Investigation of the asymmetry of the Earth's gravitational field using the representation of potentials of disks

Simple item page
dc.citation.epage35
dc.citation.issue1(32)
dc.citation.journalTitleГеодинаміка
dc.citation.spage26
dc.contributor.affiliationНаціональний університет “Львівська політехніка”
dc.contributor.affiliationLviv Polytechnic National University
dc.contributor.authorФис, Михайло
dc.contributor.authorБридун, Андрій
dc.contributor.authorЮрків, Мар`яна
dc.contributor.authorСогор, Андрій
dc.contributor.authorГубар, Юрій
dc.contributor.authorFys, Mykhailo
dc.contributor.authorBrydun, Andrii
dc.contributor.authorYurkiv, Mariana
dc.contributor.authorSohor, Andrii
dc.contributor.authorHubar, Yurii
dc.coverage.placenameЛьвів
dc.coverage.placenameLviv
dc.date.accessioned2023-07-03T08:11:41Z
dc.date.available2023-07-03T08:11:41Z
dc.date.created2028-02-22
dc.date.issued2028-02-22
dc.description.abstractУ роботі розглянуто подання зовнішнього гравітаційного поля Землі, які доповнюють його традиційну апроксимацію рядами за кульовими функціями. Необхідність додаткових засобів опису зовнішнього потенціалу продиктована потребою його вивчення та використання в точках простору, що є близькими до поверхні Землі. Саме в таких областях виникає потреба дослідження збіжності рядів за кульовими функціями та адекватного визначення значення потенціалу. Представлення зовнішнього гравітаційного поля Землі інтегралами простого та подвійного прошарку із залученням апарату апроксимації кусково-неперервної функції в середині еліпса дає змогу розширити для рядів, що подають потенціал, область збіжності до всього простору поза еліпсом інтегрування. Тому, як результат, значення гравітаційного потенціалу збігається зі значеннями цих рядів поза тілом, що містить маси надр (крім еліпса інтегрування). Це дає можливість оцінювати поведінку гравітаційного поля в приповерхневих областях та виконувати з більшою достовірністю дослідження геодинамічних процесів. Апроксимація гравітаційного поля за допомогою поверхневих інтегралів окреслює також геофізичний аспект задачі. Адже під час її розв’язання здійснюється побудова двовимірних підінтегральних функцій, що однозначно визначаються набором стоксових сталих. При цьому коефіцієнти їх розкладів у ряди визначаються за лінійними комбінаціями степеневих моментів їх функцій. Отримані розклади функцій можуть бути використані для дослідження особливостей зовнішнього гравітаційного поля, наприклад, вивчення його асиметрії відносно екваторіальної площини.
dc.description.abstractThe paper considers representations of the Earth external gravitational field, supplementing its traditional approximation by series in spherical functions. The necessity for additional means of describing the external potential is dictated by the need to study and use it at points in space close to the Earth's surface. It is in such areas that the need arises to investigate the convergence of series with respect to spherical functions and to adequately determine the value of the potential. The apparatus for approximating a piecewise continuous function in the middle of the ellipse is used for the representation of the Earth external gravitational field by the simple and double layer integrals. This makes it possible to expand the convergence region for the series supplying the potential to the entire space outside the integration ellipse. Therefore, as a result, the value of the gravitational potential coincides with the values of these series outside the body containing the interior masses (except for the integration ellipse). It becomes possible to evaluate the gravitational field behavior in surface areas and to carry out studies of geodynamic processes with greater reliability. Approximation of the gravitational field with the help of surface integrals also determines the geophysical aspect of the problem. Indeed, in the process of solving the problem we constructed two-dimensional integrands, which are uniquely determined by a set of Stokes constants. In this case, their expansion coefficients into series are defined by linear combinations of their function power moments. The resulting function schedules can be used to study the external gravitational field features, e.g., to study its asymmetry with respect to the equatorial plane.
dc.format.extent26-35
dc.format.pages10
dc.identifier.citationInvestigation of the asymmetry of the Earth's gravitational field using the representation of potentials of disks / Mykhailo Fys, Andrii Brydun, Mariana Yurkiv, Andrii Sohor, Yurii Hubar // Geodynamics. — Lviv : Lviv Politechnic Publishing House, 2022. — No 1(32). — P. 26–35.
