Journal of Geophysical Research: Planets

Estimation of the permittivity and porosity of the lunar uppermost basalt layer based on observations of impact craters by SELENE

Authors


Corresponding author: K. Ishiyama, Graduate School of Science, Tohoku University, 6–3 Aramaki Aoba, Aoba-ku, Sendai, Miyagi, 980–8578, Japan. (ishiyama@stpp.gp.tohoku.ac.jp)

Abstract

[1] We have investigated the geological conditions below two lava flow units through determining the bulk permittivity and porosity in the uppermost basalt layer to depths of a few hundred meters. We use a newly developed method based on three data sets obtained by the Lunar Radar Sounder (LRS), Multiband Imager (MI), and Terrain Camera (TC) onboard the Selenological and Engineering Explorer (SELENE; Kaguya) spacecraft. The bulk permittivity of the uppermost basalt layer is calculated as the ratio of the apparent radar depth to the thickness of the uppermost basalt layer. Its thickness can be constrained from the excavation depths of two types of craters (haloed and nonhaloed craters). These craters are identified on the basis of FeO and/or TiO2 maps created from the MI data. These excavation depths are determined based on the measurement of the crater diameter using the TC data. The apparent radar depth is derived from the time delay between the surface echo and subsurface echo measured by LRS near the craters. The bulk permittivities are estimated to be 2.8–5.5 in a lava flow unit of Mare Humorum and 4.2–18.0 in a lava flow unit of Mare Serenitatis. These bulk permittivities are indicative of porous basalt layers with the porosities of 19%–51% in the unit of Humorum and 0%–33% in the unit of Serenitatis. The estimated porosities would be mainly explained by two different sources: intrinsic voids of lava and impact-induced cracks.

1 Introduction

[2] Permittivity is a parameter that indicates how a medium is affected by an ambient electric field. Permittivity is controlled by a number of factors, including the number density of the dielectric dipole moment and the polarizability. The number density of the dielectric dipole moment is broadly dependent on the density of a mineral [e.g., Guéguen and Palciauskas, 1994; Watanabe, 2005]. Theoretical derivation of the polarizability of a material is complicated, except for simple materials such as monoatomic molecules [e.g., Watanabe, 2005].

[3] Bulk permittivities, which are permittivities of materials including the pore space, of soils, cores, and rocks collected by Apollo missions (Apollo 11–17) were measured to be 1.66–11.00 [Carrier et al., 1991]. The bulk permittivity of soils is less than ~4, and the bulk permittivity of rock samples is larger than ~4 [e.g., Olhoeft and Strangway, 1975; Carrier et al., 1991]. The bulk permittivity of Apollo samples was shown to be empirically dependent on their bulk density and composition (especially TiO2 and FeO contents) [Olhoeft and Strangway, 1975; Carrier et al., 1991; Shkuratov and Bondarenko, 2001]. The ilmenite (FeTiO3), which is the most abundant oxide mineral in the Moon [e.g., Papike et al., 1991], has high permittivity due to the high polarizability of oxygen atoms in its structure [e.g., Guéguen and Palciauskas, 1994; Watanabe, 2005].

[4] Permittivity is also an important property in the analysis of radar sounder data. The bulk permittivity of a subsurface layer contributes principally to the determination of the depth of a subsurface echo and the range resolution of a radar sounder. In the case of a subsurface echo depth, the radar sounder simply measures the time delay between a subsurface echo arrival and the surface echo arrival (Δt). The propagation speed of radio waves in lunar rocks is inline image, where c is the speed of light in vacuum, and inline image is the bulk permittivity of the subsurface material including the pore space. Therefore, the depth of a subsurface feature (d), based on radar observations is given by

display math(1)

[e.g., Ono and Oya, 2000]. The range resolution of the radar sounder is expressed as a function of the bulk permittivity in materials, through which the electromagnetic waves have propagated [e.g., Pommerol et al., 2010].

[5] The Apollo Lunar Sounder Experiment (ALSE) onboard the Apollo 17 mission detected deep (> km) subsurface echoes in some lunar maria [e.g., Peeples et al., 1978; Sharpton and Head, 1982; Cooper et al., 1994]. In addition, the Lunar Radar Sounder (LRS) onboard the Selenological and Engineering Explorer (SELENE) spacecraft detected shallower subsurface echoes reflected at depths of a few hundred meters, which result from lunar subsurface structures in the nearside maria [Ono et al., 2009; Oshigami et al., 2009; Pommerol et al., 2010]. Given that the depth of a subsurface reflector is associated with a thickness of the lava flows, it can potentially be used to understand the history of lunar volcanic activity and lunar evolution [e.g., Ono et al., 2009]. The stratigraphy surrounding lunar impact craters was recently investigated by combining the data obtained from LRS and Multiband Imager (MI) onboard SELENE spacecraft [Oshigami et al., 2012].

[6] The bulk permittivities of 8 – 9, based on Apollo basalt samples, were often used in the previous works based on lunar radar observations [e.g., Peeples et al., 1978; Cooper et al., 1994; Oshigami et al., 2009]. The previous works assumed that there is no bulk permittivity difference between Apollo basalt samples, which were collected on the lunar surface, and basalt layers below the surface. However, this assumption has not yet been fully tested. The objective of our study was to determine the bulk permittivity of basalt layers, from remote-sensing data only. We then use the bulk permittivity estimates to constrain the porosity of basalt layers because porosity can reveal geological conditions beneath the lunar surface. The lava units analyzed in this study are located at the west side of Mare Humorum, and at the middle of Mare Serenitatis. Their surface areas are ~3000 m2 in Mare Humorum [Hackwill et al., 2006] and ~10,000 m2 in Mare Serenitatis [Hiesinger et al., 2000].

