Figure 9. (a) Distribution of craters (D > 7 km) with (red fill) and without (yellow fill) boulder falls around Site 2. The epicenter of the moonquake on 3 January 1975 is shown by a white cross, and lobate scarps estimated by Kumar et al. (2019) are shown by green lines. (b) Histogram of the number of craters per unit area with and without boulder falls in relation to epicentral distance (see the text for details).
4. Discussion
We found the starting points of boulder falls to be spatially correlated with maximum ground acceleration due to meteorite impacts in region 2 at Site 1 (Figure 4a). This result strongly suggests that local ground shaking due to meteorite impacts triggered boulder falls in this region. Although we found no clear correlation in other regions at Site 1 (Figures S2b and S2d) or at Site 2 (Figure 8a), in these areas, boulder falls were not abundant, so statistical evaluation was difficult. The differences in the distribution of boulder falls may be due to differences in surface maturity, as is discussed below.
Kumar et al. (2019) estimated PGA values due to the moonquake on 3 January 1975 to be 1−4 g at Site 2 (epicentral distance about 30 km) and concluded that this moonquake along the lobate scarps triggered boulder falls at the site. Given such large acceleration, boulder falls should have been triggered not only at Site 2 but also in other craters, depending on epicentral distance. However, we found no dependence of the existence of craters with boulder falls on the distance from the epicenter of the moonquake (Figure 9). This result suggests that neither the boulder falls at Site 2 nor those in other craters around Site 2 were caused by ground shaking due to this moonquake.
Kumar et al. (2019) used the omega-square source model (e.g., Aki & Richards, 2002) to simulate seismograms stochastically, and half-space structural models of S -wave velocity and density withQi = 4000−15,000, in which scattering attenuation was not explicitly included. They assumed an S -wave velocity of 330 m/s, corresponding to the uppermost regolith layer in a half-space model. Such a very small S -wave velocity without scattering attenuation can result in large acceleration. We estimated PGA at Site 2 due to this moonquake by using the attenuation equation (equation (3)) to be about 0.1 g , which is an order of magnitude smaller than the estimates of Kumar et al. (2019). Our result suggests that the moonquake may have not caused large acceleration, although our PGA estimate may be problematic because of differences inQi and Qs structures between the Moon and Earth, as we mention in Section 2.
The mean model ages estimated at Sites 1 and 2 (5.5 and 23 Ma, respectively) (Figures S1a and S5a) are clearly younger than the formation ages of the Schrödinger basin (Imbrian period) and Laue crater (Pre-Nectarian period or later) (Wilhelms, 1987). Therefore, craters on slopes at these sites have presumably been erased by subsequent mass-wasting processes. Older boulder trails superimposed by small impact craters and younger trails that crosscut craters are found at both sites (Figures 2a and 6a). Therefore, the boulder falls were not simultaneous but occurred repeatedly as a result of local ground shaking. Such repeated shaking is more likely to be produced by meteorite impacts than by moonquakes shaking a broad area.
The large OMAT values in the upslope boulder source areas at both sites (Figures 4d and 8d) indicate that immature surfaces are exposed in these areas. According to our age estimates, Site 2 is older than Site 1; furthermore, the area with immature surfaces is smaller at Site 2 than at Site 1 (Figure 5). These findings suggest that surface degradation at Site 2 is more advanced than at Site 1. The more abundant boulder falls at Site 1 than at Site 2 (Figures 2a and 6a) reflect the existence of more boulders in the source areas at Site 1 than at Site 2. These boulders may have been produced by continuous fracturing, which may also expose immature surfaces. According to Basilevsky et al. (2013), who studied boulder survival times, the number of boulders larger than 2 m would be halved in tens of millions of years. Given the ages of the two sites, more boulders would have been destroyed at Site 2, and we found fewer boulders at Site 2 than at Site 1. At Site 1, we found more boulder falls in region 2 than in regions 1 and 3 (Figures 2a and S2). Our determinations of crater ages in regions 1−3 at Site 1 (7.5, 4.4, and 5.4 Ma, respectively) indicate that region 2 is youngest (Figure S1b). This result also supports our inference that the boulder source area is inversely related to age.