dc.identifier.citationenInvestigation of the asymmetry of the Earth's gravitational field using the representation of potentials of disks / Mykhailo Fys, Andrii Brydun, Mariana Yurkiv, Andrii Sohor, Yurii Hubar // Geodynamics. — Lviv : Lviv Politechnic Publishing House, 2022. — No 1(32). — P. 26–35.
dc.identifier.doidoi.org/10.23939/jgd2022.02.026
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/59369
dc.language.isoen
dc.publisherВидавництво Львівської політехніки
dc.publisherLviv Politechnic Publishing House
dc.relation.ispartofГеодинаміка, 1(32), 2022
dc.relation.ispartofGeodynamics, 1(32), 2022
dc.relation.referencesAntonov, V. A., Timoshkova, E. I. & Kholshevnikov,
dc.relation.referencesK. V. (1982). Comparative properties of
dc.relation.referencesvarious representations of the Earth's gravitational
dc.relation.referencesfield. Proceedings. I Oryol conference. “The study
dc.relation.referencesof the Earth as a planet by the methods of
dc.relation.referencesastronomy, geodesy and geophysics”. Kyiv, 93–108 (in Russian).
dc.relation.referencesAntonov, V. A., Timoshkova, E. I. & Kholshevnikov,
dc.relation.referencesK. V. (1988). Introduction to the theory of
dc.relation.referencesNewtonian potential. Science, Ch. ed. Phys.-Math.
dc.relation.referenceslit. (in Russian).
dc.relation.referencesAkhiezer, N. & Crane, M. O. (1938). Some questions
dc.relation.referencesof the theory of moments. Kharkov: GNTIU (in
dc.relation.referencesRussian
dc.relation.referencesAxler, S., Bourdon, P., & Wade, R. (2013). Harmonic
dc.relation.referencesfunction theory, Vol. 137. Springer Science &
dc.relation.referencesBusiness Media. https://sites.math.washington.edu/~morrow/336_18/HFT.pdf
dc.relation.referencesBateman, G. & Erdane, A. (1974). Higher transcendental
dc.relation.referencesfunctions. T. II. M.: Nauka (in Russian).
dc.relation.referencesFys, M. M, Brydun, A. M. & Yurkiv, M. I. (2018).
dc.relation.referencesMethod for approximate construction of threedimensional
dc.relation.referencesmass distribution function and
dc.relation.referencesgradient of an elipsoidal planet based on external
dc.relation.referencesgravitational field parameters. Geodynamics, 2(25), 27–36. https://doi.org/10.23939/jgdg2018.02.027
dc.relation.referencesFys, M. M, Brydun, A. M. & Yurkiv, M. I. (2019).
dc.relation.referencesResearching the influence of the mass distribution
dc.relation.referencesinhomogeneity of the ellipsoidal planet's interior
dc.relation.referenceson its stokes constants. Geodynamics, 1(26), 17–27. https://doi.org/10.23939/jgdg2019.01.017
dc.relation.referencesGrushinsky, N. P. (1983). Fundamentals of gravimetry.
dc.relation.referencesM: Science, Ch. ed. Phys.-Math. lit. (in
dc.relation.referencesRussian).
dc.relation.referencesHobson, E. W. (1953). Theory of spherical and
dc.relation.referencesellipsoidal functions. M.: Izd-vo inostr. lit. (in
dc.relation.referencesRussian).
dc.relation.referencesHofmann–Wellenhof, Dr. B. & Moritz, Dr. H. (2005).
dc.relation.referencesPhysical Geodesy. Springer. Wien- New York.
dc.relation.referencesKampé J. de Fériet, & P.E. (1926). Appell Fonctions
dc.relation.referenceshypergéometriques et hypersphériques. Paris,
dc.relation.referencesGauthier-Villars.
dc.relation.referencesKondratiev, B. P. (2007). Potential Theory. New
dc.relation.referencesmethods and problems with solutions. M.: Mir. (in
dc.relation.referencesRussian).
