Curvilinear and Cartesian Coordinates: Krasovskii's Ellipsoid and Plane Modeling, Izvestiya, Phys- ics of the Solid Earth, 2018, vol. 54, no. 4, pp. 565-573. DOI: 10.1134/S1069351318040079
Mittelholz A., Johnson C.L., Morschhauser A., A New Magnetic Field Activity Proxy for Mars From MAVEN Data, Geophysical Research Letters, 2018, vol. 45, pp. 5899-5907.
Mikhailov V.O., Timoshkina E.P., Kiseleva E.A., Khairetdinov S.A., Dmitriev P.N., Kartashov I.M., Smir- nov V.B., Problems of the Joint Inversion of Temporal Gravity Variations with the Data on Land and Sea- floor Displacements: a Case Study of the Tohoku-Oki Earthquake of March 11, 2011, Izvestiya, Physics of the Solid Earth, 2019, vol. 55, no. 5, pp. 746-752. DOI: 10.1134/S1069351319050070
Oliveira J.S., Langlais B., Pais M.A., Amit H., A modified equivalent source dipole method to model partially distributed magnetic field measurements, with application to Mercury, Journal of Geophysical Research: Planets, 2015, vol. 120, pp. 1075-1094. DOI: 10.1002/2014JE004734
Pan L., Quantin-Nataf C., Tauzin B., Michaut C., Golombek M., Lognonné P., Grindrod P., Langlais B., Gudko- va T., Stepanova I., Rodriguez S., Lucas A., Crust heterogeneities and structure at the dichotomy boundary in western Elysium Planitia and Implications for InSight lander, Icarus, 2020, vol. 338, 113511, 19 p. DOI: 10.1016/j.icarus.2019.113511
Portniaguine O., Zhdanov M., Focusing geophysical inversion images, Geophysics, 1999, vol. 64, pp. 874-887. Portniaguine O., Zhdanov M., 3-D magnetic inversion with data compression and image focusing, Geophysics,
2002, vol. 67, pp. 1532-1541.
Reshetnyak M.Yu., Spatial spectra of the geomagnetic field in the observations and geodynamo models, Izves- tiya, Physics of the Solid Earth, 2015, vol. 51, no. 3, pp. 354-361.
Salnikov А.M., Batov A.V., Gudkova T.V., Stepanova I.E., Analysis of the magnetic field data of Mars, in The Eleventh Moscow Solar System Symposium (11M-S3). 5–9 October 2020, Moscow, Space Research Insti- tute of the Russian Academy of Sciences (IKI), 2020, pp. 73-74. DOI: 0.21046/11MS3-2020
Salnikov A., Stepanova I., Gudkova T., Batov A., Analytical modeling of the magnetic field of Mars from satel- lite data using modified S-approximations, Doklady Earth Sciences, 2021, vol. 499, pp. 575-579. https://doi.org/10.1134/S1028334X21070096
Schattner U., Segev A., Mikhailov V., Rybakov M., Lyakhovsky V., Magnetic Signature of the Kinneret– Kinarot Tectonic Basin Along the Dead Sea Transform, Northern Israel, Pure and Applied Geophysics, 2019, vol. 176, pp. 4383-4399.
Shimbirev B.P., Teorija figury Zemli (Theory of the figure of the Earth), Moscow, Nedra, 1975, 432 p. [In Russian].
Stepanova I.E., On the S-approximation of the Earth’s gravity field: Regional version, Inverse Problems in Sci- ence and Engineering, 2009, vol. 17, pp. 1095-1111.
Stepanova I.E., Shchepetilov A.V., Mikhailov P.S., Analytical Models of the Physical Fields of the Earth in Re- gional Version with Ellipticity, Izvestiya, Physics of the Solid Earth, 2022, vol. 58, no. 3, pp. 406-419. DOI: 10.1134/S1069351322030089
Stepanova I.E., Shchepetilov A.V., Pogorelov V.V., Mikhailov P.S., Parametric Structural Approach to Con- structing Digital Models of the Relief and Gravitational Field of the Earth Using Analytical S- Approximations, Izvestiya, Atmospheric and Oceanic Physics, 2020, vol. 56, no. 8, pp. 859-868. https:// doi.org/10.1134/S0001433820080083
Stepanova I., Kerimov I., Raevskiy D., Shchepetilov A., Improving the methods for processing large data in geophysics and geomorphology based on the modified S- and F-approximations, Izvestiya, Physics of the Solid Earth, 2020, vol. 56, no. 3, pp. 364-378.
Strakhov V.N., Stepanova I.E., Method of S-approximations and its use in solving problems of gravimetry (re- gional version), Fizika Zemli (Izvestiya, Physics of the Solid Earth), 2002, no. 7, pp. 3-12. [In Russian].
Strakhov V.N., Stepanova I.E., Solution of gravity problems by the S-approximation method (regional version),
Izvestiya, Physics of the Solid Earth, 2002, vol. 38, no. 7, pp. 535-544.
Titov V.V., Stepanov R.A., Sokoloff D.D., Transient Regimes of the Screw Dynamo, Journal of Experimental and Theoretical Physics, 2020, vol. 130, pp. 287-292. https://doi.org/10.1134/S1063776120010100
Uieda L., Barbosa V.C.F., Braitenberg C., Tesseroids: Forward-modeling gravitational fields in spherical coor- dinates, Geophysics, 2016, vol. 81, no. 5, pp. F41-F48. DOI: 10.1190/geo2015-0204.1
Vladimirov V.V., Uravnenija matematicheskoj fiziki (Equations of mathematical physics), Moscow, Nauka, 1981, 512 p. [In Russian].
Wang Y., Kolotov I., Lukyanenko D., Yagola A., Reconstruction of magnetic susceptibility using full magnetic gradient data, Computational Mathematics and Mathematical Physics, 2020a, vol. 60, pp. 1000-1007. https://doi.org/10.1134/S096554252006010X
Wang Y., Leonov A., Lukyanenko D., Yagola A., General Tikhonov regularization with applications in geo- science, CSIAM Transaction on Applied Mathematics, 2020b, vol. 1, pp. 53-85. doi: 10.4208/csiam-am. 2020-0004
Wang Y., Lukyanenko D., Yagola A., Magnetic parameters inversion method with full tensor gradient data, In- verse Problems and Imaging, 2019, vol. 13, pp. 745-754.
Whaler K.A., Purucker M.E., A spatially continuous magnetization model for Mars, Journal of Geophysical Re- search: Planets, 2005, vol. 110, E09001, 11 p. doi: 10.1029/2004JE002393
Yagola A.G., Stepanova I.E., Titarenko V.N., Wang Y., Obratnye zadachi i metody ih reshenija. Prilozhenija k geofizike (Inverse problems and methods for their solution. Applications to geophysics), Moscow, Binom, 2014, 216 p. [In Russian].
