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Z. G. Meng, H. H. Wang, Y. C. Zheng, Y. Z. Wang, H. Miyamoto, Z. C. Cai, J. S. Ping, Y. Z. Zhu, "Several Geological Issues of Schrödinger Basin Exposed by CE-2 CELMS Data", Advances in Astronomy, vol. 2019, Article ID 3926082, 13 pages, 2019. https://doi.org/10.1155/2019/3926082
Several Geological Issues of Schrödinger Basin Exposed by CE-2 CELMS Data
The study on the Schrödinger basin may provide important clues about the formation of South Pole-Aitken (SPA) basin. In this paper, the thermophysical features of Schrödinger basin were evaluated using the Chang’E-2 microwave sounder (CELMS) data. The results are as follows. (1) The geological units are reevaluated with the CELMS data and a new geological view was provided according to the brightness temperature and emissivity maps. (2) The surface topography plays an important role in the observed CELMS data. (3) The hot anomaly in the basin floor indicates a warm substrate. (4) The pyroxene-bearing anorthosite is probably an important cause for the cold anomaly over the lunar surface. Also, the study proves the applicability of the CELMS data applying in high latitude regions to a certain extent.
Schrödinger basin is the best preserved basin of its size and laid in the southwest corner of the South Pole-Aitken (SPA) basin (Figure 1(a)), the largest and oldest impact crater on the Moon [1, 2]. The basin is superposed on the floor of SPA basin and it may likely excavate the materials from the lower crust or upper mantle [2–4]. Thus, the diversity of the materials and the special mare volcanism in the basin could provide some important information about the formation of Schrödinger basin and even SPA basin.
(a) Geographical map
(b) Geological map
Schrödinger basin, centered at (76°S, 134°E), is about 334 km in diameter. It also has an inner peak ring of 168 km in diameter represented by a discontinuous ring of mountains . Wilhelms et al.  firstly provided the geological mapping effort of this basin at 1:5M scale based on Lunar Orbiter data. Thereafter, Shoemaker et al.  improved the geological interpretation with the Clementine UV-VIS data. Using the data from the Lunar Reconnaissance Orbiter, Clementine, Lunar Prospector, and Lunar Orbiter, Mest  evaluated the contacts and structures of geological units and at last identified three groups including nine distinct units (Figure 1(b)), indicating that Schrödinger basin comprises the pre-Schrödinger crustal materials, the mafic and anorthositic materials, and the volcanic materials. Additionally, abundant fractures occur in the basin floor, some of which extend to a few hundred kilometers long. Shankar et al.  verified a heterogeneous distribution of both anorthositic and basaltic materials in the basin floor. Using remote sensing data and impact crater modeling, Kramer et al.  reevaluated the composition of materials that make up the basin wall, impact melt, and peak ring, providing a new understanding of basin-forming processes. Through analyzing the LRO LOLA data and the Chandrayaan data, Kumar et al.  concluded the boulder falls in the basin floor triggered by the recent shallow moonquakes and impact events, indicating that this is geologically active zone until now. Therefore, Schrödinger basin presents an appropriate place to evaluate the thermophysical features of the diverse materials forming the SPA and Schrödinger basins and the substrate thermal features related to the tectonic activities. This is also the motivation for us to study the basin with the microwave sounder (CELMS) data.
The CELMS instrument was onboard Chinese Chang’E-2 (CE-2) satellite, which is designed to measure the thermal emission of the shallow lunar surface in microwave domain. The CELMS data are of special significance in the current lunar geological study, which has been proved by Meng et al.  and Hu et al.  through evaluating the mare volcanism in Mare Imbrium. Meng et al.  also gave a distinctly different view about Mare Crisium using the CE-2 CELMS data compared to the optical data and indicated a new understanding about the mare volcanism there. This hints to the potential applications of the CELMS data to better understand the thermal evolution of the Moon.
However, Schrödinger basin is located in high latitude regions, which has harsh topographic and illuminating conditions. To testify the applicability of the CELMS data in such conditions is also our motivation. In this paper, Section 2 thoroughly describes the processing of the CELMS data. Section 3 analyses the MTE features of the geological units in the basin. The geological applications are discussed in Section 4. Section 5 presents the conclusions.
