Effect of crack direction around laboratory-scale craters on material bulk permittivity

The impact of meteorites forms craters on celestial surfaces, below which cracks are formed. Lunar geological conditions around such craters have been estimated based on permittivity surveys by radar exploration. The relationship between density and permittivity was empirically determined using Apollo soil and rock samples. In this manner, radar exploration enabled the geological survey of the moon. However, based on the effective medium theory, even for equal densities, crack direction can change the permittivity. Here, we show the relationship between crack direction and physical parameters (i.e., the bulk density, bulk permittivity, and loss tangent) around craters based on impact experiments. We characterize three types of cracks (concentric, radial, and corner cracks) around a ∼9.1-cm-diameter crater. The crack volume fraction was gradually decreased as the distance from the crater center increased. The decrease was particularly remarkable in the area within the crater radius, arising from the concentric and radial cracks. The bulk density, bulk permittivity, and loss tangent showed clear inverse correlations with the crack volume fraction. We found that the effective medium model, considering the effect of crack direction, explained the bulk permittivity distribution around the crater. In addition, the effective medium models, assuming the regolith contains spherical basalt grains and the rock includes aligned cracks, could successfully explain the results of the density and permittivity of Apollo sample. The estimated permittivity of the pore-free lunar basalt was ∼15. These results provide suggestions for application of the effective medium model in the derivation of the bulk density from the bulk permittivity determined by radar observations. (1) If the lunar mare subsurface layer has a permittivity lower than ∼4–5 and is in regolith condition, its bulk density should be estimated from an effective medium model isotropically containing spherical pore-free basalt grains with a permittivity of ∼15 in a vacuum. (2) If the lunar mare subsurface layer has a permittivity larger than ∼4–5 and is in rock condition, its bulk density should be estimated from an effective medium model, assuming the void distribution or crack direction against the electric field of radar pulses in basalt rock with a permittivity of ∼15.