2 Analytical Methods

2.1 Estimation of Bulk Permittivity in the Uppermost Lunar Basalt Layer

[7] The bulk permittivity (inline image) in the uppermost basalt layer, which is the permittivity of a layer including pore space, can be calculated from equation ((1)):

display math(1’)

where dradar is the apparent radar depth, which is a function of Δt measured by a radar observation. Because dradar is obtained by substituting inline image = 1 to equation ((1)), it should be noted that dradar is not equal to the thickness of the uppermost basalt layer (d). We consider a simple model to determine dradar and d (Figure 1). This model is composed of two types of subsurface layers: namely an uppermost basalt layer and a lower basalt layer. These layers have a different mineral composition, and are composed of a pile of smaller scale layers that cannot be resolved by LRS. d is estimated using two types of impact craters: haloed crater and nonhaloed crater. In general, impact crater can be classified into these crater types [Weider et al., 2010]. “Haloed crater” is defined as a crater for which the related ejecta have a different mineral composition (TiO2 and FeO wt %) from that of the uppermost basalt layer (Figure 1). This crater type is formed when a large meteorite collides with the lunar surface and excavates through to the lower basalt layer. Conversely, “nonhaloed crater” is defined as a crater for which the related ejecta have the same chemical composition (TiO2 and FeO wt %) as that of the uppermost basalt layer (Figure 1). This crater type is formed when a small meteorite collides with the lunar surface and does not penetrate through the entire uppermost basalt layer. The estimation method of d consists of three steps: (i) the search of impact craters, (ii) the discrimination of haloed and nonhaloed impact craters, and (iii) the estimation of the excavation depths of these craters.

Figure 1.

Schematic cross section of the lunar geological structure model used in this study. An uppermost basalt layer overlies a lower basalt layer. The different (clear and stippled) shading indicates the different mineral compositions and bulk permittivities. The homogeneous thickness of the uppermost basalt layer (d) is constrained from the excavation depths of the nonhaloed and haloed craters (dnon and dh: dnon < d < dh), shown using the rosy brown color. These depths can be estimated from their rim-to-rim diameters. We assume that the electromagnetic wave emitted by LRS is reflected at the horizontal boundary between the layers. After an incident wave is emitted at t = 0, LRS receives the waves, reflected at the lunar surface at t = t0/2 and at the boundary at t = (t0 + Δt)/2. The apparent radar depth of the uppermost basalt layer (dradar) can therefore be obtained by the expression inline image, where c is the speed of light in vacuum. The bulk permittivity range of the uppermost basalt layer is calculated from equations ((2a)) and ((2b)), using the parameters (dradar, dh, and dnon).

[8] First, we look for impact craters using the data obtained from MI and Terrain Camera (TC) onboard the SELENE spacecraft. We use three data sets: the 750 nm map data (albedo image data) obtained from MI [Ohtake et al., 2008], and the Ortho images and Digital Terrain Models (DTMs) data produced by the TC data [Haruyama et al., 2008]. The TC data is useful for searching small impact craters because the TC data has the high spatial resolution: 10 m/pixel at the SELENE nominal altitude of 100 km [Haruyama et al., 2008].

[9] Second, we discriminate the haloed crater and the nonhaloed crater by searching the ejecta blanket with different composition around impact craters. These compositions are investigated within ~1 crater radii beyond the rims of impact craters, as performed by Weider et al. [2010]. These crater types is discriminated by using the MI TiO2 and FeO map data [Otake et al., 2012], produced from the algorithms proposed by Lucey et al. [2000]. Lucey's alogorithms take into consideration the effects of space weathering, so that we can derive the iron and titanium abundances without those effects. The geochemical maps produced in this study have the spatial resolution of 120 m/pixel, and the standard deviation of FeO is 0.81 wt % and that of TiO2 is 0.43 wt % [Otake et al., 2012]. We first search haloed craters; after that, nonhaloed craters are searched in the vicinity of the haloed craters.

[10] Third, the excavation depths of the found craters are estimated in order to constrain the thickness of the uppermost basalt layer (d) (Figure 1). Weider et al. [2010] determined the thickness of the lunar basalt layer using the excavation depth (dexc), which can be calculated from the rim-to-rim diameter of the impact crater (Dcrater): dexc = 0.1 × 0.84 × Dcrater [Melosh, 1989]. This relationship can be applied in the case that Dcrater is smaller than 15 km. In this study, Dcrater is measured directly by using the ortho image data and DTMs data. The thickness of the uppermost basalt layer (d) can thus be constrained by the excavation depths of a haloed crater (dh) and the depth of a nonhaloed crater (dnon): dnon < d < dh (Figure 1). These depths have an error (Δd = ±0.84 m) caused from the spatial resolution of TC data (10 m/pixel).

[11] The apparent radar depth (dradar) is determined around craters by using LRS/B-scan display, which is time-versus-range plot for showing the radar data [Kobayashi et al., 2002]. Synthetic aperture radar (SAR) processing [Kobayashi et al., 2012] is applied to the LRS data in order to robustly identify the subsurface echoes. The synthetic aperture is 5 km, and the spatial resolution of the LRS data is 600 m along the track direction and approximately 5 km along the cross-track direction [Kobayashi et al., 2012]. The range resolution of LRS is 75 m in vacuum [Ono and Oya et al., 2000]. The error (Δdradar) of dradar is defined as Δdradar = ±75 m.

[12] Finally, the bulk permittivity of the uppermost basalt layer is calculated from equation ((1’)). The minimum and maximum bulk permittivities (inline image and inline image) are determined by the minimum and maximum thickness (dmin and dmax) of d, which are determined by the excavation depths of the haloed crater (dh) and the nonhaloed crater (dnon):

display math(2a)
display math(2b)

where inline image < inline image < inline image. These permittivities have an error, which is derived from two errors of dradar and dh or dnon. The parameters used for the calculation of the bulk permittivity are listed in Table 1.

[13] In this study, we assume (a) a horizontal boundary between the uppermost basalt layer and the lower basalt layer and (b) that the electromagnetic wave, emitted by LRS, can be reflected between the uppermost basalt layer and the underlying basalt layer, which can be identified by the mineral contrast seen in multiband images (Figure 1). As for the assumption (a), the distance between the haloed and nonhaloed craters must be limited. If the subsurface boundary is tilted and the distance between them is far, the thickness of the uppermost basalt layer cannot be determined correctly. Thus, the distance between them should be as small as possible. In this study, nonhaloed craters are found within ~6 km from a haloed crater. In addition, a maximum distance between the craters (the haloed and nonhaloed craters) and the LRS nadir point is also limited within ~6 km. As for the assumption (b), we must consider whether a buried regolith layer is formed between the uppermost basalt layer and the underlying basalt layer because the many subsurface echoes detected by LRS are reflected in buried regolith layers [Ono et al., 2009; Oshigami et al., 2009; Oshigami et al., 2012]. The detail of the assumption (b) is discussed in section 4.1.