2. Data Processing
2.1. CELMS Data Processing
The CELMS data used in the study were collected from the CE-2 satellite, which operated at 3.0, 7.8, 19.35, and 37 GHz channels. The observation time was from October 2010 to May 2011. The incident angle is 0°, and the temperature sensitivity is better than 0.5 K. A detailed description of the CELMS data was given by Cai and Lan  and Meng et al. .
According to the range of Schrödinger basin, more than 600 tracks of swath CELMS data were acquired. For the brightness temperature (TB) is heavily influenced by the surface temperature, or surface illumination [12, 16], the hour angle is introduced to describe the measured TB in different time spans [11, 13, 15, 19, 20]. Additionally, the quantity of the selected CELMS data is more than five times as that with a similar area in low latitude regions . However, after overlying the obtained CELMS data on Schrödinger basin (Figure 2), 1° spatial resolution along the latitude and very high spatial resolution along the longitude are clearly presented.
The soundly large quantity of the CELMS data means that the TB maps at multiple time periods can be generated (Figure 3). But just as in Figure 3, we may obtain the CELMS data at 8 and 14 o’clock. Unfortunately, there occurs an apparent position problem in Figure 3, which is indicated by the red line. The position of the TB in the left side of the red line apparently does not match that of the TB in the right side, hinting that the CELMS data at this time are not proper. After carefully checking the original CELMS data, the CELMS data at 0 and 10 o’clock are proper to generate the TB maps of Schrödinger basin, which can represent the TB at nighttime and daytime.
(a) 8 o’clock
(b) 14 o’clock
Thereafter, the CELMS data processing procedure is similar to that suggested by Meng et al. . For the linear interpolation method can slightly alter the original data, it is employed to generate the TB maps with a spatial resolution of 0.25° × 0.25° (Figure 4).
(a) 10 o’clock
(b) 0 o’clock
Figure 4 presents that the TB distribution is strongly latitude-dependent. E.g., the TB variation at 37 GHz with latitude from the north to the south is more than 100 K at daytime and about 90 K at midnight. But the TB in the central basin floor is only about 10 K higher than its vicinity. That is, the TB variation with the latitude is much larger than that resulted from the thermophysical parameters of the lunar regolith . Therefore, this latitude-dependent impact must be eliminated before using the generated TB maps.
Thus, the standard TB of every latitude is proposed. Firstly, one TB is selected for every latitude on the condition that the (FeO+TiO2) abundance, surface slope, and rock abundance are similar in all selected positions. Here, the selection criteria are same as Meng et al. . The composition, surface slope, and rock abundance data are referred through JMARS software. The selected TB for every channel is presented as a dash line in Figure 5. Thereafter, a fitting curve is made according to the selected TB, which is defined as the standard TB for every latitude (Figure 5).
(a) 10 o’clock
(b) 0 o’clock
Finally, the normalized TB (nTB) can be calculated using the TB divided by the standard TB along the corresponding latitude. Figure 6 is the 37-GHz nTB maps at 10 and 0 o’clock, which shows that the latitude-dependent effect of the TB maps is well eliminated.
(a) 10 o’clock
(b) 0 o’clock
2.2. Image Cut and Overlaying
Figure 6 indicates a new different view about Schrödinger basin compared to the optical data, hinting at the potential geological applications of the CELMS data in high latitude regions. Largely, the nTB behaviors show a good correlation with the topography, e.g., the northern interior wall with reduced solar illumination, and the composition, e.g., in the peak ring with relatively higher nTB. However, the nTB difference among the geological units is still not distinct. This mainly resulted from the nTB values in Granswindt crater (111.2°E, 79.4°S) in the southwest and Nefed’ev crater (135.8°E, 81.1°S) in the south, whose nTB is lowest in the selected regions, and from the southern interior wall of Grotrian crater (128.3°E, 66.2°S), whose nTB is almost highest at daytime. Fortunately, the three mentioned regions are all situated beyond Schrödinger basin. Thus, to better understand the thermophysical features of the geological units, only the nTB within Schrödinger basin is kept, which is cut according to the boundary given by Mest  (Figures 7 and 8). Figures 7 and 8 show that the difference among the geological units is well strengthened compared to that in Figure 6.
