Difference of brightness temperatures between 19.35 GHz and 37.0 GHz in CHANG’E-1 MRM: implications for the burial of shallow bedrock at lunar low latitude

Abstract

Indications of buried lunar bedrock may help us to understand the tectonic evolution of the Moon and provide some clues for formation of lunar regolith. So far, the information on distribution and burial depth of lunar bedrock is far from sufficient. Due to good penetration ability, microwave radiation can be a potential tool to ameliorate this problem. Here, a novel method to estimate the burial depth of lunar bedrock is presented using microwave data from Chang’E-1 (CE-1) lunar satellite. The method is based on the spatial variation of differences in brightness temperatures between 19.35 GHz and 37.0 GHz (ΔTB). Large differences are found in some regions, such as the southwest edge of Oceanus Procellarum, the area between Mare Tranquillitatis and Mare Nectaris, and the highland east of Mare Smythii. Interestingly, a large change of elevation is found in the corresponding region, which might imply a shallow burial depth of lunar bedrock. To verify this deduction, a theoretical model is derived to calculate the ΔTB. Results show that ΔTB varies from 12.7 K to 15 K when the burial depth of bedrock changes from 1 m to 0.5 m in the equatorial region. Based on the available data at low lunar latitude (30°N–30°S), it is thus inferred that the southwest edge of Oceanus Procellarum, the area between Mare Tranquillitatis and Mare Nectaris, the highland located east of Mare Smythii, the edge of Pasteur and Chaplygin are the areas with shallow bedrock, the burial depth is estimated between 0.5 m and 1 m.

Keywords

moon / CE-1 / brightness temperature / bedrock / burial depth

Introduction

After billions of years of volcanism and high-velocity impacts by numerous meteoroids, most of the lunar bedrock is covered by a layer of regolith. The burial depth of bedrock is not uniform, which might be due to different evolutionary processes during the late period ( Heiken et al., 1991). Determination of burial depth of bedrock can help us to understand the formation of regolith, impact process and relative age of the lunar surface ( Oberbeck and Quaide, 1968; Wilhelms and McCauley, 1971; Bart et al., 2011).

Burial depths of lunar bedrock have been investigated by direct and indirect explorations. The former includes seismic studies ( Watkins and Kovach, 1973; Cooper et al., 1974; Nakamura et al., 1975) and electromagnetic multi-frequency probing ( Strangway et al., 1975). A burial depth of about 7 m at the Apollo 17 landing site is deduced from a sharp change in dielectric properties, based on a study of electromagnetic multi-frequency probing with 32 MHz and 16 MHz made at these sites ( Strangway et al., 1975). Similar results are obtained from the Apollo 17 seismic profiling experiment, which suggested the transition zone from soil to rock is about 8.5 m below the surface ( Olhoeft and Strangway, 1975). On the other hand, indirect explorations which are mainly based on morphological techniques ( Oberbeck and Quaide, 1968; Quaide and Oberbeck, 1968; Shoemaker et al., 1969), radar, and microwave radiometer techniques ( Shkuratov and Bondarenko, 2001; Fa and Jin, 2007, 2010) show a great potential to reveal the burial depth of bedrock. Based on the radar data, Shkuratov and Bondarenko ( 2001) estimates the regolith thickness on lunar highland ranges from 1.0 m to 18.0 m and from 1.5 m to 10.0 m on lunar mare. More recently, similar results were obtained by Fa and Jin ( 2010) by interpreting microwave radiometer data. However, most of the above studies using radar and microwave radiometer detection focused on the areas with thick regolith and paid little attention to the areas with thin regolith (0.5–1 m). Determination of the areas with shallow bedrock is helpful to interpret radar data and design future exploration.

In recent years, successive launches of Chang’E-1 (2007), Chang’E-2 (2010) and Chang’E-3 (2013) marked the beginning of a new era in Chinese lunar research. Chang’E-1(CE-1) was equipped with a four-frequency-channel MRM (Microwave Radiometer) for measuring the microwave emission of the Moon from a 200 km orbit. During 16 months of monitoring, global brightness temperature data spanning lunar day and night were obtained. Some primary results pertaining to regolith distribution have been reported ( Jiang and Wang, 2008; Jiang et al., 2009; Jiang and Jin, 2010). In this study, we present a novel way to investigate distribution and burial depth of shallow bedrock. The brightness temperature difference, or difference in penetrated depth, between two high-frequency channels, 19.35 GHz and 37.0 GHz, defined as ΔTB= TB_19.35 – TB_37.0, is discussed in relation to burial depth.