dc.relation.referencesKusche J., Schmidt R., Petrovic S., & Rietbroek R.,
dc.relation.references(2009). Decorrelated GRACE time-variable
dc.relation.referencesgravity solutions by GFZ and their validation
dc.relation.referencesusing a hydrological model. Journal of Geodesy, 83, 10, 903–913, http://doi.org/10.1007/s00190-009-0308-3
dc.relation.referencesLanderer F., Dickey J., & Zlotnicki V. (2010).
dc.relation.referencesTerrestrial water budget of the Eurasian pan-
dc.relation.referencesArctic from GRACE satellite measurements
dc.relation.referencesduring 2003-2009. J Geophys Res Atmos, D 23115. doi:10.1029/2010JD014584
dc.relation.referencesLandkof, N. S. (1966). Fundamentals of modern
dc.relation.referencespotential theory, M. (in Russian).
dc.relation.referencesMarchenko, A. N., Abrikosov, O. A. & Tsyupak, I. M.
dc.relation.references(1985). Point mass models and their use in the
dc.relation.referencesorbital method of satellite geodesy. 2. Application
dc.relation.referencesof point mass models for differential refinement of
dc.relation.referencesthe orbits of artificial Earth satellites (AES).
dc.relation.referencesKinematics and physics of celestial bodies, 1(5),72–80. (in Russian).
dc.relation.referencesMarchenko A. N., Lopushanskyi A. N. (2018).
dc.relation.referencesChange in the zonal harmonic coefficient C20,
dc.relation.referencesEarth’s polar flattening, and dynamical ellipticity
dc.relation.referencesfrom SLR data. Geodynamics 2(25), 5–14,
dc.relation.referenceshttps://doi.org/10.23939/jgd2018.02.005
dc.relation.referencesMeshcheryakov, G. A. (1991). Problems of potential
dc.relation.referencestheory and the generalized Earth. Moscow:
dc.relation.referencesScience, Ch. ed. physical-mat. lit. (in Russian).
dc.relation.referencesNational Imagery and Mapping Agency Technical
dc.relation.referencesReport TR 8350.2 Third Edition, Amendment 1, 1
dc.relation.referencesJan 2000, “Department of Defense World
dc.relation.referencesGeodetic System 1984”.
dc.relation.referencesOstach, O. M. & Ageeva, I. N. (1982). Approximation
dc.relation.referencesof the external gravitational field of the Earth to the
dc.relation.referencesmodel of gravitating point masses. Proceedings of
dc.relation.referencesthe I Oryol Conference. “The study of the Earth as a
dc.relation.referencesplanet by the methods of astronomy, geodesy and
dc.relation.referencesgeophysics”. Kyiv: Naukova Dumka, 106–107 (in
dc.relation.referencesRussian)
dc.relation.referencesPavlis, N. K., Holmes, S. A., Kenyon, S. C. & J. K.
dc.relation.referencesFactor. (2008). An Earth Gravitational Model to
dc.relation.referencesdegree 2160: EGM2008. EGU General Assembly.
dc.relation.referencesGeophysical Reaseach Abstracts. vol. 10, p. 2
dc.relation.references(EGU2008-A-018991). https://cir.nii.ac.jp/crid/1570009750863657728
dc.relation.referencesPellinen, L. P. (1978). Higher geodesy (Theoretical
dc.relation.referencesgeodesy). M.: Nedra (in Russian).
dc.relation.referencesSacerdote F, & Sanso F. (1991). Holes in Boundary
dc.relation.referencesand Out-of-Boundary Data. 1st International
dc.relation.referencesSymposium of the International Commission for
dc.relation.referencesthe GeoidAt: June 11–13, 1990 Milan, ItalyVolume:
dc.relation.referencesIAG Symposia no. 106 “Determination of the
dc.relation.referencesGeoid, Present and Future”, pp. 349–356.
dc.relation.referenceshttps://link.springer.com/chapter/10.1007/978-1-4612-3104-2_41
dc.relation.referencesShkodrov, V. G. & Ivanova, V. G. (1988). Asymmetry
dc.relation.referencesof the planet's gravitational field relative to the
dc.relation.referencesequatorial plane. Proceedings of the II Oryol
dc.relation.referencesConference. “The study of the Earth as a planet by
dc.relation.referencesthe methods of astronomy, geodesy and geophysics”.
dc.relation.referencesKyiv: Naukova Dumka, 66–71 (in Russian).
dc.relation.referencesTarakanov, Yu. A. & Cherevko, T. N. (1979).