(a) 3 GHz
(b) 7.8 GHz
(c) 19.35 GHz
(d) 37 GHz
(a) 3 GHz
(b) 7.8 GHz
(c) 19.35 GHz
(d) 37 GHz
What is more, the geological units have been fully studied by Mest  and Kramer et al. . To improve the understanding of the geological meanings of the nTB maps, the interpretation result by Mest  is vectorized and overlaid on the nTB maps in black line. Also, the WAC image is overlaid by the 37-GHz-channel nTB at daytime and midnight to postulate the detailed distribution of the nTB values (Figure 9). The coincidence between the nTB performances and the geological units as well as the topographic terrains is largely good, indicating the rationality of the generated nTB maps.
(a) 10 o’clock
(b) 0 o’clock
2.3. Emissivity Maps Generation
In high latitude regions, the CELMS data will experience harsher solar illumination conditions compared to the low latitude regions [14, 15, 19]. This phenomenon is obviously indicated by the lowest values in the northern wall and by the highest values in the southern wall. Thus, how to eliminate the topographic impact is a crucial issue for the applications of the CELMS data.
Up to now, the surface temperature has been fully studied by means of the numerical simulation by Meng et al. , He et al. , and Hu et al. . Therefore, the surface temperature was simulated with improved Racca model  using the CE-1 LAM data, which was recommended by Hu et al.  for its coincidence with the footprint of the CELMS data. For the parameters used, the reader can be referred to . The original solar irradiance is the average value. Moreover, the time used is at 10 o’clock, which is corresponding to the daytime CELMS data used in this study. Then, the ratio between the generated TB and the surface temperature is the emissivity of the lunar regolith at the corresponding channel (Figure 10).
(a) 3 GHz
(b) 7.8 GHz
(c) 19.35 GHz
(d) 37 GHz
Compared to Figure 7, Figure 10 indicates that the influence from the surface topography is weakened to some extent, which can be expressed by the emissivity in the northern and southern interior walls. Thus, the emissivity map is also employed to provide supplements to improve understanding of the MTE features of the geological units.
However, the simulated surface temperature is in ideal conditions, which is not suitable for the real environment during the CELMS observation. Thus, the introduction of the surface temperature and the estimated emissivity are employed only for referring.
3. MTE Features of Schrödinger Basin
Mest  identified three groups in Schrödinger basin, including Schrödinger basin materials, Schrödinger plains formation, and Schrödinger volcanic formation. Figures 7 and 8 indicate similar nTB behaviors about Schrödinger basin. That is, though the TB at daytime is higher than that at nighttime, the region with relatively higher nTB at daytime also shows relatively higher values at nighttime and vice versa. This presents special microwave thermal emission (MTE) features about the materials in the basin.
3.1. Schrödinger Basin Materials Group
Unit INspr is the incomplete peak ring of mountainous terrain, which displays moderate albedo in Clementine images but is mottled in high-resolution LROC images . Figures 7 and 8 indicate that the unit has rather low nTB values at daytime and midnight, especially at 3.0 GHz maps. The regions with low nTB apparently form an incomplete ring, coinciding well with its terrain. But, several regions around (127.3°E, 72.3°S), (129.0°E, 75.3°S), (134.4°E, 71.6°S), and (143.0°E, 75.2°S) present the relatively higher nTB than their vicinities. Combined with the topography map, such regions are slopes originating to the solar illumination, indicating the strong influence of the topography on the nTB. Even so, much more regions of the unit show considerably low nTB values, implying that the material of the unit can be represented by the low MTE feature. Zheng et al.  and Meng et al.  proposed that the low MTE is directly related to the low (FeO +TiO2) abundance (FTA). This means that the material of the unit will be severely low in FTA. Figure 10 indicates that the unit has a low emissivity, indicating a high density of the material in this unit combined with the relationships expressed by .
Unit INsr includes the materials that form the topographic rim crest and the interior wall of Schrödinger basin. But the nTB in the unit is heavily impacted by the surface topography. At daytime, the nTB in the north interior wall is lowest within the study area, while the south interior wall indicates the highest nTB. A similar phenomenon occurs in the nighttime nTB maps. Such phenomenon also exists in Tycho crater [26, 27], indicating the cold and hot TB anomalies over the lunar surface. This makes it difficult to recognize the MTE features of the material in this unit.
3.2. Schrödinger Plains Group
The floor of Schrödinger basin is identified as five plains-forming units, including the rugged plains material (INsrp), hummocky plains material (INshp), the lower member of the smooth plains material (Isspl), the upper member of the smooth plains material (Isspu), and the knobby plains material (Iskp) .
