Theoretical calculation of tidal Love numbers of the Moon with a new spectral element method

The tidal Love numbers of the Moon are a set of nondimensional parameters that describe the deformation responses of the Moon to the tidal forces of external celestial bodies. They play an important role in the theoretical calculation of the Moon’s tidal deformation and the inversion of its internal structure. In this study, we introduce the basic theory for the theoretical calculation of the tidal Love numbers and propose a new method of solving the tidal Love numbers: the spectral element method. Moreover, we explain the mathematical theory and advantages of this method. On the basis of this new method, using 10 published lunar internal structure reference models, the lunar surface and lunar internal tidal Love numbers were calculated, and the influence of different lunar models on the calculated Love numbers was analyzed. Results of the calculation showed that the difference in the second-degree lunar surface Love numbers among different lunar models was within 8.5%, the influence on the maximum vertical displacement on the lunar surface could reach ±8.5 mm, and the influence on the maximum gravity change could reach ±6 μGal. Regarding the influence on the Love numbers inside the Moon, different lunar models had a greater impact on the Love numbers h₂ and l₂ than on k₂ in the lower lunar mantle and core.