2.2 Determining the Grain Permittivity

[14] The bulk permittivities of Apollo samples were measured and summarized in the previous works [e.g., Olhoeft and Strangway, 1975; Carrier et al., 1991]. They revealed that the bulk permittivity (inline image) strongly depended on the bulk density (ρbulk):

display math(3)

ρbulk can be expressed as a function:

display math(4)

where P is the porosity of the uppermost basalt layer, and ρgrain is the grain density, which indicates the density of the uppermost basalt layer without any pore space. ρgrain can be empirically given as a function of mineral composition (FeO and TiO2) based on Apollo samples [Huang and Wieczorek, 2012]:

display math(5)

Therefore, the bulk permittivity can be expressed as a function of P, FeO, and TiO2 in the uppermost basalt layer. Supposing P = 0, we can define the grain permittivity:

display math(6)

This indicates the permittivity of the uppermost basalt layer without any pore space. The bulk permittivity is lower than the grain permittivity (i.e., inline image < inline image), so that the grain permittivity can give the upper limit of the permittivity for the uppermost basalt layer.

[15] The mineral composition of equation ((5)) is determined from multiband imaging of the ejecta blanket around the deepest nonhaloed craters. We suppose that this ejecta composition gives a composition of the uppermost basalt layer. If the uppermost basalt layer has a homogeneous composition, this supposition is valid. The error of the grain permittivity is determined from the standard deviations of the algorithms for the derivation of iron and titanium [Otake et al., 2012] and/or the standard deviation of the ejecta composition. These errors are described in section 2.1 and Table 1.

2.3 Estimation of the Porosity in the Uppermost Basalt Layer

[16] Porosity is an important parameter for constraining lunar geological conditions. The porosity of the uppermost basalt layer (P) can be estimated from equations ((3)), ((4)), and ((5)):

display math(7)

where inline image is the bulk permittivity estimated in the uppermost basalt layer. The minimum and maximum porosities (Pmin and Pmax; Pmin < P < Pmax) are given as

display math(8a)
display math(8b)

Equations ((8a)) and ((8b)) are based on equations ((2a)), ((2b)), and ((7)). dradar is the apparent radar depth of the uppermost basalt layer. dnon and dh are the excavation depths of the nonhaloed crater and haloed crater (dnon < dh). The mineral composition (TiO2 and FeO) is based on the ejecta composition of the deepest nonhaloed crater (Figure 1), which gives a composition of the uppermost basalt layer in this study.

[17] The errors of Pmin and Pmax can be estimated from the errors of dnon or dh, and dradar and ejecta composition (TiO2 and FeO). The errors of dh, dnon, and dradar are relatively larger than that of the ejecta composition, so that we evaluate the errors of the porosity using three parameters.

3 Results

[18] We have searched all Mare regions for favorable combinations of haloed crater, nonhaloed crater, and subsurface radar echoes, but we have found only two regions, Unit 85 of Mare Humorum and Unit S13 of Mare Serenitatis, suitable for our analysis (Figures 2a and 2b). The diameters of the found craters were smaller than 15 km (Table 1). The mineral composition (TiO2 and FeO) of the interior of some haloed craters appears different than their ejecta. We infer that it is caused by the inaccuracy of the reflectance data of MI due to the steep slope inside the small craters (i.e., due to topographic effects), or the collapse of the wall, the composition of which is the same as the uppermost basalt layers.

Figure 2.

(a) FeO map in Mare Humorum and (b) TiO2 map in Mare Serenitatis. The maps were derived using the MI data and the algorithms of Lucey et al. [2000]. The boundaries of the lava flow units are shown as blue curves, and the unit numbers, based on Hackwill et al. [2006] and Hiesinger et al. [2000], are indicated in black. The numbers of the haloed craters are indicated in white. White arrows show the locations of haloed craters. Haloed crater 1 in Unit 85 of Mare Humorum is evident in the FeO map. Haloed craters 1 to 6 in Unit S13 of Mare Serenitatis are evident in the TiO2 map.

3.1 Unit 85 of Mare Humorum

[19] We looked for impact craters in Unit 85 of Mare Humorum using the albedo image (MI/750 nm) data, the Ortho image data, and DTMs data. In order to estimate the thickness of the uppermost basalt layer (see Figure 1), haloed craters first were found using FeO and TiO2 maps (Figure 2a). A crater was found at 316.65°E, 25.97°S in Unit 85 of Mare Humorum (Table 2, Figures 4a, and 4b). The ejecta around the crater clearly have a different mineral composition (TiO2 and FeO wt %) from that of Unit 85 of Mare Humorum (Figures 3a and 4c); we could identify a haloed crater in this unit. We did not identify any other haloed craters in Unit 85 of Mare Humorum, probably because other haloed craters, older and larger than the one observed, are covered by the ulterior lava flows. Then, we looked for nonhaloed craters in the vicinity of the haloed crater. We identified a crater, located at 316.73°E, 25.85°S. The ejecta composition around the crater is similar to those of Unit 85 of Mare Humorum (Figures 3a and 4c); this crater is a nonhaloed crater, the deepest nonhaloed crater in the vicinity of the haloed crater.

Figure 3.

Abundance of TiO2 versus FeO for ejecta of the haloed and nonhaloed craters in (a) Unit 85 of Mare Humorum and (b) Unit S13 of Mare Serenitatis. The TiO2 and FeO abundances were derived using the algorithms of Lucey et al. [2000]. The TiO2 and FeO abundances around the nonhaloed craters are similar to that of the uppermost basalt layer (i.e., Unit 85 and Unit S13), while the TiO2 and FeO abundances around the haloed crater are quite distinct from the uppermost basalt layer. Thus, the thickness of the uppermost basalt layer (d) can be constrained by using the excavation depths of the haloed and nonhaloed craters (dh and dnon: dnon < d < dh), obtained from the TC/DTMs and Ortho image data (See Figure 1).

Figure 4.

Analysis results of Crater Combination 1 in Unit 85 of Mare Humorum. (a) MI 750 nm image. (b) MI 750 nm image showing the track along the LRS data (red dashed line) and the tracks along the crater's cross section (green dashed lines). (c) FeO map created using MI data. (d) Cross section of the haloed crater obtained using TC/DTM data. (e) Cross section of the nonhaloed crater obtained using TC/DTM data. (f) B-scan display obtained by LRS. The arrow shows the location of the crater. The LRS track is shown as the red dashed line in Figure 4b. (g) B-scan display with the trace of the subsurface echo (red dashed line). The apparent radar depth is obtained around the red point of Figure 4b.

