Figure 1. (a) Topography of the Moon and the locations of Sites 1 and 2 (red and blue star, respectively). (b) Site 1 (red star) and lobate scarps (yellow lines) in the Schrödinger basin. (c) Site 2 (blue star), lobate scarps (yellow lines), and the epicenter assumed by Kumar et al. (2019) for a moonquake on 3 January 1975 (black cross) in Laue crater.
We used the following relationship between crater diameter (D , m) and the seismic moment (M 0, Nm) derived by Teanby and Wookey (2011):
,
where a = 8.8 × 10−3, b = 0.32, c= 4.8 × 10−9, d = 1.24, k is the seismic efficiency (2.0 × 10−5), and geis gravitational acceleration on the Earth. We convertedM 0 to Mw by using the following equation (Kanamori, 1977):
.
We first used equations (4) and (5) to estimateMw values for the meteorite impacts that created individual small craters. Then, using equation (3), we calculated PGA values from Mw values of meteorite impacts at individual points in each study area. We set the epicenter at the center of each small crater, and used the PGA at the crater rim for acceleration within the crater. We adopted the maximum acceleration at each point among PGA values calculated for all small craters.
Space weathering, mainly due to the solar wind, causes lunar surface optical features to become darker and redder and can be evaluated by OMAT (Lucey et al, 1995, 2000; Otake et al., 2012), obtained by using the following equation:
,
where R 750 and R 950 are reflectance values at wavelengths of 750 nm and 950 nm, respectively. Thus, high OMAT values indicate a fresh surface. We estimated OMAT values from MI data in these two bands obtained by KAGUYA.
We used ENVI 5.6 software to generate map-projected LROC NAC and KAGUYA mosaic images, on which we traced boulder trails and small craters and calculated OMAT values. We inferred starting points of boulder falls from our trail traces. Some trails could not be clearly traced because of degradation by subsequent mass wasting; in such cases, we determined the highest point of each trail. We measured the diameters of small craters by assuming that they were circular. We also used SAOImageDS9 software (Joye & Mandel, 2003) to map small craters, boulder trails, and boulder sources. We used Generic Mapping Tools (GMT) (Wessel & Smith, 1998) to calculate the direction of the upslope gradient vector and the magnitude of the gradient scalar and to map lunar topography, slope gradients, distributions of small craters, boulder trails and sources, and PGA distributions.
3. Results
3.1. Site 1 in the Schrödinger Basin
Our estimated locations of small impact craters (D ≥ 5 m) and their diameters and boulder trail locations at Site 1 in the Schrödinger basin are shown in Figure 2a. Many boulders are located in upslope areas near the basin rim (areas enclosed by green lines in Figure 2a). Such areas are called boulder sources by Kumar et al. (2016). Some boulders had moved downslope, leaving trails (Figure 2c). Older trails are superimposed by small impact craters, whereas younger trails crosscut craters (Figure 2a, yellow and green lines, respectively). Our detected boulder trails and boulder sources are mostly consistent with those detected by Kumar et al. (2016). Small craters and boulder trails are not uniformly distributed in our study area. Boulder trails are more abundant in the central region than in the NW and SE regions (Figure 2a), but the density of small craters is larger in the NW and SE regions than in the central region (Figure 2b). In some areas below the boulder sources (enclosed by blue lines in Figure 2a), there are fewer small craters and boulder trails. We estimated the mean surface model age at Site 1 to be about 5.5 Ma, based on the CSFD of small impact craters ranging from 10 to 200 m in diameter (Figure S1a). It is clear that crater density is smaller in the study area than on the basin floor and the outer part of the basin rim (north and south of the study area, respectively); thus, the study area is younger than surrounding areas.
Using equation (3) and the procedure described in Section 2, we estimated the spatial distribution of maximum acceleration due to impacts and compared the result with the estimated starting points of boulder falls (Figure 3). Many starting points of boulder falls were found in areas where the acceleration due to impacts was large, especially in the central part of our study area. To consider the relationship between maximum acceleration and boulder fall starting points quantitatively, we subdivided the study area into 600 m × 600 m grids, and then averaged the maximum acceleration and counted the number of starting points within each grid (Figure S2a). We found that the relationship between the averaged maximum acceleration and the number of starting points differed among three regions (regions 1 to 3 in Figure S2). The relationship is clearest in region 2 (magenta rectangle in Figure 3; Figure 4a) and less clear in regions 1 and 3 (Figures S2b and S2d, respectively). In region 2, the number of starting points increases with increasing averaged acceleration (correlation coefficient R= 0.58; Figure 4a). In regions 1 and 3, there are fewer boulder trails than in region 2, but small craters are more abundant (Figure 3). These differences among the regions may be attributable to the further progression of slope degradation in regions 1 and 3, which are older than region 2. We discuss this point later.
We also compared the mean slope angle with the density of small craters in each of the three regions (Figure S3a). Most small craters are in downslope and upslope areas, where slope angles are relatively small (Figures 2b and S3a), and the density of small craters tends to decrease as the slope angle (>25°) increases (Figure 4b). This tendency is weaker where slope angles are gentle (<25°) because Site 1 was selected as a relatively steeply sloping area along the basin wall; as a result, there are few data points in gently sloping areas.
Comparison of estimated OMAT values with boulder source areas (enclosed by solid gray lines in Figure 5a) showed large OMAT values, which were mainly associated with upslope areas, to be highly correlated with boulder source areas. This result indicates that boulder source areas are characterized by relatively fresh materials. Moreover, OMAT values decrease downslope (Figure 5a), indicating that soils are more mature in downslope areas. Comparison of average OMAT values in 230 m × 230 m grids with the density of small craters in the grids showed that small crater density decreases as OMAT values increase (Figure 4c); this trend is similar to that found between small crater density and slope angle (Figure 4b). Comparison of OMAT values with slope angles (Figure 4d) indicated that the smallest OMAT value for each slope angle systematically increases with increasing slope angle, whereas larger OMAT values show more scatter, although they tend to increase as the slope angle increases. These features suggest that the maturity of the crater wall surface is related to the slope angle.