Constraining the parameters of the Andrade rheological model in Earth’s mantle based on the Love numbers of the М2 lunar semidiurnal tide

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Abstract

For the first time we showed that the often-used approximation of the Andrade rheology with only one parameter is oversimplified and might lead to incorrect conclusions when studying the internal structure of the planets of the Solar System. Instead, we used an Andrade rheology with two empirical parameters: α and ζ. Earth’s viscoelastic Love numbers for the principal lunar semidiurnal tide M2 were computed for two viscosity profiles and for 16100 different combinations of α and ζ values. The comparison of the computed Love numbers with its measured values allowed us to constrain the set of values of both parameters that successfully describe the rheological properties of Earth’s mantle.

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About the authors

D. O. Amorim

Moscow Institute of Physics and Technology

Author for correspondence.
Email: amorim.dargilan@gmail.com
Russian Federation, Dolgoprudny

T. V. Gudkova

Sсhmidt Institute of Physics of the Earth of the Russian Academy of Sciences

Email: gudkova@ifz.ru
Russian Federation, Moscow

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2. Fig. 1. The areas in which each of the 6 conditions used in Table 2 is fulfilled separately for the RVR are shown in black.

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3. Fig. 2. The number of satisfied conditions as a function of α and ζ for different viscosity distributions η: RNV model (left), RVV model (right). Black pixels indicate regions and in which all six conditions from Table 2 are satisfied simultaneously.

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4. Fig. 3. Ranges of α and ζ values, at which all 6 conditions from Table 2 are simultaneously fulfilled for RNV and RVV. Their intersection is shown in green. The combinations of Andrade parameters that are most suitable for describing the rheology of the Earth are between the parabolas and .

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