Unit INsrp is mainly distributed outside of the peak ring, which is stratigraphically the oldest plains material on the basin floor. The unit shows relatively higher nTB in the northern, western, and southern parts, while the nTB changes greatly from north portion to the south and with frequency. The great change of the nTB performance makes it difficult to recognize the MTE features of the material in this unit.
Unit INshp occupies much of the basin floor along the northern and western walls, and in the south where the peak ring is most discontinuous. The nTB and emissivity performances of the unit are similar to that of unit Insrp in the close areas, indicating the uniformity of the materials MTE features in the two units.
Unit Isspu primarily occurs in the center of Schrödinger basin, which presents as lower and slightly less cratered than unit Isspl. Interestingly, the unit has the second highest nTB within the basin floor, which is just lower than the regions with enhanced solar illumination. This indicates that the unit can be represented by the high MTE feature and the material here is fairly high in FTA. Figure 10 indicates that the emissivity is high here, indicating a relatively lower density of the material in this unit.
Unit Isspl is found just inside the peak ring, displaying moderate to high albedo with a small number of superposed craters. Interestingly, nearly in all boundaries between this unit and unit INspr, the nTB and emissivity differences are not clear. A similar phenomenon also occurs in the boundaries between this unit and unit Isspu. Generally, Figure 10 indicates that the emissivity in most part of the unit is similar to that in unit Isspu, implying the uniformity of the densities of the materials in two units.
Unit Iskp is located along the southern basin wall with fairly high albedo. The nTB distribution of the unit is obviously affected by the surface topography, which is higher in the southern portion near the south interior wall but lower in the northern portion. Even so, the nTB is lower than the nearby regions along the same latitude, indicating that the unit should be represented by the low MTE feature. Moreover, the nTB and emissivity performances of the unit are similar to that of unit Inspr in the close areas, indicating the uniformity of the materials MTE features in the two units.
3.3. Schrödinger Volcanic Formation
Volcanic materials are concentrated in the northern and eastern parts of the basin inside the peak ring. The formation is made up of four patches of dark plains materials unit (Isdp) and dark mantle material unit (Elsdm) .
The largest patch of unit Isdp is mainly located along the northern part of the peak ring, and other three patches of this unit are located around unit EIsdm. The unit displays smooth, relatively featureless, low-albedo surfaces. But, not only at nTB maps but also at emissivity map is the difference between this unit and unit Isspu not clear, indicating the uniformity of the materials MTE features in the two units.
Unit Elsdm is located in the southeastern part of the basin floor within the peak ring, which has a relatively smooth, lightly cratered surface with low albedo. There exists an ovoidal cone, which has been identified as the source of pyroclastic eruptions [7, 28]. In nTB and emissivity maps, the values in this unit are apparently lower than the nearby unit Isspu, particularly at 3.0 GHz channel, while the nTB values are apparently higher than those in unit INspr. This not only indicates the difference of the materials MTE features in these regions, but also hints at the applicability of the CELMS data in the high latitude regions.
4. Geological Applications
4.1. Potential Geological Applications
The nTB behaviors present a distinctly different view about Schrödinger basin compared to the visible images.
To basin materials formation, unit INspr indicates the low nTB and emissivity values, hinting the existence of the materials with high density.
To plains formation, the difference between units INsrp and INshp is not clear both in nTB maps and in emissivity maps. Though the nTB and emissivity values change greatly from the south to north part of the basin, they show identical features in the close regions. This means the uniformity of the materials in the two units.
Also, the difference between units Isspl and Isspu is not clear, indicating the uniformity of the materials in the microwave range. Additionally, the nTB and emissivity performances make it difficult to identify the MTE features of units INsrp and INshp, but the emissivity values in unit Isspl are apparently higher than those in unit Insrp in the southern part of the basin floor, indicating that the materials in units Isspl and Isspu are different from units INsrp and INshp.
To volcanic formation, unit Isdp is hard to identify from the unit Isspu in the nTB and emissivity maps. That is, units Isdp and Isspl indicate the similar nTB and emissivity performances as unit Isspu, indicating the uniformity of the materials in the three units in microwave range.
Here, unit Elsdm indicates the special nTB and emissivity performances compared to the other units. The material here is identified as the dark mantle deposit or pyroclastic deposit [2, 29]. Thus, the nTB and emissivity maps indicate the special thermophysical features of the deposits in high latitude regions.