[20] The excavation depths of the nonhaloed and haloed craters (dnon and dh) were estimated to be dnon = 214 ± 0.84 m and dh = 300 ± 0.84 m (Figures 4d and 4e), calculated from the rim-to-rim diameters of nonhaloed and haloed craters: 2.55 km and 3.57 km, respectively (Table 1). Thus, the thickness of the uppermost basalt layer (i.e., the thickness of Unit 85 of Mare Humorum) (d) was constrained to be in the range: 214–300 m. In parallel, the subsurface reflector was also identified in the vicinity of these craters at an apparent radar depth (dradar) of 500 ± 75 m at 316.67°E, 25.80°S by using LRS/B-scan display (Figures 4f and 4g). The bulk permittivity (inline image) was estimated to lie between 2.8(+0.9/−0.8) and 5.5(+1.8/−1.6) in Unit 85 of Mare Humorum from equations ((2a)) and ((2b)). This estimated bulk permittivity corresponds approximately to the bulk density that lies between 1.6(+0.4/−0.5) g cm−3 and 2.6(+0.4/−0.5) g cm−3 based on equation ((3)).

[21] The pore-free grain permittivity (inline image) of the uppermost basalt layer in Unit 85 of Mare Humorum can be estimated to be 8.1 ± 1.0 from equations ((5)) and ((6)). The values used for the calculation of inline image are 1.96 ± 0.43 wt % for TiO2 and 15.20 ± 0.81 wt % for FeO. The difference between the bulk and grain permittivities can be explained by the porosity of the uppermost basalt layer. This porosity is thus estimated to lie between 19(+16/−14)% and 51(+16/−14)% using equations ((8a)) and ((8b)).

3.2 Unit S13 of Mare Serenitatis

[22] In Unit S13 of Mare Serenitatis, we also looked for impact craters using the albedo image data, the Ortho image data, and DTMs data. Haloed craters first were searched using FeO and TiO2 maps. Five craters were identified by using TiO2 map (Figure 2b). The ejecta composition around these craters have a different mineral composition (TiO2 and FeO wt %) than Unit S13 of Mare Serenitatis (Figure 3b); we could identify five haloed craters. Then, we looked for nonhaloed craters in the vicinity of the haloed craters. Several nonhaloed craters were identified because their ejecta compositions are similar to those of Unit S13 of Mare Serenitatis (Figures 3b, 5c, and 6c). Following the identification of the haloed and nonhaloed craters, the excavation depth is calculated from the rim-to-rim diameters of these craters in order to constrain the thickness of the uppermost basalt layer (i.e., the thickness of Unit S13 of Mare Serenitatis) (Figures 5d, 5e, 6d, and 6e). The excavation depths of the identified haloed craters (dh) ranged from 169 ± 0.84 m at 17.25°E, 22.62°N to 733 ± 0.84 m at 15.43°E, 19.63°N, and the excavation depths of nonhaloed craters (dnon) ranged from 63 ± 0.84 m at 16.82°E, 24.48°N to 118 ± 0.84 m at 15.53°E, 19.72°N (Tables 1 and 2). Thus, we could constrain the thickness of Unit S13 of Mare Serenitatis to be 118–169 m. On the other hand, we can also point out by using LRS/B-scan display that the apparent radar depths (dradar) lay between 357 ± 75 m and 571 ± 75 m (Table 1, Figures 5f, 5g, 6f, and 6g). If the uppermost basalt layer (Unit S13) has a homogeneous thickness and bulk permittivity (See Figure 1), the apparent radar depth should not be changed. However, the results of the apparent radar depth suggest that the thickness of Unit S13 of Mare Serenitatis is not homogeneous. So we have derived the bulk permittivity range by using each crater combination (CC) of haloed crater and nonhaloed crater. Based on the derived bulk permittivity ranges, we could constrain the bulk permittivity of Unit S13 of Mare Serenitatis.

Figure 5.

Analysis results of Crater Combination 5 in Unit S13 of Mare Serenitatis. (a) MI 750 nm image. (b) MI 750 nm image showing the track along the LRS data (red dashed line) and the tracks along the crater's cross section (green dashed lines). (c) FeO map created using MI data. (d) Cross section of the haloed crater obtained using TC/DTM data. (e) Cross section of the nonhaloed crater obtained using TC/DTM data. (f) B-scan display obtained by LRS. The arrow shows the location of the crater. The LRS track is shown as the red dashed line in Figure 5b. (g) B-scan display with the trace of the subsurface echo (red dashed line). The apparent radar depth is obtained around the red point of Figure 5b.

Figure 6.

Analysis results of Crater Combination 6 in Unit S13 of Mare Serenitatis. (a) MI 750 nm image. (b) MI 750 nm image showing the track along the LRS data (red dashed line) and the tracks along the crater's cross section (green dashed lines). (c) FeO map created using MI data. (d) Cross section of the haloed crater obtained using TC/DTM data. (e) Cross section of the nonhaloed crater obtained using TC/DTM data. (f) B-scan display obtained by LRS. The arrow shows the location of the crater. The LRS track is shown as the red dashed line in Figure 6b. (g) B-scan display with the trace of the subsurface echo (red dashed line). The apparent radar depth is obtained around the red point of Figure 6b.

Table 1. Details of the Craters and Estimated Bulk Permittivities in Unit 85 of Mare Humorum and Unit S13 of Mare Serenitatisa
DiscriminationCrater Combination Numberinline imageDcrater (m)dh (m)dnon (m)dradar (m)TiO2 and FeO of Ejecta
AverageStandard Deviation
TiO2 (wt %)FeO (wt %)TiO2 (wt %)FeO (wt %)
  1. a

    dh: Excavation depths of haloed craters. dnon: Excavation depths of nonhaloed craters. Dcrater: Diameters of impact craters. dradar: Apparent radar depths of the subsurface boundary identified by LRS. inline image: Bulk permittivities calculated by equation ((1’)).

