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Geophysical Research Letters
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Supporting Information for
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Regolith stratigraphy at the Chang’E-3 landing site
as seen by Lunar Penetrating Radar
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Wenzhe Fa1*, Meng-Hua Zhu2, Tiantian Liu1, Jeffery B. Plescia3
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1Institute
of Remote Sensing and Geographical Information System, Peking University, Beijing, China.
Science Institute, Macau University of Science and Technology, Macau, China.
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The Johns Hopkins University Applied Physics Laboratory, Laurel, Maryland, USA.
*E-mail: wzfa@pku.edu.cn.
2Space
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Contents of this file
Text S1 to S5
Figures S1 to S11
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Introduction
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This supporting information provides:
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S1: Optical images of the CE-3 landing site;
S2: Regolith thickness over the CE-3 landing site;
S3: Ages of small craters;
S4: LPR data processing and subsurface structure identification;
S5: Turnover times of the regolith;
Figures S1-S11: Figures for text S1-S5.
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S1. Optical images of the CE-3 landing site
In the optical image, there are two distinct geologic units in the northern region of Mare
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Imbrium (Fig. S1a), the dark I22 and the bright I5 [Hiesinger et al., 2000]. The CE-3 landing
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site is in the northern portion of unit I22, about 10-15 km from the boundary between the
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geologic units I22 and I5 (Fig. S1b). The CE-3 landing site is about 50 m from the rim of the
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500 m CE-3 crater (Fig. S1c). In the Clementine Ultraviolet/Visible (UVVIS) image (Fig. S1d)
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[Eliason et al., 1999], unit I22 shows a very blue color, indicating a high titanium abundance,
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whereas unit I5 has a red color, corresponding to a low titanium abundance.
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S2. Regolith thickness over the CE-3 landing region
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In this study, regolith thickness over the CE-3 landing region (unit I22) is estimated using
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two methods: morphology of small fresh craters [Quaide and Oberbeck, 1968; Fa et al.,
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2014] and the excavation depth of craters with the threshold diameter between rocky and
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rock-free craters [Wilcox et al., 2005].
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High-resolution optical images show that the morphology of small fresh craters can be
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classified into four types: normal, central mound, flat-bottomed, and concentric [Quaide and
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Oberbeck, 1968]. Laboratory impact experiments found that these crater types could be
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used to estimate regolith layer thickness [Quaide and Oberbeck, 1968]: a normal crater
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forms when D/d (D: crater diameter; d: regolith thickness) is smaller than a value between
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3.8 and 4.2, a concentric crater forms when D/d is larger than a value between 8 and 10, and
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a central mound or flat-bottomed crater forms when D/d has a value between that forms a
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normal and
a concentric crater.
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Here we used two LROC Narrow Angle Cameras (NACs) images (M1144922100LE and
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M1144922100RE) with a spatial resolution of ~1.6 m/pixel and an incidence angle of 56.5°
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for crater counting. The study area is 8.1 km × 12.2 km (Fig. S2). In total, 1557 small fresh
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craters with diameters from 11 to 145 m were counted, of which 1189 are normal craters,
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334 are flat-bottomed craters, and 34 are concentric craters (Fig. S3). Because the
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illumination angle (33.5°) is larger than typical value of regolith repose angle (31°), shadow
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effect correction is not required in regolith thickness estimation [Quaide and Oberbeck,
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1968; Fa et al., 2014]. Using the relation between regolith thickness and crater morphology,
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Fig. S4 shows the cumulative distributions of regolith thickness estimated from normal
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(red) and concentric (blue) craters. From Fig. S4, the median regolith thickness for the mare
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around the CE-3 landing site is about 8 m.
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Based on rock population, small craters can be classified as distinctly blocky (type A), a few
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blocks (type B), and no blocks (type C) (Fig. S5) [Wilcox et al., 2005]. In a cratering event, a
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crater of type A or B will have penetrated the entire regolith layer and excavated the
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coherent substrate to some extent, bringing at least a few rocks (arrows in Fig. S5a and b) to
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the surface. In contrast, a crater of type C excavates only regolith, and therefore no blocks
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from the substrate occur on the surface. Regolith breccias may form in any of these cases.
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Regolith thickness can be estimated using the crater excavation depth with the threshold
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diameter between type A and B craters and type C craters. Here, the excavation depth is
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simply assumed as 1/10 of the crater diameter [Pike, 1974].
