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Relation of Different Type Love–Shida Numbers Determined with the Use of Time-Varying Incremental Gravitational Potential

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Abstract

There are different equations to describe relations between different classes of Love–Shida numbers. In this study with the use of the time-varying gravitational potential an integral relation was obtained which connects tidal Love–Shida numbers (h, l, k), load numbers (h′, l′, k′), potential free Love–Shida numbers generated by normal (h″, l″, k″) and horizontal (h‴, l‴, k‴) stresses. The equations obtained in frame of present study is the only one which

  • holds for every type of Love–Shida numbers,

  • describes a relationship not between different, but the same type of Love–Shida numbers,

  • does not follow from the sixth-order differential equation system of motion usually applied to calculate the Love–Shida numbers.

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Acknowledgements

We thank the Guest Editor David Crossley and an anonymous reviewer colleague for their helpful comments. The research described in this paper was completed during research stay of P. Varga (01.03.2016–31.05.2016) supported by the Alexander Humboldt Foundation at the Department of Geodesy and Geoinformatics, Stuttgart University. P. Varga thanks Professor Nico Sneeuw for the excellent research conditions provided by him. Financial support from the Hungarian Scientific Research Found OTKA (Project K125008) is acknowledged.

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Authors and Affiliations

  1. Seismological Observatory, Institute of Geodesy and Geophysics, Budapest, Hungary

    Peter Varga

  2. Department of Geodesy and Geoinformatics, Stuttgart University, Stuttgart, Germany

    Erik Grafarend & Johannes Engels

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  1. Peter Varga
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  2. Erik Grafarend
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  3. Johannes Engels
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Correspondence to Peter Varga.

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Varga, P., Grafarend, E. & Engels, J. Relation of Different Type Love–Shida Numbers Determined with the Use of Time-Varying Incremental Gravitational Potential. Pure Appl. Geophys. 175, 1643–1648 (2018). https://doi.org/10.1007/s00024-017-1532-z

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  • DOI: https://doi.org/10.1007/s00024-017-1532-z

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