dc.relation.referencesInterpretation of large-scale gravitational anomalies
dc.relation.referencesof the Earth. Academy of Sciences of the
dc.relation.referencesUSSR. Physics of the Earth, 4, 25–42 (in Russian).
dc.relation.referencesZavizion, O. V. (2000). Self-gravitating disks as a
dc.relation.referencesmeans of describing the external gravitational
dc.relation.referencesfields of celestial bodies. Kinematics and physics
dc.relation.referencesof celestial bodies, 16 (5), 477–480 (in Ukrainian).
dc.relation.referenceshttp://dspace.nbuv.gov.ua/handle/123456789/150089
dc.relation.referencesZavizion, O. V. (2001) On the determination of the
dc.relation.referencesdensity of equigravity rods, which are used to
dc.relation.referencesdescribe the external gravitational field of giant
dc.relation.referencesplanets. Kinematics and physics of celestial
dc.relation.referencesbodies, 17(1), 89–92. (in Ukrainian). http://dspace.nbuv.gov.ua/handle/123456789/149869
dc.relation.referencesenAntonov, V. A., Timoshkova, E. I. & Kholshevnikov,
dc.relation.referencesenK. V. (1982). Comparative properties of
dc.relation.referencesenvarious representations of the Earth's gravitational
dc.relation.referencesenfield. Proceedings. I Oryol conference. "The study
dc.relation.referencesenof the Earth as a planet by the methods of
dc.relation.referencesenastronomy, geodesy and geophysics". Kyiv, 93–108 (in Russian).
dc.relation.referencesenAntonov, V. A., Timoshkova, E. I. & Kholshevnikov,
dc.relation.referencesenK. V. (1988). Introduction to the theory of
dc.relation.referencesenNewtonian potential. Science, Ch. ed. Phys.-Math.
dc.relation.referencesenlit. (in Russian).
dc.relation.referencesenAkhiezer, N. & Crane, M. O. (1938). Some questions
dc.relation.referencesenof the theory of moments. Kharkov: GNTIU (in
dc.relation.referencesenRussian
dc.relation.referencesenAxler, S., Bourdon, P., & Wade, R. (2013). Harmonic
dc.relation.referencesenfunction theory, Vol. 137. Springer Science &
dc.relation.referencesenBusiness Media. https://sites.math.washington.edu/~morrow/336_18/HFT.pdf
dc.relation.referencesenBateman, G. & Erdane, A. (1974). Higher transcendental
dc.relation.referencesenfunctions. T. II. M., Nauka (in Russian).
dc.relation.referencesenFys, M. M, Brydun, A. M. & Yurkiv, M. I. (2018).
dc.relation.referencesenMethod for approximate construction of threedimensional
dc.relation.referencesenmass distribution function and
dc.relation.referencesengradient of an elipsoidal planet based on external
dc.relation.referencesengravitational field parameters. Geodynamics, 2(25), 27–36. https://doi.org/10.23939/jgdg2018.02.027
dc.relation.referencesenFys, M. M, Brydun, A. M. & Yurkiv, M. I. (2019).
dc.relation.referencesenResearching the influence of the mass distribution
dc.relation.referenceseninhomogeneity of the ellipsoidal planet's interior
dc.relation.referencesenon its stokes constants. Geodynamics, 1(26), 17–27. https://doi.org/10.23939/jgdg2019.01.017
dc.relation.referencesenGrushinsky, N. P. (1983). Fundamentals of gravimetry.
dc.relation.referencesenM: Science, Ch. ed. Phys.-Math. lit. (in
dc.relation.referencesenRussian).
dc.relation.referencesenHobson, E. W. (1953). Theory of spherical and
dc.relation.referencesenellipsoidal functions. M., Izd-vo inostr. lit. (in
dc.relation.referencesenRussian).
dc.relation.referencesenHofmann–Wellenhof, Dr. B. & Moritz, Dr. H. (2005).
dc.relation.referencesenPhysical Geodesy. Springer. Wien- New York.
dc.relation.referencesenKampé J. de Fériet, & P.E. (1926). Appell Fonctions
dc.relation.referencesenhypergéometriques et hypersphériques. Paris,
dc.relation.referencesenGauthier-Villars.
