Comparison of the Effects of Different Viscoelastic and Temperature Models on the Theoretical Tidal Response of the Moon

Abstract

AbstractThe existence of an attenuating layer that is partially molten at the bottom of the lunar mantle has long been debated, mainly because different viscoelastic models yield varying interpretations. Through a combination of different viscoelastic and temperature models, we study the theoretical tidal response of the Moon. As viscoelastic models, we consider the Maxwell, Burgers, Andrade, and Sundberg‐Cooper model, where the Burgers and Andrade models each comprise two different scenarios. Determining which viscoelastic model is most suitable for the Moon is difficult since more than one combination of viscoelastic and temperature models satisfies the observed period dependence of the lunar tidal quality factor Q. Further inversion reveals that most viscoelastic models potentially satisfy the monthly observations of the Moon; however, only the Maxwell and Andrade models satisfy the period‐dependent Q while remaining consistent with the observed tidal Love numbers k2 and h2. We ultimately suggest that the Andrade model with β = μα−1η−α, where α and β are the empirical parameters, μ is unrelaxed shear modulus, and η is viscosity, is more suitable for the Moon because the Maxwell model underestimates the mantle viscosity and the viscous dissipation at short periods. Based on our model assumptions and the currently available observations, a partially molten layer with a grain size on the order of 10–100 µm, in which the temperature changes drastically may exist at the bottom of the lunar mantle.