Table 1 indicates a small difference in nTB values among the geological units, indicating some interesting information about the geological units as follows. First, unit INsrp represented by Positions 2 and 9 has the highest nTB values. Interestingly, unit INshp represented by Positions 4, 6, and 11 has similar statistics to unit INsrp. Second, unit Isspu represented by Position 1 is lower than that in unit INsrp. Third, unit Elsdm represented by Position 5 has the third highest nTB values. Fourth, unit INspr represented by Positions 3 and 7 apparently has the lowest nTB values. Finally, the change of the nTB with frequency in unit Isspl represented by Position 8 is similar to that of unit INsrp, indicating the difference in material MTE features. Combined with the emissivity map, unit Isspl is consistent with unit Isspu.
Therefore, a new geological understanding about Schrödinger basin can be obtained based on nTB and emissivity maps and statistics of sample regions (Table 1). Here, at least in microwave range, the basin floor can be categorized into four geological zones. The first zone comprises the previous units INsrp and INshp. The second zone comprises the previous units INspr and Iskp. The third zone includes the previous units Isspl, Isspu, and Isdp. And the fourth zone is unit Eldsm.
The new geological understanding also means that though the surface features are not identical for the nearby geological unit, the MTE parameters of the materials are consistent. However, the strong topographic effect and the rather small nTB differences among the geological units hint that the CELMS data are not suitable to study the regolith thermophysical features and the mare volcanism in high latitude regions.
4.2. nTB Anomalies
At least four nTB anomalies occur in Schrödinger basin. Two anomalies are hot, which mainly include the southern interior wall and the central part of the basin floor. The other two are cold, including the northern interior wall and unit INspr.
Hot and cold TB anomalies are always an interesting topic in the current lunar study [12, 15, 19, 27, 30, 31], but the causes for the cold anomaly have long been in intense debate. Gong and Jin  and Hu et al.  attributed the hot and cold TB anomaly to the existence of the rocks. But Salisbury and Hunt  and Meng et al.  thought that the surface topography and its orientation are the decisive factors for TB anomaly. The nTB behaviors in Schrödinger basin apparently prove the latter explanation, because the cold nTB anomaly in the northern interior wall obviously resulted from the deficiency of the solar heating in a day, while the hot anomaly in the southern interior wall is apparently brought by the enhanced solar heating. Moreover, combined with the simulation results, the hot anomaly in the regions around (127.3°E, 72.3°S), (129.0°E, 75.3°S), (134.4°E, 71.6°S), and (143.0°E, 75.2°S) also validates the strong influence of the solar heating on the anomaly of this kind.
However, there also exists another kind of hot and cold anomaly.
Firstly, in the central and southern parts of the basin floor, the nTB is high no matter at daytime and at midnight, indicating a hot anomaly here. A similar phenomenon also exists in the basin floors of Orientale, Hertzsprung, and Crisium [13, 18, 20]. Using the theoretical model and the CE-2 CELMS data, Meng et al. [13, 20] attributed the hot TB anomaly to the probably warm substrate.
However, to verify the conclusion, the influence of the surface topography and regolith composition must be eliminated at first. Interestingly, the emissivity maps and the topography both indicate a relatively flat surface in this region, indicating the negligible impact of the topography. Moreover, Meng et al.  and Hu et al.  suggested the strong influence of the ilmenite content on the local TB. Similar findings are also proved by the observed CELMS data in Mare Imbrium and Orientale, where the mare basalts with higher ilmenite content indicate a higher TB at daytime [11, 20]. The regolith in these regions is more mafic than the nearby regions , but the nTB behaviors are opposed to the simulation results by Meng et al.  and Hu et al.  and observations in Mare Imbrium and Orientale [11, 20]. Thus, the regolith composition also cannot interpret the hot anomaly.
Again, the only left cause for the hot nTB anomaly is the warm substrate.
Additionally, Lu et al.  found two apparent mascons in the central and south parts of Schrödinger basin. The formation of the mascons is always related to the volcanic activity in lower crust or upper mantle [35, 36]. Thus, the existence of the two mascons hints at an ever-existing strong volcanic activity in the deep lunar crust in Schrödinger basin. What is more, there occur abundant fractures in the basin floor, some of which have been proved to be related to the volcanic activity in depth . This is a new evidence of the ever-existed strong tectonic activities in Schrödinger basin.