dc.relation.referencesenKondratiev, B. P. (2007). Potential Theory. New
dc.relation.referencesenmethods and problems with solutions. M., Mir. (in
dc.relation.referencesenRussian).
dc.relation.referencesenKusche J., Schmidt R., Petrovic S., & Rietbroek R.,
dc.relation.referencesen(2009). Decorrelated GRACE time-variable
dc.relation.referencesengravity solutions by GFZ and their validation
dc.relation.referencesenusing a hydrological model. Journal of Geodesy, 83, 10, 903–913, http://doi.org/10.1007/s00190-009-0308-3
dc.relation.referencesenLanderer F., Dickey J., & Zlotnicki V. (2010).
dc.relation.referencesenTerrestrial water budget of the Eurasian pan-
dc.relation.referencesenArctic from GRACE satellite measurements
dc.relation.referencesenduring 2003-2009. J Geophys Res Atmos, D 23115. doi:10.1029/2010JD014584
dc.relation.referencesenLandkof, N. S. (1966). Fundamentals of modern
dc.relation.referencesenpotential theory, M. (in Russian).
dc.relation.referencesenMarchenko, A. N., Abrikosov, O. A. & Tsyupak, I. M.
dc.relation.referencesen(1985). Point mass models and their use in the
dc.relation.referencesenorbital method of satellite geodesy. 2. Application
dc.relation.referencesenof point mass models for differential refinement of
dc.relation.referencesenthe orbits of artificial Earth satellites (AES).
dc.relation.referencesenKinematics and physics of celestial bodies, 1(5),72–80. (in Russian).
dc.relation.referencesenMarchenko A. N., Lopushanskyi A. N. (2018).
dc.relation.referencesenChange in the zonal harmonic coefficient P.20,
dc.relation.referencesenEarth’s polar flattening, and dynamical ellipticity
dc.relation.referencesenfrom SLR data. Geodynamics 2(25), 5–14,
dc.relation.referencesenhttps://doi.org/10.23939/jgd2018.02.005
dc.relation.referencesenMeshcheryakov, G. A. (1991). Problems of potential
dc.relation.referencesentheory and the generalized Earth. Moscow:
dc.relation.referencesenScience, Ch. ed. physical-mat. lit. (in Russian).
dc.relation.referencesenNational Imagery and Mapping Agency Technical
dc.relation.referencesenReport TR 8350.2 Third Edition, Amendment 1, 1
dc.relation.referencesenJan 2000, "Department of Defense World
dc.relation.referencesenGeodetic System 1984".
dc.relation.referencesenOstach, O. M. & Ageeva, I. N. (1982). Approximation
dc.relation.referencesenof the external gravitational field of the Earth to the
dc.relation.referencesenmodel of gravitating point masses. Proceedings of
dc.relation.referencesenthe I Oryol Conference. "The study of the Earth as a
dc.relation.referencesenplanet by the methods of astronomy, geodesy and
dc.relation.referencesengeophysics". Kyiv: Naukova Dumka, 106–107 (in
dc.relation.referencesenRussian)
dc.relation.referencesenPavlis, N. K., Holmes, S. A., Kenyon, S. C. & J. K.
dc.relation.referencesenFactor. (2008). An Earth Gravitational Model to
dc.relation.referencesendegree 2160: EGM2008. EGU General Assembly.
dc.relation.referencesenGeophysical Reaseach Abstracts. vol. 10, p. 2
dc.relation.referencesen(EGU2008-A-018991). https://cir.nii.ac.jp/crid/1570009750863657728
dc.relation.referencesenPellinen, L. P. (1978). Higher geodesy (Theoretical
dc.relation.referencesengeodesy). M., Nedra (in Russian).
dc.relation.referencesenSacerdote F, & Sanso F. (1991). Holes in Boundary
dc.relation.referencesenand Out-of-Boundary Data. 1st International
dc.relation.referencesenSymposium of the International Commission for
dc.relation.referencesenthe GeoidAt: June 11–13, 1990 Milan, ItalyVolume:
dc.relation.referencesenIAG Symposia no. 106 "Determination of the
dc.relation.referencesenGeoid, Present and Future", pp. 349–356.
