Estimation of Bulk Permittivity of the Moon’s Surface Using Lunar Radar Sounder On-board Selenological and Engineering Explorer
Keigo Hongo International Business Machine Hiroaki Toh ( [email protected] ) Graduate School of Science, Kyoto University https://orcid.org/0000-0003-3914-5613 Atsushi Kumamoto Department of Geophysics, Graduate School of Science, Tohoku University
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Keywords: Selenological and Engineering Explorer, frequency modulated continuous wave radar, bulk permittivity, loss tangent, subsurface re ectors
Posted Date: April 3rd, 2020
DOI: https://doi.org/10.21203/rs.3.rs-20561/v1
License: This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License
Version of Record: A version of this preprint was published on September 22nd, 2020. See the published version at https://doi.org/10.1186/s40623-020-01259-2. 1 Estimation of Bulk Permittivity of the Moon’s Surface Using
2 Lunar Radar Sounder On-board Selenological and
3 Engineering Explorer
4 Keigo Hongo, Division of Earth and Planetary Sciences, Graduate School of Science,
5 Kyoto University
6 Hiroaki Toh, Division of Earth and Planetary Sciences, Graduate School of Science,
7 Kyoto University
8 Atsushi Kumamoto, Department of Geophysics, Graduate School of Science, Tohoku
9 University
10 Corresponding Author: Hiroaki Toh
11 12 Abstract
13 Site-dependent bulk permittivities of the lunar uppermost media were estimated based
14 on the data from Lunar Radar Sounder onboard the Selenological and Engineering
15 Explorer (SELENE). It succeeded in sounding almost all over the Moon’s surface in a
16 frequency range around 5 MHz to detect subsurface reflectors beneath several lunar
17 maria such as Mare Imbrium. However, it is necessary to estimate the permittivity of
18 the surface regolith of the Moon in order to determine the actual depths to those
19 reflectors instead of apparent depths assuming a speed of light in the vacuum. In this
20 study, we determined site-dependent bulk permittivities by two-layer models consisting
21 of a surface regolith layer over a half-space with uniform but different physical
22 properties from the layer above. Those models consider the electrical conductivity as
23 well as the permittivity, whose trade-off was resolved by utilizing the correlation
24 between titanium content and measured physical properties of lunar rock samples.
25 Distribution of the titanium content on the Moon’s surface had already been derived by
26 spectroscopic observation from SELENE as well.
27 Four lunar maria, viz., Mare Serenitatis, Oceanus Procellarum, Mare 28 Imbrium, and Mare Crisium, were selected as regions of evident reflectors, where we
29 estimated the following four physical properties of each layer, i.e., bulk permittivity,
30 porosity, loss tangent and electrical conductivity to conclude the actual depths of the
31 reflectors are approximately 200m on average. The bulk permittivity ranges from 2.96
32 at Mare Imbrium to 6.37 at Oceanus Procellarum, whereas the porosity takes the values
33 between 1.8% to 41.1% in the respective maria. It was found that although the bulk
34 permittivity of the four lunar maria differs from a mare to a mare, it shows a good
35 correlation with their composition, viz., their titanium content.
36
37 Keywords
38 Selenological and Engineering Explorer, frequency modulated continuous wave radar,
39 bulk permittivity, loss tangent, subsurface reflectors
40
41 1. Introduction
42 The first exploration of the Moon’s subsurface structure was conducted by Apollo
43 Lunar Sounder Experiment (ALSE) aboard Apollo 17 launched in 1972. ALSE 44 observed the reflected echoes of the radar transmitted from the mother ship orbiting
45 above the lunar equator. Objectives of ALSE were subsurface exploration of the
46 Moon and profiling/imaging of its surface. To achieve those, ALSE was operated at a
47 few frequency bands of 5, 15 and 150MHz with linearly increasing frequency (chirp
48 signals) so as to improve the penetration depth and the ranging resolution. The largest
49 penetration depth of approximately 1.3km was achieved by the 5MHz operation with an
50 apparent resolution of 300m. However, both the depth and the resolution are
51 dependent on the permittivity inside the Moon. ALSE detected horizontal reflectors at
52 an apparent depth of about 1km beneath Mare Serentatis and Mare Crisium (Peeples et
53 al., 1978; Phillips et al., 1973a, b) by its limited observation from several orbits.