 
Unit 85 of Mare Humorum
Haloed crater 112.83570300-5001.5212.480.210.65
Nonhaloed crater 15.52550-2145001.9615.200.230.63
 
Unit S13 of Mare Serenitatis
Haloed crater 112.12920245-3574.6217.700.440.45
Nonhaloed crater 1-890-75-3.0317.280.330.24
Haloed crater 222.52690226-3574.1917.480.550.26
Nonhaloed crater 232.1750-633573.2017.700.380.48
Haloed crater 33-2010169--4.1617.570.500.14
Nonhaloed crater 3-1370-115-3.3917.320.510.19
Haloed crater 442.73130263-4294.6617.600.680.30
Nonhaloed crater 418.01200-1014293.2617.100.360.46
Haloed crater 554.22490209-4294.1916.960.550.19
Nonhaloed crater 537840-714293.2916.630.630.38
Haloed crater 660.68730733-5714.3217.670.630.27
Nonhaloed crater 6181400-1185002.4317.250.440.34
Table 2. Details of the Locations of Haloed/Nonhaloed Craters and LRS Nadir Points
DiscriminationCrater Combination NumberCrater LocationLRS Nadir PointDistance
Latitude [deg]Longitude [deg]Latitude [deg]Longitude [deg]LRS ~ Halo [km[LRS ~ Nonhalo [km]Halo ~ Nonhalo [km]
Unit 85 of Mare Humorum
Haloed crater 11−25.97316.65−25.80316.675.2-4.9
Non-haloed crater 1−25.85316.73−25.80316.67-2.2
Unit S13 of Mare Serenitatis
Haloed crater 1124.6716.7824.5316.804.3-4.8
Non-haloed crater 124.5316.7024.5316.83-3.6
Haloed crater 2224.5016.9224.4816.793.6-2.8
Non-haloed crater 224.4816.8224.4816.79-0.8
Haloed crater 3322.6217.25----2.9
Non-haloed crater 322.6217.33----
Haloed crater 4421.3216.8521.4016.743.9-1.9
Non-haloed crater 421.3816.8721.4016.74-3.7
Haloed crater 5520.5816.2320.5016.272.7-1.7
Nonhaloed crater 520.6216.2720.5016.27-3.6
Haloed crater 6619.6315.4319.7315.636.3-4.0
Non-haloed crater 619.7215.5319.7315.63-2.7

[23] The bulk permittivities were estimated to lie between 2.5(+1.2/−0.9) and 32.1(+16.2/−12.6) from the Crater Combination of Haloed crater 2 and Nonhaloed crater 2 (i.e., CC2), between 2.7(+1.0/−0.9) and 18.0(+7.3/−5.9) from CC4, between 4.2(+1.7/−1.4) and 37.0(+14.6/−12.7) from CC5, and between 0.6(+0.1/−0.2) and 18.0(+6.1/−5.2) from CC6 (see Table 1). If Unit S13 of Mare Serenitatis has an uniform bulk permittivity, it should be limited within the range overlapped by them: 4.2(+1.7/−1.4) to 18.0(+6.1/−5.2). The minimum value is limited from Haloed crater 5 (Figures 5a, 5c, and 5d), and the maximum value is limited from Nonhaloed crater 6 (Figures 6a, 6c, and 6e). This estimated bulk permittivity corresponds approximately to the bulk density that lies between 2.2(+0.5/−0.6) g cm−3 and 4.4(+0.5/−0.5) g cm−3 based on equation ((3)).

[24] The grain permittivity (inline image) of the uppermost basalt layer in Unit S13 of Mare Serenitatis was estimated to be 8.4 ± 1.1 from equations ((5)) and ((6)) using the following values: TiO2 = 2.43 ± 0.44 wt %, and FeO = 17.25 ± 0.81 wt %. The difference between the grain and bulk permittivities can be explained by the porosity of the uppermost basalt layer. This porosity is estimated to lie between −36(+16/−13)% and 33(+19/−16)% using equations (8a) and (8b). The negative porosity is due to the depth of the shallowest nonhaloed crater. Porosity, however, must be positive, so that the estimated porosity lies between 0% and 33(+19/−16)%.

4 Discussion

[25] We have shown that the estimated bulk permittivity of the uppermost basalt layer is constrained within a narrow range (2.8–5.5) in Unit 85 of Mare Humorum, while it shows a wide range (4.2–18.0) in Unit S13 of Mare Serenitatis. These results indicate that these uppermost basalt layers have many voids; the estimated porosities are 19%–51% in Unit 85 of Mare Humorum and 0%–33% in Unit S13 of Mare Serenitatis.

[26] This study, however, has been employed a strong implicit assumption, which is that a buried regolith layer that produces the subsurface echo lies between the uppermost basalt layer and the underlying basalt layer. In section 4.1, the validity of its assumption is discussed. In this study, an empirical relation between bulk density and bulk permittivity (equation ((3))) was employed, but there is also a theoretical relation between them. In section 4.2, the equivalence between the empirical relation and the theoretical relation is discussed. In section 4.3, we discuss the relative contribution of porosity sources for terrestrial volcanic materials, and then, it is compared with the relative contributions of lunar porosity sources to the estimated porosities.

4.1 Implicit Assumption in Determination of the Bulk Permittivity

[27] The method for estimating the bulk permittivity of the uppermost basalt layer is based on a strong implicit assumption. This assumption is that a buried regolith layer that contributes to the subsurface echo lies between the uppermost basalt layer and the underlying basalt layer (Figure 1). Oshigami et al. [2012] showed that the echo intensity of the subsurface echo observed by LRS could not be explained by the mineral composition gap only, so that the buried regolith is required between them. We can suppose that the echo intensity depends on the thickness of the buried regolith layer because interferences are occurred between waves reflected at the upper and lower boundaries of the buried regolith layer. We first investigate the thickness of the buried regolith layer between the uppermost unit (Unit S13) and the underlying unit in Mare Serenitatis, and then, we discuss whether LRS can observe the electromagnetic wave reflected in the buried regolith layer on the basis of the results of Ono et al. [2009] and Hiesinger et al. [2000].

[28] The thickness of the buried regolith layer can be estimated from the difference between the eruption ages of Unit S13 and the underlying unit with supposing a regolith accumulation rate. The regolith accumulation rate decreases with time: 5 m/Ga in 4.0–3.5 Ga ago, 2 m/Ga in 3.5–3.0 Ga ago, and 1 m/Ga in 3.0–0 Ga ago (Figure 7). This is based on three models of Hörz et al. [1991], which assumed linear and nonlinear impact flux models at Apollo 11 and 12 landing sites. In order to estimate the age of the underlying unit of Unit S13, we first confirm the ejecta composition (FeO and TiO2) of the largest haloed crater, which is the same with the composition of the underlying unit of Unit S13. Based on the information of ejecta composition, we searched for surface lava flow units with similar compositions in Mare Serenitatis using FeO and TiO2 maps created from the MI data. Assuming that these surface lava flow units are the same age as the underlying unit of Unit S13, we can estimate the eruption age of the underlying unit of Unit S13.

