Abstract
Site-dependent bulk permittivities of the lunar uppermost media with thicknesses of tens to hundreds meters were estimated based on the data from Lunar Radar Sounder onboard the Selenological and Engineering Explorer (SELENE). It succeeded in sounding almost all over the Moon’s surface in a frequency range around 5 MHz to detect subsurface reflectors beneath several lunar maria. However, it is necessary to estimate the permittivity of the surface regolith of the Moon in order to determine the actual depths to those reflectors instead of apparent depths assuming a speed of light in the vacuum. In this study, we determined site-dependent bulk permittivities by two-layer models consisting of a surface regolith layer over a half-space with uniform, but different physical properties from the layer above. Those models consider the electrical conductivity as well as the permittivity, whose trade-off was resolved by utilizing the correlation between iron–titanium content and measured physical properties of lunar rock samples. Distribution of the iron–titanium content on the Moon’s surface had already been derived by spectroscopic observation from SELENE as well. Four lunar maria, Mare Serenitatis, Oceanus Procellarum, Mare Imbrium, and Mare Crisium, were selected as regions of evident reflectors, where we estimated the following four physical properties of each layer, i.e., bulk permittivity, porosity, loss tangent and electrical conductivity to conclude the actual depths of the reflectors are approximately 200 m on average. The bulk permittivity ranges from 2.96 at Mare Imbrium to 6.37 at Oceanus Procellarum, whereas the porosity takes the values between 1.8 and 41.1% in the respective maria. It was found that although the bulk permittivity of the four lunar maria differs from a mare to a mare, it shows a good correlation with their composition, viz., their iron–titanium content.
Symmetry analysis of a Lane-Emden-Klein-Gordon-Fock system with central symmetry