Data

There are four channels in the CE-1 MRM, i.e., 3.0 GHz, 7.8 GHz, 19.35 GHz, and 37.0 GHz. According to the microwave transmission properties, the penetration depths of the four channels in CE-1 MRM are about 5 m, 2 m, 1 m, and 0.5 m, respectively ( Jiang and Wang, 2008; Li et al., 2010). The spatial resolution is about 35 km for the channels 7.8 GHz, 19.35 GHz, and 37 GHz, and 50 km for 3.0 GHz. The sensitivity of the MRM is about 0.5 K ( Jiang and Wang, 2008; Jiang et al., 2009; Zheng et al., 2012). In this study, the brightness temperature data from the 19.35 GHz and 37 GHz from CE-1 MRM channels are used.

Brightness temperatures (TB) of the two high-frequency channels reveal the heat radiation characteristics of the shallow lunar subsurface. Therefore, the differences between the brightness temperatures of two channels can be used to study the shallow structural properties of the lunar surface. Because the spatial resolutions (35 km) and the orientation of the antenna are the same for the two channels, the areas monitored by the two channels are identical at any time. Thus, difference of brightness temperatures (ΔTB) between two channels reflects the different vertical properties. Topography may have an impact on TB_37.0 and TB_19.35. But ΔTB denotes the difference between two brightness temperatures, so we think the impact of topography on ΔTB is negligible. Observation time is another factor that can influence TB_37.0 and TB_19.35. For the same area, variable solar radiation with time can change the temperature of the lunar surface and the contribution of lunar surface to TB, which could change ΔTB. To minimize the effect of observation time and surface temperature, data in a smaller time range during nighttime are preferred when estimating the burial depth of bedrock. To evaluate the time effect on ΔTB, data from different times at several typical areas are examined (Fig. 1). Figure 2 shows the influence of time interval (Δt) on the fluctuation of ΔTB (δ). It can be seen that, when the range of observation times is within 20 min, the change of ΔTB is less than 0.5 K, close to the radiometric sensitivity of the two channels of the MRM. Therefore, in this study, the TB data from high-frequency channels within 20 min near lunar midnight (00:20–00:40 and 01:00–01:20) during two monitoring periods (November 27, 2007‒February 4, 2008 and May 15, 2008‒July 28, 2008) are selected for discussing the distribution and burial depth of bedrock at low lunar latitude. (30°N–30°S).

Results and discussion

Figures 3 and 4 show spatial variation of ΔTB at lunar low latitude. The largest ΔTB can be found at the southwest edge of Oceanus Procellarum, the area between Mare Tranquillitatis and Mare Nectaris and the eastern highland of Mare Smythii. In these regions, ΔTB is usually larger than 12.7 K and the maximum is close to 14 K.

According to the analysis above, while the observation times of selected data are within 20 min around the midnight, the time effect on ΔTB is less than 0.5 K. But calculated ΔTB values ranges from 2 K to 14 K in some areas. Thus, we think the effect of observation time on ΔTB is insignificant. Such large variation in ΔTB values in low lunar latitudes should be attributed to another reason. The effect of topography on ΔTB is also excluded since it affects TB_37.0 and TB_19.35 simultaneously. Thus, the large variation in ΔTB values as shown in Figs. 3 and 4 might be caused by significant difference of vertical structure, e.g., the burial depth of bedrock.

To examine this deduction, the geomorphology of the regions which have large ΔTB values is investigated using the LOLA DEM data. In the contour maps (Figs. 5–8), the areas with large ΔTB values are always accompanied by dense contours, indicating a large change in elevation and steep slope in these areas. More specifically, the regions with large ΔTB values are usually located in the transition zone between a negative landform and a positive landform.

To detail the characteristics of topography at special regions with large ΔTB, the eastern highland of Mare Smythii (circle marked with A and B in Figs. 3 and 7) and Chaplygin crater (circle marked with C in Figs. 3 and 8) are further analyzed. Both region A and B are located at the steep sides of the crater (Fig. 7). The elevation differences of these areas are 4,319 m and 3,132 m, respectively. And region C also shows a large elevation difference with 3,044 m. Due to large elevation difference, it is difficult for regolith to accumulate during the later impact of meteoroid ( Heiken et al., 1991; Bandfield et al., 2011). Reasonably, the burial depth of bedrock is relatively shallow in these regions and shows a correlation with the large ΔTB.