Figure 7.

Models for lunar regolith accumulation rate, which change with time. The orange line shows the model used in this study. Three dashed lines show the models of Hörz et al. [1991], which assumed linear and nonlinear impact flux models at Apollo 11 and 12 landing sites.

[29] The average ejecta composition of the largest haloed crater is TiO2 of 4.32 wt % and FeO of 17.67 wt % in Unit S13 of Mare Serenitatis. We, however, must note that the ejecta composition do not indicate an original composition of the underlying unit of Unit S13 because of the mixture of the materials of Unit S13 and the underlying unit [e.g., Giguere et al., 2000]. Since the average surface composition of the analyzed unit has TiO2 of 3.21 wt % and FeO of 16.97 wt % in Unit S13 of Mare Serenitatis, the original composition of the lower basalt layer is estimated to be larger than TiO2 of 4.32 wt % and FeO of 17.67 wt % in Unit S13 of Mare Serenitatis. The corresponding surfaces to their compositions are shown in Figure 8. We can select out the possible underlying units of Unit S13 as follows: S26, S25, S21, S19, S18, S16, S11, S10, S9, and S2 [Hiesinger et al., 2000] (Figures 8b and 8c). The higher unit number means the younger lava flow unit, so that the underlying unit of Unit S13 must have the unit number lower than S13: S11, S10, S9, and S2. The eruption age of the underlying unit of Unit S13 is therefore within a range of 3.55–3.76 Ga, and the eruption age of Unit S13 is 3.49 Ga [Hiesinger et al., 2000]; the exposed time of the lower basalt layer below Unit S13 is estimated to be 0.06–0.27 Ga. Based on the regolith accumulation rate mentioned above, the thickness of the buried regolith layer is estimated to be 0.3–1.3 m in Unit S13 of Mare Serenitatis.

Figure 8.

Distribution maps of area that meet the following conditions of FeO and TiO2 abundance, superposed on the albedo image of Mare Serenitatis: (a) the albedo image, (b) FeO > 17.67 (wt %), and (c) TiO2 > 4.32 (wt %). These conditions indicate an original mineral composition of the lower basalt layer that lies beneath Unit S13 (the uppermost basalt layer) of Mare Serenitatis (See Figure 1).

[30] In addition, we can estimate the thickness of the buried regolith layer by using the result of Ono et al. [2009], in which the regolith layer below Unit S28 was identified to be on Unit S11 by the data obtained from LRS. The eruption ages of S28 and S11 are 2.84 Ga and 3.55 Ga, respectively [Hiesinger et al., 2000]. The thickness of the buried regolith layer is estimated to be 1.4 m by using the regolith accumulation rate employed in this study. We can expect that the buried regolith layer with a thickness of larger than 1.4 m can be detected by LRS. However, we should note that the above consideration does not suggest the minimum thickness of the buried regolith layers that LRS can detect.

[31] If Unit S13 (i.e., the uppermost basalt layer) covered on the upper surface of Unit S2 (i.e., the lower basalt layer), we can estimate that the thickness of the buried regolith layer is 1.3 m, which may be detected by LRS as reported by Ono et al. [2009]. We can therefore conclude that the subsurface echoes analyzed in this study are from the boundary between these units. On the other hand, if Unit S13 covered on the upper surface of Unit S11, we can estimate that the thickness of the buried regolith layer between these units is 0.3 m. Unfortunately, we have not confirmed whether the buried regolith layer with such thickness can be detected by LRS or not. In this case, we cannot conclude whether the subsurface echoes analyzed in this study are from the boundary between Unit S13 and Unit S11, or from a boundary below Unit S11. If the buried regolith layer with the thickness of 0.3 m can be detected by LRS, the bulk permittivity of Unit S13 is consistent with the result estimated in this study. Although if LRS cannot detect its buried regolith layer, the bulk permittivity of Unit S13 is estimated to be smaller than the result estimated in this study.

4.2 Another Model for Estimating Bulk Density

[32] In the derivation of the bulk density from the bulk permittivity of the uppermost basalt layer, we used empirical equation ((3)). Fa and Wieczorek [2012] suggested that the relation between the bulk density and bulk permittivity could be explained by a constant grain permittivity and Maxwell-Garnett theory. This theory is one of the effective medium theories, which allows us to treat an inhomogeneous permittivity medium as a homogeneous permittivity medium [e.g., Dolgaleva, 2012]. In this theory, dielectric spherical inclusions (i.e., vesicles with a radius of R) are supposed to be embedded in a host medium (i.e., a basalt). It is also supposed that the distance between these inclusions (L) is much larger than R, and L must be much smaller than the wavelength (λ) of the electromagnetic wave: RLλ. These suppositions mean no electromagnetic interactions between the inclusions. The Maxwell-Garnett theory can be expressed as [e.g., Fa and Wieczorek, 2012]:

display math(9)

where vesicles have the permittivity in vacuum ((1)). Fa and Wieczorek [2012] showed that inline image was 2.75 for ρbulk = 1.7 g cm−3 using Apollo soil samples. Thus, we can obtain the relationship between inline image and ρgrain:

display math(9')

By substituting equation ((9')) into equation ((9)), the relationship between inline image and ρbulk can be also obtained:

display math(10)

[33] Equation ((10)) is consistent with equation ((3)) because the both relations were derived based on the analyses of Apollo samples. Therefore, the bulk density and the porosity estimated in this study will not change even if we use the theoretical equation instead of the empirical equation.

4.3 Relative Contributions of the Different Sources to the Estimated Porosity

[34] In this study, the porosity of the uppermost basalt layer was estimated using a theoretical approach. Based on the estimated porosity, lunar geological conditions are discussed through the determination of the relative contributions of four different porosity sources, which are categorized into

  1. [35] intrinsic voids of lava (vesicles and microcracks),

  2. [36] impact-induced cracks (microcracks and macrocracks),

  3. [37] lava tubes, and

  4. [38] surface and buried regolith layers.