The correlation between boulder falls and acceleration due to meteorite impacts in region 2 at Site 1 and the lack of a clear dependence of boulder falls around Site 2 on moonquake epicentral distance suggest that boulder falls were not triggered by moonquakes along lobate scarps but by meteorites that repeatedly struck crater slopes and generated small craters.
Our finding that the density of small craters decreases with increasing slope angle at both Sites 1 and 2 (Figures 4b and 8b) is consistent with results obtained by Basilevsky (1976) for other craters. We also found that the density of small craters decreases with increasing OMAT values at Site 1 (Figure 4c), although a similar tendency was not clear at Site 2 (Figure 8c). We further found that OMAT values increase with increasing slope angle at both sites (Figures 4d and 8d). We note that small craters and boulder falls are rare in the areas below the boulder sources at Site 1 (areas enclosed by blue lines in Figure 2a) where the OMAT values are relatively small (Figure 5a).
Considering all of these results, we propose a mass-wasting model for the slopes at Sites 1 and 2 as follows. A surface regolith layer overlying the bedrock, consisting of brecciated rocks or megaregolith, was formed during the Late Heavy Bombardment (Hartmann, 1973). In steeply sloping areas, this surface layer is thin because fine regolith tends to move downward under the influence of gravity. Therefore, in such areas, the bedrock can be more easily fractured by meteorite impacts, which produce rock fragments and boulders and, therefore, boulder source areas (Figure 10a). These boulders move downward when ground shaking due to meteorite impacts occurs (Figure 10a). In steeply sloping areas, however, craters are not clearly visible because the surface regolith layer is thin, and if boulder falls occur, they do not leave clear trails. Furthermore, fresh regolith generated upslope moves downward and tends to erase boulder trails and small craters in areas below boulder sources. In gently sloping downslope areas, accumulation of regolith from upslope causes the surface layer to become thicker and older (Figure 10b). When meteorites strike these areas and trigger boulder falls, clear craters and boulder trails can be formed in the thick regolith layer (Figure 10b). Repetition of these processes, however, makes the slope gentler and the surface layer thicker and results in the degradation of the crater wall (Figure 10c), and eventually, meteorite impacts no longer produce boulders and boulder trails.
This model consistently explains the distributions of boulder sources (Figure 5), boulder trails (Figures 2a and 6a), small craters (Figures 2b and 6b), and OMAT values (Figure 5) at Sites 1 and 2. Moreover, the differences in their distributions among regions 1−3 at Site 1, whose ages vary between 4.4 and 7.5 Ma, suggest that the processes described by our model can occur relatively rapidly, over about a million years. In addition, the weak relationships between ground acceleration and boulder abundance (Figure 8a) and between small crater density and slope angle (Figure 8c) at Site 2 (age 23 Ma) suggest that crater wall degradation at this site is advanced and implies that complete degradation can occur in a few tens of millions of years.
Previous crater degradation models (e.g., Ross, 1968; Fassett & Thomson, 2014) take account of redistributions of ejecta generated by meteorite impacts by using the diffusion equation to explain crater topography. In future studies, the boulder and regolith transport on crater walls described by our model should be quantitively examined to extend these previous models. According to Fassett and Thomson (2014), the diffusion equation does not well explain the topographic features of crater rims, which may be related instead to our proposed processes.
The results of this study suggest that boulder falls at Sites 1 and 2 were caused by meteorite impacts. Bickel et al. (2020, 2021) also proposed meteorite impacts produced boulders from rocks that had been fractured in the Late Heavy Bombardment. Although our model is similar to their concept, we examined in detail boulder generation processes by meteorite impacts in upslope areas with thin surface regolith layers. Furthermore, we provide a complete crater degradation model that accounts for boulder generation, boulder falls, and regolith movement. Bickel et al. (2020, 2021) also showed that boulder falls can be found over the entire lunar surface. In future studies, the universality of our mass-wasting model should be evaluated by investigating boulder sources, boulder trails, small carters, and OMAT values in other areas. The effects of shallow moonquakes should also be investigated in such areas. Comprehensive studies of the cause of boulder falls would contribute to better understanding of mass wasting related to the formation and degradation of lunar craters and new insights into ongoing dynamic activities on the lunar surface.