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The same region in the same LROC NAC images was selected for rocky and rock-free crater
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counting. In total, 318 craters with diameters from 30 to 770 m were counted, of which 33
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are type A, 73 are type B, and 212 are type C (Fig. S6). Fig. S7 shows the relative
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distribution of the counted A, B, and C type craters, and the threshold diameter between
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type A and B and type C is about 85 m. Therefore, the regolith thickness is estimated to be
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about 8.5 m.
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S3. Ages of small craters
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According to Basilevsky [1976], the lifetime of a crater can be estimated as
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𝑇(𝐷) = {
2.5𝐷, 𝐷 < 160 m
8𝐷 − 900 , 𝐷 > 160 m
(1)
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where T is the crater lifetime in Myr, and D is the diameter of a crater in m. Using crater
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morphology, density of surface rocks, inner wall slope, and depth/diameter ratio, a typical
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bowl-shaped crater can be classified into morphological class A, AB, B, BC, and C. Each
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morphological class represents a different degradation stage, with class A representing
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young fresh and class C representing old and degraded. For each morphological class, a
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lifetime fraction is further assigned (A+AB: 0-3%; B: 3-20%; BC: 20-50%; C: 50-100%).
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Then, the age of a crater is estimated as the product of the lifetime and its fraction. The
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accuracy of the estimated age is about 30% [Basilevsky, 1976].
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Using the LROC DTM, slope of the inner wall and depth/diameter ratio of the CE-3 crater are
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calculated to be about 18° and 1/10, respectively. In addition, images from the CE-3 rover-
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mounted panorama cameras and LROC show that there are abundant rocks in the interior
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region, whereas almost no meter-scale rocks beyond the crater rim. Therefore, the CE-3
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crater is classified as morphologic class B, and it is very close to class AB. The lifetime of a
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500 m crater is about 3.1 Gyr, and hence the age of the CE-3 crater is 3.1 Gyr × 3-20% = 93-
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620 Myr. Since morphological prominence of the CE-3 crater is very close to class AB, its age
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can be approximated as 100 Myr with an uncertainty of 30 Myr.
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S4. LPR data processing and subsurface structure identification
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For LPR high frequency channel, the transceiver antenna is chosen as bow tie antenna [Fang
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et al., 2014]. The bow tie antenna is designed with a half-ellipse shape, and is loaded by
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parallel resistors in order to absorb the reflected current at the edge of the antenna.
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Laboratory measurements of the antenna system [Fang et al., 2014] show that the antenna
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can produce a good waveform and antenna ringing can be effectively reduced. Ground
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experiments of the LPR proto [Zhang et al., 2014] show that the LPR performance can meet
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the designed specifications (detection ability and range resolution). In this study, the LPR
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raw data were processed through repetitive observation removal, noise reduction,
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horizontal band removal, band-pass filtering (Fig. 2a), compensation of geometrical
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spreading and dielectric attenuation (Fig. 2b), and range migration (Fig. 2c) in sequence.
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There were LPR observations when the Yutu rover stopped, and repetitive observation
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removal is applied to remove the nearly identical LPR traces and other erroneous traces.
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Horizontal band removal is conducted to remove the influence of complex coupling effect
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between the antenna and the lunar surface. To reduce the lower and higher frequency
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noises, band-pass filtering is further applied. Geometrical spreading makes the amplitude of
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the LPR echo fall off in proportion to the traveled distance, and dielectric loss can attenuate
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LPR signals when propagate in the lunar subsurface. Compensation of geometrical
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spreading and dielectric attenuation is applied to balance the amplitudes of the LPR echoes
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at different depth. A time-domain diffraction stacking range migration method is further
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used to reduce the clutters caused by subsurface discrete targets.
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In the band-pass filtering, a sine-squared function is used
0,
1
sin2 [𝜋2(𝑓𝑓−𝑓
)],
2 −𝑓1
1,
𝐻(𝑓) =
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sin2 [𝜋( 𝑓4−𝑓 )],
{
𝑓 < 𝑓1
𝑓1 ≤ 𝑓 ≤ 𝑓2
𝑓2 ≤ 𝑓 ≤ 𝑓3
2 𝑓4 −𝑓3
𝑓3 ≤ 𝑓 ≤ 𝑓4
0,
𝑓 > 𝑓4
(2)
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where the lower and higher cutoff frequencies are selected as 𝑓1 = 50 MHz and 𝑓4 = 650
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MHz, and 𝑓3 and 𝑓4 are chosen as 150 and 500 MHz. All the LPR data were processed using a
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set of homebrew codes.