To discuss the relationship between burial depth of bedrock and ΔTB, Aristarchus, Copernicus and Bullialdus Crater (circle marked with D–F in Fig. 4, respectively) are investigated. After analyzing weathering degree, rock concentration and regolith thickness of large craters, Bandfield et al. ( 2011) concluded that regolith thickness is negatively correlated to rock concentration in craters, i.e., high rock concentration often comes with thin regolith thickness and shallow bedrock. According to the rock concentrations given by Bandfield et al. ( 2011), Aristarchus Crater with the highest rock concentration has the shallowest bedrock while Bullialdus Crater has the deepest (Fig. 9). In addition, the ages of these craters can also provide some information on the burial depth of bedrock. Usually, accumulation of regolith is relatively limited and bedrock burial is shallow in young craters because of the weak weathering degree ( Mendell, 1976). Among the three craters, Aristarchus Crater is the youngest one while Bullialdus Crater is the oldest ( Neukum and König, 1976). Thus, the same conclusion can be reached that the bedrocks in Aristarchus Crater and Bullialdus Crater are the shallowest and deepest respectively among the three craters. With the analysis of CE-1 MRM data, ΔTB of Aristarchus, Copernicus and Bullialdus are 11.2 K, 10.3 K and 6.6 K, respectively. Thus it is obvious that ΔTB values show an opposite trend with burial depths of bedrock at the three craters. Aristarchus Crater with shallow bedrock shows the largest ΔTB while Bullialdus Crater is the opposite case.

As shown above, large ΔTB has the potential to be an indicator of shallow burial depth of bedrock. According to the penetrated depths of 19.35 GHz and 37.0 GHz channels, ΔTB is mainly controlled by the properties of the subsurface layer from 0.5 m to 1 m. When bedrock is buried deeper than 1 m, this layer is full of regolith. When depth to bedrock is less than 1 m, there is some bedrock in this layer. Different structures and properties of this layer might lead to distinct ΔTB values. Based on the theory of microwave radiative transfer, Jin and Fa ( 2011) proposed a three-layer model to simulate TB theoretically. In their model, the temperature of top layer is considered to be constant, which however is not appropriate since the temperature gradient is very large in the first two centimeters from the top ( Vasavada et al., 2012). Vasavada et al. ( 1999) used a two-layer model to calculate the temperatures at different depths. Their data show that at depths greater than 20 cm temperature remains fairly constant. Thus, in our study, the lunar regolith from the top to 20 cm is regarded as the first layer, where temperature changes significantly. The second layer is the lunar regolith layer from 20 cm to the boundary between regolith and bedrock. The third layer is bedrock. The temperatures in the latter two layers are assumed to be constant. Thus, the equation is given as follows,

(1) \mathrm{T}\mathrm{B}=\left(\mathrm{1}-r_{\mathrm{01}}\right)\left[k_{a\mathrm{1}}{\displaystyle \underset{\mathrm{0}}{\overset{d_{\mathrm{1}}}{\int }}{T}_{\mathrm{1}}\left(z\right)}{\mathrm{e}}^{-k_{a\mathrm{1}}z}\mathrm{d}z+r_{\mathrm{12}}{\mathrm{e}}^{-k_{a\mathrm{1}}{d}_{\mathrm{1}}}{k}_{a\mathrm{1}}{\displaystyle \underset{\mathrm{0}}{\overset{d_{\mathrm{1}}}{\int }}{T}_{\mathrm{1}}\left(z\right)}{\mathrm{e}}^{-k_{a\mathrm{1}}\left(d_{\mathrm{1}}-z\right)}\mathrm{d}z\right]+\left(\mathrm{1}-r_{\mathrm{01}}\right)\left(\mathrm{1}-r_{\mathrm{12}}\right)\left(\mathrm{1}-{\mathrm{e}}^{-k_{a\mathrm{2}}{d}_{\mathrm{2}}}\right)\left(\mathrm{1}+r_{\mathrm{23}}{\mathrm{e}}^{-k_{a\mathrm{2}}{d}_{\mathrm{2}}}\right){\mathrm{e}}^{-k_{a\mathrm{1}}{d}_{\mathrm{1}}}{T}_{\mathrm{2}}+\left(\mathrm{1}-r_{\mathrm{01}}\right)\left(\mathrm{1}-r_{\mathrm{12}}\right)\left(\mathrm{1}-r_{\mathrm{23}}\right){\mathrm{e}}^{-k_{a\mathrm{1}}{d}_{\mathrm{1}}}{\mathrm{e}}^{-k_{a\mathrm{2}}{d}_{\mathrm{2}}}{T}_{\mathrm{3}},

