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Stochastic modelling of polyhedral gravity signal variations. Part I: First-order derivatives of gravitational potential.

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Title: Stochastic modelling of polyhedral gravity signal variations. Part I: First-order derivatives of gravitational potential.
Authors: Gavriilidou, Georgia1 (AUTHOR) georgiaga@topo.auth.gr, Tsoulis, Dimitrios1 (AUTHOR) tsoulis@auth.gr
Source: Journal of Geodesy. Mar2025, Vol. 99 Issue 3, p1-31. 31p.
Subjects: Legendre's functions, Line integrals, Spherical coordinates, Cartesian coordinates, Stochastic models
Abstract: The stochastic modelling of a finite mass distribution can provide a new perspective on the dynamic evaluation of time variable gravity fields. The algorithm for estimating variations of spherical harmonic coefficients implied by corresponding shape changes is implemented for the first-order derivatives of the gravitational potential. The described algorithm uses the spherical harmonic synthesis formula expressed in Cartesian coordinates that includes the derived Legendre functions (DLFs). Here, we expand the estimation process by implementing also the traditional spherical harmonic synthesis formula of normalized associated Legendre functions (ALFs) expressed in spherical coordinates. The variations obtained by applying the two approaches are compared with gravity signal differences induced by the modelled shape changes using the line integral analytical approach. The numerical comparisons refer to three asteroid shape models of Eros, Didymos and Dimorphos. The first-order derivative values provided by the DLF expressions and their variations using ALF are closer to the analytical method's results. The highest calculated differences refer to ΔVz with their mean value reaching 37% with respect to the other components obtained by all methods. Finally, the respective harmonic series converge to a fixed numerical value at a maximum expansion degree equal to 15 near Brillouin sphere and 5 as the distance of the computation point increases. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Geodesy is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Stochastic modelling of polyhedral gravity signal variations. Part I: First-order derivatives of gravitational potential.
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Geodesy%22">Journal of Geodesy</searchLink>. Mar2025, Vol. 99 Issue 3, p1-31. 31p.
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  Data: <searchLink fieldCode="DE" term="%22Legendre's+functions%22">Legendre's functions</searchLink><br /><searchLink fieldCode="DE" term="%22Line+integrals%22">Line integrals</searchLink><br /><searchLink fieldCode="DE" term="%22Spherical+coordinates%22">Spherical coordinates</searchLink><br /><searchLink fieldCode="DE" term="%22Cartesian+coordinates%22">Cartesian coordinates</searchLink><br /><searchLink fieldCode="DE" term="%22Stochastic+models%22">Stochastic models</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: The stochastic modelling of a finite mass distribution can provide a new perspective on the dynamic evaluation of time variable gravity fields. The algorithm for estimating variations of spherical harmonic coefficients implied by corresponding shape changes is implemented for the first-order derivatives of the gravitational potential. The described algorithm uses the spherical harmonic synthesis formula expressed in Cartesian coordinates that includes the derived Legendre functions (DLFs). Here, we expand the estimation process by implementing also the traditional spherical harmonic synthesis formula of normalized associated Legendre functions (ALFs) expressed in spherical coordinates. The variations obtained by applying the two approaches are compared with gravity signal differences induced by the modelled shape changes using the line integral analytical approach. The numerical comparisons refer to three asteroid shape models of Eros, Didymos and Dimorphos. The first-order derivative values provided by the DLF expressions and their variations using ALF are closer to the analytical method's results. The highest calculated differences refer to ΔVz with their mean value reaching 37% with respect to the other components obtained by all methods. Finally, the respective harmonic series converge to a fixed numerical value at a maximum expansion degree equal to 15 near Brillouin sphere and 5 as the distance of the computation point increases. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Geodesy is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1007/s00190-025-01937-7
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      – Code: eng
        Text: English
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        PageCount: 31
        StartPage: 1
    Subjects:
      – SubjectFull: Legendre's functions
        Type: general
      – SubjectFull: Line integrals
        Type: general
      – SubjectFull: Spherical coordinates
        Type: general
      – SubjectFull: Cartesian coordinates
        Type: general
      – SubjectFull: Stochastic models
        Type: general
    Titles:
      – TitleFull: Stochastic modelling of polyhedral gravity signal variations. Part I: First-order derivatives of gravitational potential.
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            – D: 01
              M: 03
              Text: Mar2025
              Type: published
              Y: 2025
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              Value: 99
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            – TitleFull: Journal of Geodesy
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