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Fig. 2a shows the observations after noise reduction, and is suitable for near surface (<3 m)
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structure identification according to echo strength. Because of the geometrical spreading
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and dielectric attenuation, the strength of radar echoes decreases dramatically with depth.
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These two losses were compensated so deep subsurface echoes become stronger and more
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obvious (Fig. 2b). As the CE-3 crater is young and the landing site is only ~50 m from its
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rim, the LPR survey line is within the continuous ejecta region. Buried rocks in the ejecta
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make the observed LPR image chaotic, and cause additional scattering loss of the incident
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radar waves. Range migration in time domain (aka diffraction stacking) is further applied to
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reduce clutters caused by buried rocks and make deep subsurface feature clearly (Fig. 2c).
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The high-frequency antennas are about 0.273 m from the surface, and the one-way travel
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time is offset in the processed LPR images so that zero time (and also zero depth)
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corresponds to the level of the surface. Rectification of surface topography in LPR image is
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impossible because no topographic data at centimeter scale are available. In Fig. 2a, depths
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of some radar returns are smaller than zero. Compensation of dielectric attenuation and
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range migration were conducted for those echoes with depth larger than zero. Therefore, in
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Fig. 2b and c, there are no echoes for depth smaller than zero. At the navigation points (C, D,
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E/S1, S2, S3, and S4), there were no LPR observations, and the rover may have moved a
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small distance. As a result, when these individual observations were mosaicked, there are
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unavoidable vertical strips at these navigation points (Fig. 2b and c). However, these
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artifacts do not affect the identified subsurface structure in any significant way. The lateral
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distance in Figs. 2 and S8 is calculated from the coordinates of the navigation points in Fig.
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1, which were given in the LPR raw data.
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Subsurface structure was identified from all the three images in Fig. 2. Given the large
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dynamic range of the received radar echoes, the brightness and contrast of local image were
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adjusted in some cases in order to confidently identify subsurface features. The reworked
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zone and the ejecta were identified in Fig. 2a and b. Though there are numerous, chaotic
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layers in the reworked zone and the ejecta, lateral continuity of layers in the reworked zone
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is generally larger than those in the ejecta (Fig. S8a and b). Layers in the reworked zone
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were identified mainly based on Fig. S8a. The ejecta layer contains more subsurface features
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than the paleoregolith. In addition, as seen in Fig. S8b, radar echo strength from the ejecta is
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much stronger than that from the paleoregolith. The interface between the paleoregolith
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and the transition zone is identified by the increase in the strength of the radar echoes (cyan
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lines in Fig. 2b as a conservative base, and reflector 2 as the deepest base). It should be
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noted that from the LPR image, the transition from one zone to another is gradational. Since
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these zones were mainly formed from continuous impacts of meteoroids, there should be no
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abrupt transition from one zone to another from the viewpoint of geology.
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In GPR images, the echo of a discrete scatterer (e.g., rock, void) is a hyperbola [Daniels,
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2004]. In this study, a rock is identified as the vertex of a hyperbola (Fig. S9). Given to the
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large dynamic range of the received echo, the contrast and brightness of local LPR image
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were adjusted in order to identify a rock confidently. In Fig. 3a, the dots represent the
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identified rocks. The number of rocks at a given depth along the survey line is counted from
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Fig. 3a, then normalized by the length of the survey line (85.5 m), and finally, the histogram
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of rock number as a function of depth (Fig. 4b) is obtained by binning the normalized
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number of rocks along depth with a width of 0.5 m.
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In GPR image, the trace of the received radar echo from a buried rock is a hyperbola (Fig.
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S9d). The shape of a hyperbola depends on the antenna height, the depth of buried rock, and
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the real part of the dielectric permittivity [Daniels, 2004]. Fig. S8a-c shows four typical
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hyperbolas in the LPR images that are produced by buried rocks. Fig. S8d show the
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simulated traces of LPR echoes with dielectric permittivity of 1.0, 2.0, 3.0, 5.0 and 7.0 for the
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subsurface, where the antenna height is 0.273 m, and the depth of the buried rock is 1.5 m.
