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.