where, d₁ is the thickness of the first layer and equal to 0.2 m; d₂ is the thickness of second layer which is variable; T₁(z), T₂ and T₃ are the physical temperatures of the three layers, respectively; z is the depth from the top in the first layer. Definitions of all the other parameters in Eq. (1) are referred in the study of Jin and Fa ( 2011). According to Fa and Jin ( 2007), T₂=T₃=255 K are used to calculate the TB. The mean dielectric constant of lunar rock equal to 6.84+0.342i measured at several Apollo landing sites (Heiken et al., 1991) is used in this study. Dielectric constant of lunar regolith is a function of density (ρ) and content (S) of FeO+TiO₂ ( Heiken et al., 1991). And ρ changes with depth while S can be calculated with the data of Clementine ( Fa and Jin, 2007). In Eq. (1), T₁(z) can be calculated from the following exponential equation ( Vasavada et al., 1999),

(2) T_{\mathrm{1}}\left(z\right)=A{e}^{-\beta z}+B,

when z=0 and z=d₁=0.2 m,

(3) T_{\mathrm{1}}\left(\mathrm{0}\right)=A+B,

(4) T_{\mathrm{1}}\left(\mathrm{0.2}\right)=A{\mathrm{e}}^{-\mathrm{0.2}\beta }+B=T_{\mathrm{2}}=T_{\mathrm{3}}.

Values of T₁(0) at different latitudes are listed in Table 1 ( Bandfield et al., 2011). Based on the data from DivRDR (ch7), β can be supposed to be 20. With the parameters mentioned above, the theoretical ΔTB when the bedrock burial depths are 0.5 m and 1 m are given in Table 2 and 3. From the tables, it can be seen that theoretical ΔTB increases slightly with latitude when bedrock burial is shallow. At the equatorial regions, the theoretical ΔTB is ~12.7 K when bedrock burial depth is 1 m, and it is ~15 K when bedrock burial depth is 0.5 m. According to ΔTB shown in Figs. 3 and 4, it can thus be inferred that the bedrock burial depths are between 0.5 m and 1 m in some regions of high ΔTB values, such as the southwest edge of Oceanus Procellarum, the southern edge of Mare Tranquillitatis, the eastern highlands of Mare Smythii, and the edges of Pasteur and Chaplygin carters. Most of lunar bedrock is burial deeper than 1 m at low latitude (Fig. 10).

Conclusions

The microwave data obtained by CE-1’ MRM provide an opportunity to investigate the burial depth of lunar bedrock. To minimize the effect of measurement time (or solar radiation) on ΔTB, data close to midnight (00:20–00:40 and 01:00–01:20) are chosen. Based on the spatial variation in ΔTB values, the southwest edge of Oceanus Procellarum, the area between Mare Tranquillitatis and Mare Nectaris, and the eastern highland of Mare Smythii show large ΔTB values which are generally greater than 12.7 K, and the maximum is close to 14 K. Contour maps of these areas show that all of them are in the transition zone between a negative landform and a positive landform where elevation changes rapidly. That might indicate a shallow burial depth of bedrock in these areas. Based on theoretical calculations, ΔTB ranges from 12.7 K to 15 K when the burial depth of bedrock is between 0.5 m and 1 m at the equatorial regions. With these results, the burial depth of bedrock in the southwest edge of Oceanus Procellarum, the southern edge of Mare Tranquillitatis, the eastern highlands of Mare Smythii, and the edges of Pasteur and Chaplygin crater are estimated to range from 0.5 m to 1 m.

This study presents a new way to study the vertical structure of the lunar surface and, especially, to estimate the burial depth of bedrock using ΔTB between high-frequency channels. However, it should be noted that calculated ΔTB is an average value in a large area due to the limitation of spatial resolution of MRM. Thus, the inferred burial depth of bedrock also represents an average depth in that area. In the future, high-resolution microwave data will be helpful to determine accurately the distribution of shallow bedrock.

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