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By comparing the shape of the observed LPR echo with the simulated trace [Arcone et al.,
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1998], real part of the dielectric permittivity can be estimated. The real part of the dielectric
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permittivity of the subsurface materials is estimated as 2.4 for the hyperbola in Fig. S8a, 2.5
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for Fig. S8b, and 3.4 for Fig. S8c. In total, we analyzed more than 50 typical hyperbolas in the
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LPR images, and the results show that the real part of the dielectric permittivity is 3.2 on
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average, corresponding to a bulk density of 1.8 g/cm3.
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S5. Turnover times of the regolith
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Regolith turnover rate at different depth is estimated based on the model proposed by
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Shoemaker et al. [1970] and Gault et al. [1974], and summarized by Melosh [1989]. If a
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crater of diameter D disturbs the regolith to a depth of 𝑑 = 𝐷⁄4, then the average length of
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time between subsequent turnovers roughly equals the time that must elapse before the
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fractional area covered by craters of diameter 𝐷 = 4𝑑 or larger equals one. Overturn time,
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tovr, of the regolith, can be written as,
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2(𝑏−2)
𝑑
𝑏−2
𝑡𝑜𝑣𝑟 ≈ 3𝜋𝑏𝑐 (ℎ )
𝑒𝑞
𝑡𝑠𝑢𝑟
𝑒𝑞
(3)
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where tsur is the surface age, b and c are the power and the coefficient in the cumulative
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distribution of crater number, 𝑁 = 𝑐𝐷 −𝑏 , and ceq is the coefficient in the crater number in
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the equilibrium population,𝑁𝑒𝑞 = 𝑐𝑒𝑞 𝐷 −2. b usually varies from 2.9 to 3.4 for craters smaller
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than 4 km in diameter [Gault, 1970]. If equilibrium occurs at a crater density of about four
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percent of geometry saturation, then ceq is equal to 0.046 [Melosh, 1989]. heq is the
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maximum likely thickness, and can be calculated as
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(4)
ℎ𝑒𝑞 = 𝐷𝑒𝑞 ⁄4
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where Deq is the equilibrium diameter that can be determined directly from the cumulative
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size-frequency distribution of craters. In equation (3), it is assumed that craters formed in
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loose regolith. According to Shoemaker et al. [1970], craters formed in loose regolith are
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about six times larger than craters formed in solid bedrock. As a result, overturn time in
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loose regolith is about one sixth as that in solid bedrock.
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Number of times the regolith has been overturned over the surface age, tsur, is
3𝜋𝑏𝑐𝑒𝑞
𝑑
−(𝑏−2)
𝑁𝑜𝑣𝑟 ≈ 2(𝑏−2) (ℎ )
𝑒𝑞
(5)
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Fig. S10a shows the counted craters for a region surrounding the CE-3 crater that is beyond
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the continuous ejecta, and Fig. S10b shows the counted craters for the CE-3 landing region.
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Using the counted craters, equilibrium diameters over the geologic unit I22 (Fig. S10a) and
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the CE-3 landing region (white box in Fig. S10b) are identified as 161 m and 3.85 m,
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respectively. Fig. S11 shows turnover time and number of turnovers for the newly formed
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regolith and the paleoregolith, where the ages of the newly formed regolith and the
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paleoregolith are 100 Myr and 2.96 Gyr, respectively, and b=3.4. As can be seen, for the
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newly formed regolith, the ejecta have been overturned about 315, 12.5, and 0.5 times at
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depths of 0.01, 0.1 and 1 m. Within the first meter, number of turnovers for the
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paleoregolith is about 186 times larger than that of the newly formed regolith at the same
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depth.
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References
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Arcone, S. A., D. E. Lawson, A. J. Delaney, J. C. Strasser, and J. D. Strasser (1998), Ground-
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penetrating radar reflection profiling of groundwater and bedrock in an area of
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discontinuous permafrost, Geophysics, 63, 1573–1584.
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Basilevsky, A. T. (1976), On the evolution rate of small craters, Proc. Lunar Sci. Conf., 7,
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Daniels, D. (2004), Ground Penetrating Radar, The Institution of Electrical Engineers,
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Eliason, E., C. Isbell, E. Lee, T. Becker, L. Gaddis, A. McEwen, and M. Robinson (1999), The
Clementine UVVIS Global Lunar Mosaic, Lunar and Planetary Institute, Houston.
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Fa, W., T. Liu, M.-H. Zhu, and J. Haruyama (2014), Regolith thickness over Sinus Iridum:
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surface: Criteria and implications, Radio Sci., 5, 273–291.