These porosity sources can be considered to explain the estimated porosities, which are 19%–51% in Unit 85 of Mare Humorum and 0%–33% in Unit S13 of Mare Serenitatis. In this section, terrestrial porosity sources are first discussed, and then, their porosities are compared with the porosity sources in two particular lunar areas in the following subsections.

4.3.1 Intrinsic Voids (Vesicles and Microcracks)

[39] The terrestrial basaltic flows have intrinsic voids: vesicles and microcracks [Robertson and Peck, 1974]. Outgassing of volatile elements forms vesicles during the crystallization of lava flows, so that the gas rises in the molten lava as bubbles, and either escape to the surface or collects near the cooled surface of lava flows [Robertson and Peck, 1974]. The surface of the lava flow is also expected to be irregular due to outgassing of volatile elements. Besides, the relatively rapid cooling of lava flows produces microcracks across grains and along grain boundaries because of differential thermal contraction of different minerals and glass [Robertson and Peck, 1974]. Likewise, in the Moon, the outgassing of volatile elements (CO, CO2, and sulfur species) produces vesicles [e.g., Taylor et al., 1991], and the relatively rapid cooling of lava flows would also produce microcracks.

[40] In the terrestrial basaltic lava erupted in Kilauea Volcano, Hawaii, on 21–23 August 1963, the porosity of the intrinsic voids was investigated by Peck et al. [1966]. The thickness of the lava left in Alae pit crater is ~15 m. The maximum porosity (~40%) appears near the surface, and the observed porosities are mainly attributed to vesicles, 1–8 mm in size [Peck et al., 1966]. The porosity changes at depth of 0.3–4 m, but the porosity is constant (~10%) at the depth below 3–4 m [Peck et al., 1966]. Thus, the porosity is ~10% for this terrestrial lava flow with a few tens of meters. However, we cannot confirm whether this lava flow shows the general properties of the terrestrial lava flows. At least, we can point out that this terrestrial lava flow is good sample in comparison with the lunar lava flow because the thickness of its lava flow (~15 m) is the same order as the one of lunar lava flows [e.g., Hiesinger et al., 2002].

[41] The intrinsic voids of lunar basalt rocks also were investigated as documented in the lunar sample catalog (http://curator.jsc.nasa.gov/lunar/compendium.cfm). The Apollo sample 15016 has vesicles of 1–5 mm, resulting in ~50% porosity. If the analyzed uppermost basalt layer is composed of basalts similar to Apollo sample 15016, the estimated porosity could be explained by the intrinsic voids alone. However, Apollo sample 15016 is a rare sample, and the other samples have little intrinsic voids [e.g., Kiefer et al., 2012]. Recently, the porosity and density of Apollo samples were reanalyzed by using the bead method and helium pycnometry measurements, which provide the precise porosity (1%–3%) and density (10–30 kg m−3) [Kiefer et al., 2012]. The typical porosity and bulk density of mare basalt are, respectively, ~7% (2%–10%) and 3010–3270 kg m−3 [Kiefer et al., 2012]. Thus, the porosity corresponding to intrinsic voids in the lunar basalt is ~7% on average, consistent with the intrinsic voids included in a terrestrial basaltic lava (~10%). We must note that the porosities estimated in this study have been derived over two particular areas that might be showing average characteristics but might also be a very particular case such as Apollo sample 15016.

4.3.2 Impact-Induced Cracks (Microcracks and Macrocracks)

[42] When meteorites impact the lunar surface, the scattered material (ejecta) produces the lunar regolith layer with a high porosity (40%–50%) [e.g., Carrier et al., 1991], while impact-induced cracks (microcracks and macrocracks) are formed inside lunar subsurface layers [e.g., Cooper et al., 1974; Consolmagno et al., 2008; Kiefer et al., 2012]. For two impact craters in Sweden, the porosity created by the impact-induced cracks was investigated using gravity field observation [Henkel et al., 2010]. The layer with cracks is a few hundred meters thick. The porosity decreases with depth, and the basement of impact craters has the high void ratio (< 15%) [Henkel et al., 2010]. The relative porosity of the terrestrial impact-induced cracks is thus estimated to be less than 15%.

[43] The Apollo basalt samples probably contain impact-induced microcracks [Kiefer et al., 2012]; the average porosity (~7%) of Apollo basalt samples is formed by the intrinsic voids and the impact-induced microcracks. However, impact-induced macrocracks would be not contained inside these samples because all Apollo samples are as small as the sizes that we can take hold it. The existence of macrocracks was suggested by lunar seismic velocity observations [Cooper et al., 1974]. Furthermore, the fact that there are no global-scale contractional or extensional features on the Moon also has been explained by cracking of the outer layer of the Moon [e.g., Shearer et al., 2006]. However, the amount of macrocracks has not been estimated so far. The amount of porosity created by macrocracks is estimated in this study for the first time. The amount of porosity is described in section 4.3.5.

4.3.3 Lava Tubes

[44] Lava tubes are well-known basaltic volcanic features on Earth [e.g., Hörz, 1985]. Hörz et al. [1991] suggested a relation between the formation processes of the lunar lava tubes and the lunar sinuous rilles; the origin of the rilles is a collapsed lava tube or an open lava channel. The typical heights and widths of the terrestrial lava tubes are a few meters, and their typical length is 1–2 km [Hörz, 1985], but the relative porosity of the terrestrial lava tubes is unknown. The width, depth, and length of the lunar rilles are 30–50 times larger than those of the terrestrial rilles [Hörz et al., 1991].

[45] If lava tubes exist inside the analyzed lava flow units, some part of the estimated porosities, which are 19%–51% in Unit 85 of Mare Humorum and 0%–33% in Unit S13 of Mare Serenitatis, would be explained. However, the lunar pits, which imply the existence of lunar lava tubes, have been found in a few regions only: Mare Ingenii, Mare Tranwuillitatis, and Marius Hills [Haruyama et al., 2009; Haruyama et al., 2012; Robinson et al., 2012]. We do not expect lava tubes in the analyzed areas: Unit 85 of Mare Humorum and Unit S13 of Mare Serenitatis. In addition, we could not find subsurface echoes, which would suggest lava tubes in these units (Figures 4f, 5f, and 6f). Therefore, it is probable that lunar lava tubes do not contribute significantly to the porosity estimated in this study.