dc.relation.referencesenhttps://link.springer.com/chapter/10.1007/978-1-4612-3104-2_41
dc.relation.referencesenShkodrov, V. G. & Ivanova, V. G. (1988). Asymmetry
dc.relation.referencesenof the planet's gravitational field relative to the
dc.relation.referencesenequatorial plane. Proceedings of the II Oryol
dc.relation.referencesenConference. "The study of the Earth as a planet by
dc.relation.referencesenthe methods of astronomy, geodesy and geophysics".
dc.relation.referencesenKyiv: Naukova Dumka, 66–71 (in Russian).
dc.relation.referencesenTarakanov, Yu. A. & Cherevko, T. N. (1979).
dc.relation.referencesenInterpretation of large-scale gravitational anomalies
dc.relation.referencesenof the Earth. Academy of Sciences of the
dc.relation.referencesenUSSR. Physics of the Earth, 4, 25–42 (in Russian).
dc.relation.referencesenZavizion, O. V. (2000). Self-gravitating disks as a
dc.relation.referencesenmeans of describing the external gravitational
dc.relation.referencesenfields of celestial bodies. Kinematics and physics
dc.relation.referencesenof celestial bodies, 16 (5), 477–480 (in Ukrainian).
dc.relation.referencesenhttp://dspace.nbuv.gov.ua/handle/123456789/150089
dc.relation.referencesenZavizion, O. V. (2001) On the determination of the
dc.relation.referencesendensity of equigravity rods, which are used to
dc.relation.referencesendescribe the external gravitational field of giant
dc.relation.referencesenplanets. Kinematics and physics of celestial
dc.relation.referencesenbodies, 17(1), 89–92. (in Ukrainian). http://dspace.nbuv.gov.ua/handle/123456789/149869
dc.relation.urihttps://sites.math.washington.edu/~morrow/336_18/HFT.pdf
dc.relation.urihttps://doi.org/10.23939/jgdg2018.02.027
dc.relation.urihttps://doi.org/10.23939/jgdg2019.01.017
dc.relation.urihttp://doi.org/10.1007/s00190-009-0308-3
dc.relation.urihttps://doi.org/10.23939/jgd2018.02.005
dc.relation.urihttps://cir.nii.ac.jp/crid/1570009750863657728
dc.relation.urihttps://link.springer.com/chapter/10.1007/978-1-4612-3104-2_41
dc.relation.urihttp://dspace.nbuv.gov.ua/handle/123456789/150089
dc.relation.urihttp://dspace.nbuv.gov.ua/handle/123456789/149869
dc.rights.holder© Інститут геології і геохімії горючих копалин Національної академії наук України, 2022
dc.rights.holder© Інститут геофізики ім. С. І. Субботіна Національної академії наук України, 2022
dc.rights.holder© Національний університет “Львівська політехніка”, 2022
dc.rights.holder© Fys Mykhailo, Brydun Andrii, Yurkiv Mariana, Sohor Аndrii, Hubar Yurii
dc.subjectасиметрія гравітаційного поля
dc.subjectЗемля
dc.subjectпотенціал
dc.subjectсфера Б’єрхамера
dc.subjectстоксові постійні
dc.subjectthe gravitational field asymmetry
dc.subjectEarth
dc.subjectpotential
dc.subjectBjerhamer sphere
dc.subjectStokes constants
dc.subject.udc528.21
dc.subject.udc551.24
dc.titleInvestigation of the asymmetry of the Earth's gravitational field using the representation of potentials of disks
dc.title.alternativeДослідження асиметрії гравітаційного поля Землі, поданого потенціалами плоских дисків
dc.typeArticle

Files

Original bundle
Now showing 1 - 2 of 2
No Thumbnail Available
Name:
2022n1_32__Fys_M-Investigation_of_the_asymmetry_26-35.pdf
Size:
653.52 KB
Format:
Adobe Portable Document Format
Download
No Thumbnail Available
Name:
2022n1_32__Fys_M-Investigation_of_the_asymmetry_26-35__COVER.png
Size:
1.53 MB
Format:
Portable Network Graphics
Download
License bundle
Now showing 1 - 1 of 1
No Thumbnail Available
Name:
license.txt
Size:
1.92 KB
Format:
Plain Text
Description:
Download

Collections

Геодинаміка. – 2022. – №1(32)