Gault, D. E., F. Hörz, D. E. Brownlee, and J. B. Hartung (1974), Mixing of the lunar regolith,
Proc. Lunar Sci. Conf., 7, 2365–2386.
Hiesinger, H., R. Jaumann, G. Neukum, and J. W. Head (2000), Ages of mare basalts on the
lunar nearside, J. Geophys. Res., 105, 29239–29275.
Melosh, H. J. (1989), Impact Cratering: A Geologic Process, Oxford University Press, New
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Pike, R. J. (1974), Depth/Diameter relations of fresh lunar craters: Revision from spacecraft
data, Geophys. Res. Lett., 1, 291–294.
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Quaide, W. L., and V. R. Oberbeck (1968), Thickness determinations of the lunar surface
layer from lunar impact craters, J. Geophys. Res., 73, 5247–5270.
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Wilcox, B. B., M. S. Robinson, P. C. Thomas, and B. R. Hawke (2005), Constraints on the depth
and variability of the lunar regolith, Meteorit. Planet. Sci., 40, 695–710.
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Zhang, H. B., et al. (2014), Performance evaluation of lunar penetrating radar onboard the
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rover of CE-3 probe based on results from ground experiments, Research in Astron.
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Astrophys., 14, 1633–1641.
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Figure S1. The CE-3 landing region as shown in LROC images: (a) Mare Imbrium, (b) the
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northern Mare Imbrium, and (c) the CE-3 landing region (M102285549LE). (d) The
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Clementine false-color composite map (red: 750 nm/415 nm; green: 750 nm/950 nm; and
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blue: 415 nm/750 nm) for the northern Mare Imbrium.
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Figure S2. All the counted small fresh craters over a region (8.1 km × 12.2 km) in geologic
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unit I22 surrounding the CE-3 landing site, where the red, green, and blue dots indicate
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normal, flat-bottomed, and concentric craters, respectively.
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Fig. S3. (a) Percentage of normal (red), flat-bottomed (green), and concentric (blue) craters
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as a function of crater diameter for all the counted craters. Relative distributions of (b)
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normal, (c) flat-bottomed, and (d) concentric craters as a function of crater diameter.
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Figure S4. Cumulative distribution of regolith thickness (percentage of area with regolith
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thickness smaller than a given value) estimated from normal (red) and concentric (blue)
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craters. The horizontal error bars show the uncertainty in the regolith thickness, and the
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vertical error bars indicate the uncertainty in the percentage of the area for a given regolith
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thickness, which is calculated based on the one standard deviation (1σ) of the counted
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crater numbers with a Poisson distribution.
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Figure S5. Three types of small craters with different rock populations: (a) a distinctly
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blocky crater (type A), (b) a crater with a few blocks (type B), and (c) a rock-free crater
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(type C). The white arrows indicate the location of surface rocks.
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Figure S6. A LROC NAC image (mosaicked from M1144922100LE and M1144922100RE)
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showing the counted rocky and rock-free craters over the region surrounding the CE-3
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crater. Red dots represent rocky craters, green dots indicate craters with a few rocks, and
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blue dots are rock-free craters.
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Figure S7. The distribution of blocky types A, B, and C craters as a function of diameter for
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the region surrounding the CE-3 crater. The threshold diameter between type A and B
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craters and type C craters is 80-90 m.
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Figure S8. (a) Layers in the reworked zone as in the LPR raw data after horizontal band
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removal and band-pass filtering. (b) The ejecta layer in the LPR image after compensation
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for geometrical spreading and dielectric attenuation, and the cyan line indicates the base of
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the ejecta. The white boxes show four typical hyperbolas produced by buried rocks. (c) The
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paleoregolith as seen in the LPR image processed after range migration, and the red arrows
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indicate four reflectors within the paleoregolith.
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Figure S9. (a-c) LPR images showing typical hyperbolas produced by buried rocks (white
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boxes in Fig. S8b). The hyperbolas are indicated by the black arrows. (b) The traces of GPR
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echoes from a buried rock with different dielectric permittivity of the lunar subsurface
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material. The depth of buried rock is 1.5 m, and the height of the antenna is 0.273 m.
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Figure S10. The counted craters over (a) a region surrounding the CE-3 crater that is
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beyond the continuous ejecta, and (b) the CE-3 landing region.
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Figure S11. (a) Regolith turnover time as a function of depth for the newly formed regolith
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(the black line) and paleoregolith (the red line). (b) Numbers of turnover for the newly
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formed regolith (the black line) and the paleoregolith (the red line).