The hot anomaly, the abundant fractures, and the occurrence of the mascons indicate a new view about the volcanic activity in Schrödinger basin. This may provide some interesting information about the formation of the SPA basin and the mare volcanism of the lunar farside, deserved to be further studied with more sources of data in future.
Secondly, in unit INspr, the nTB is always lower than the nearby units, while the solar illumination here is not apparently lower than the nearby regions, indicating the existence of a cold anomaly here. The causes for the low nTB anomaly are still under debate until now.
First, the cold anomaly is obviously not related to the surface topography, for it is widely distributed in the peak ring. Some regions of the peak ring are originating to the solar illumination, while the nTB here is still rather low.
Second, Gong and Jin  and Hu et al.  suggested that the rock abundance is responsible for the cold anomaly at night using the theoretical model. They also suggested that the cold anomaly at night should be a hot anomaly at noon. But the nTB here is low both at daytime and at night, indicating that the rock abundance does not interpret the cold anomaly.
Third, Hu et al.  thought the ilmenite content is one of the main causes for the TB anomalies found in the CELMS map. Also, Meng et al.  evaluated the relationship between the nTB performances in the cold anomalies surrounding Mare Crisium and the corresponding rock abundance and ilmenite content, and the results also hint that a special material with rather low ilmenite should also be responsible for the cold anomaly. Furthermore, the TB behaviors around Copernicus crater verified that the cold anomaly is likely brought by a special material with rather low ilmenite content .
That is, the composition should undertake the main cause for the low nTB anomaly.
Therefore, the existence of the cold nTB anomaly in unit INspr indicates that the source material, pyroxene-bearing anorthosite , is probably an important cause for the cold anomaly of the lunar surface, which also deserved to be further studied in future.
One more phenomenon should be paid attention to. Such cold anomaly is not only limited in unit INspr. The crater ejecta in the southwest part of the basin floor and just inside the peak ring also shows low nTB and emissivity values as unit INspr, even if the regions are close to the southern interior wall. Additionally, the nTB and emissivity in unit Iskp are apparently lower than the vicinity along the same latitude, indicating that the material in this unit should be represented by low values. The nTB and emissivity in the northern part of unit Iskp are also similar to unit INspr. The crater ejecta represents the materials from the depth layer. Therefore, combined with the previous discussions, this phenomenon means that the materials in the depth layer of the basin floor excavated by the crater are similar to the peak ring. This is helpful to better understand the formation of Schrödinger basin and even the SPA basin according to the crater formation mechanism, which deserves to be further studied with more sources of data and even in situ observations.
In this paper, the nTB maps derived from CE-2 CELMS data were systematically used to study the microwave thermophysical features of Schrödinger basin, which give some different aspects compared to the previous understandings. The main results are as follows.
(1) The geological units are reevaluated with the CE-2 CELMS data and the statistics of typical regions, which shows a different geological perspective compared to the visible results.
(2) The nTB anomalies in the interior basin wall indicate the strong influence of the topography and its orientation.
(3) The hot nTB anomaly in the basin floor indicates the likely warm substrate. Combined with the existence of the mascons and abundant floor fractures, the strong tectonic activity should ever exist in Schrödinger basin, which will be helpful to improve understanding the formation of the Schrödinger basin and even the SPA basin.
(4) The cold nTB anomaly in unit INspr indicates that the pyroxene-bearing anorthosite is probably an important cause for the cold anomaly over the lunar surface.
Generally, the CELMS data are feasible to study the thermophysical features of the geological units in high latitude regions to some extent, which will expand our knowledge about the south and north poles. However, the surface topography strongly alters the TB and nTB performances, and more work should be done to further understand the important findings in this study.
The CELMS data can be downloaded from the website http://www.clep.org.cn/. The processed CELMS data and the brightness temperature maps about Schrödinger basin can be freely shared by email.
Conflicts of Interest
The authors declare that there are no conflicts of interest regarding the publication of this paper.
The authors express their gratitude to the National Natural Science Foundation of China under Grants [41490633, 41590851, and 41802246], the opening fund of State Key Laboratory of Lunar and Planetary Sciences (Macau University of Science and Technology) [No. 119/2017/A3], and the Science and Technology Development Fund of Macau [Grant 0012/2018/A1]. Thanks are also due to the graduate Lele Hou for preparing the resulting images of the manuscript. The WAC image was downloaded from http://wms.lroc.asu.edu/lroc/search.
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