4.3.4 Surface and Buried Regolith Layers

[46] Regolith formed by the meteorites impacts is ubiquitous on the lunar surface, and its porosity roughly ranges from 40% to 50% [e.g., Carrier et al., 1991]. Such surface and buried regolith layers hardly exist in the Earth compared with the Moon because the Earth has an atmosphere; the relative porosity of the terrestrial regolith layer is negligible. The thickness of the lunar surface regolith layer was investigated by various methods [McKay et al., 1991; Shkuratov and Bondarenko, 2001; Kobayashi et al., 2010; Fa and Jin, 2010; Bart et al., 2011]. The average thicknesses of the surface regolith layers are 4–5 m in maria and 7.6–15 m in highlands [McKay et al., 1991; Shkuratov and Bondarenko, 2001; Fa and Jin, 2010].

[47] Besides, the regolith layer exists also between buried basalt layers. The existence of buried regolith layers was suggested by radar sounder observations [e.g., Ono et al., 2009; Oshigami et al., 2009]. The uppermost basalt layer in the analyzed units have a thickness of a few hundred meters: 214–300 m in Unit 85 of Mare Humorum and 118–169 m in Unit S13 of Mare Serenitatis as determined by the excavation depths of haloed and nonhaloed craters. Since the typical thickness of lunar lava flows is 30–60 m [Hiesinger et al., 2002], the uppermost basalt layer can be composed of several lava flows. Therefore, sufficiently thin buried regolith layers, which cannot be detected by LRS, may exist inside the analyzed units, but they hardly contribute to an increase of the porosity of the uppermost basalt layer because the thicknesses of the uppermost basalt layers would be much thicker than the total thickness of the surface and buried regolith layers. Even if the regolith layer has a high porosity, the relative contribution of surface and buried regolith layers to the estimated porosities would be negligible.

4.3.5 Summary

[48] The relative contribution of four different porosity sources to the estimated porosity was investigated in two particular lunar areas, and then, these were summarized in Table 3. Four porosity sources are categorized into (i) intrinsic voids of lava, (ii) impact-induced cracks, (iii) lava tubes, and (iv) surface and buried regolith layers. The lunar intrinsic porosity (vesicles and microcracks) is ~7% on average. The lunar lava tubes and surface and buried regolith layers do not contribute to the bulk porosity in the area investigated. The remaining porosity can therefore be explained by macrocracks; the amounts of the macrocracks are 12%–44% in Unit 85 of Mare Humorum and less than 26% in Unit S13 of Mare Serenitatis. On the other hand, the terrestrial porosity sources are summarized in Table 4. The intrinsic porosity of a terrestrial lava is ~10% on average, and the terrestrial impact-induced cracks is less than 15%. The relative porosity of the terrestrial lava tubes is unknown. The terrestrial regolith layer hardly exists, so that its relative porosity is negligible. Thus, the estimated relative porosities of macrocracks may be higher than that of the Earth (see Tables 3 and 4). This difference may be caused from the long impact history in the Moon.

Table 3. Relative Contributions of Four Different Sources in Two Particular Lunar Areas
 Relative Porosity (%)
Unit 85 of Mare HumorumUnit S13 of Mare Serenitatis
Vesicles and microcracks~7~7
Macro cracks12–44< 26
Lava tubes00
Surface and buried regolith layers~0~0
Total (estimated porosity)19–510–33
Table 4. Relative Contributions of Four Different Sources in the Earth
 Relative Porosity (%)
Earth
  1. a

    Peck et al. [1966].

  2. b

    Henkel et al. [2010].

Vesicles and microcracks~10a
Impact-induced cracks< 15b
Lava tubes-
Surface and buried regolith layers~0

[49] In lunar highlands, the average porosity of the upper few kilometers was estimated to be 12% [Wieczorek et al., 2012]. Based on the results of observations of the lunar seismic velocity, Cooper et al. [1974] predicted that the amounts of the void created by macrocracks decrease with depth because this void is vanished by the load of the rocks; the porosity of the near-surface highlands is higher than the porosity at a deeper depth. If the near-surface porosity is higher than 12% in the highlands, it may be consistent with the porosities of two near-surface mare regions estimated in this study: 19%–51% in Unit 85 of Mare Humorum and 0%–33% in Unit S13 of Mare Serenitatis.

5 Conclusions

[50] We have developed and presented a method to estimate the bulk permittivity of the uppermost lunar basalt layer in order to examine lunar geological conditions. The bulk permittivity was calculated from the ratio of the apparent radar depth, obtained by LRS, to the thickness of the uppermost basalt layer, which is limited by the excavation depths of haloed and nonhaloed craters observed by the MI and TC instruments. In addition, the grain permittivity was calculated by empirical equations, utilizing data from Apollo samples, and the ejecta composition (TiO2 and FeO) of the nonhaloed crater.

[51] Bulk permittivities in the uppermost basalt layer were estimated to be 2.8–5.5 in Unit 85 of Mare Humorum and 4.2–18.0 in Unit S13 of Mare Serenitatis. In the previous works based on lunar radar observations, bulk permittivites of 8–9 had been assumed [e.g., Peeples et al., 1978; Cooper et al., 1994; Oshigami et al., 2009]. They are similar with the grain permittivity in the uppermost basalt layer estimated in Unit 85 of Mare Humorum (8.1 ± 1.0) and that in Unit S13 of Mare Serenitatis (8.4 ± 1.1). The bulk permittivity range estimated in this study is, however, much less than them. The difference between the estimated bulk and grain permittivities can be explained by the porosity in the uppermost basalt layer. The porosities were estimated to be 19%–51% in Unit 85 of Mare Humorum and 0%–33% in Unit S13 of Mare Serenitatis. These porosities were indicative of the highly porous basalt, which could be explained mainly by the intrinsic voids and the impact-induced cracks. The amounts of the macrocracks were estimated to be 12%–44% in Unit 85 of Mare Humorum and less than 26% in Unit S13 of Mare Serenitatis.

[52] Our method to estimate permittivity enables lunar geological conditions to depths of a few hundred meters to be examined for the first time. This method should also prove useful for investigation of near-surface geological conditions on other planets, satellites, and asteroids.

Acknowledgments

[53] We are grateful to M. A. Wieczorek and A. Pommerol for thoughtful and constructive comments in their review of this paper. We used the observation data obtained by the SELENE (Kaguya) spacecraft. We would like to express our appreciation to all members of the Kaguya project team for processing and analyzing the data. This study was supported by Tohoku University International Advanced Research and Education Organization.

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