54 Lunar Radar Sounder (LRS) is a Frequency Modulated Continuous Wave
55 radar equipped with SELenological and ENgineering Explorer (SELENE) launched in
56 2007. Because it was the first Japanese spacecraft to the Moon, it also has a Japanese
57 name of KAGUYA coined after a princess believed to live on the Moon. Like ALSE,
58 LRS also aimed at subsurface exploration of the Moon using high frequency chirp
59 signals ranging from 4 through 6MHz. Major differences, however, from ALSE were 60 its deeper penetration depth and finer resolution, which were 5km and 75m in vacuum
61 and were much better than those of ALSE (Ono and Oya, 2000; Ono et al., 2008).
62 Spatial coverage of SELENE was excellent in the sense that all of the Moon’s surface
63 including the far side was covered by the sounder observation from SELENE’s polar
64 orbits with an averaged altitude of 100km above the Moon’s surface. The total
65 duration of the sounder observation summed up to as long as 100 days. As a result,
66 Ono et al. (2009) reported presence of subsurface reflectors beneath several lunar maria.
67 Apparent depths to those reflectors were a few hundreds of meters but we need to know
68 the permittivity beneath the Moon’s surface for conversion of those values to the true
69 depths. Furthermore, quantitative delineation of the Moon’s subsurface structure such
70 as the true depths to the reflectors leads to understand the origin and evolution of our
71 Moon. It, therefore, is very important to analyze the LRS data of SELENE, which
72 provided unprecedented radar sounding in terms of both quality and quantity.
73 Another example of planetary radar sounding can be found in Mars. Mars
74 Advanced Radar for Subsurface and Ionosphere Sounding on-board Mars Express in
75 2003 detected presence and quantity of not dry but water ice accumulated in 76 the Mars’s polar cap (Picardi et al., 2005; Plaut et al., 2007). Presence of water ice on
77 Mars was further confirmed by Shallow Radar Sounder aboard Mars Reconnaissance
78 Orbiter in 2005. Karlsson et al. (2015) found the water ice even in Mars’s mid-
79 latitudes, while Holt et al. (2010) revealed a complex sedimentary structure beneath the
80 Mars’s northern polar cap. These new findings are expected to elucidate the past
81 Mars’s climate and/or traces of paleo-oceans on Mars.
82 On the other hand, JUpiter ICy moon Explorer (JUICE) by European Space
83 Agency (ESA) is planned to launch in 2022. According ESA (2014), Radar of Icy Moon
84 Exploration aboard JUICE is going to conduct radar sounding of three icy Galilean satellites,
85 i.e., Europa, Ganymede and Calisto so as to explore the subsurface structures, ice, water and
86 their composition. Those sounding will be of great help for detecting subsurface oceans of
87 those moons, which may constitute cradles for extraterrestrial lives.
88 Unlike the sample return missions, the past and future radar sounding from
89 spacecrafts illustrates efficiency, certainty and wide spatial coverage of planetary-scale
90 exploration by radar sounders. In order to improve applicability of radar sounding, the
91 LRS data have been combined with model calculation of electromagnetic (EM) wave 92 propagation (Ono et al., 2009; Bando et al., 2015) and data by laser altimetry to estimate
93 the thickness of the regolith layer on top of the Moon as well as to improve the ranging
94 resolution of LRS itself by application of data processing techniques originally
95 developed for synthetic aperture radars (Kobayashi et al., 2007; Kobayashi et al., 2012).
96 Ono et al. (2009) argued the possibility of detection of the subsurface regolith
97 layer sandwiched by basaltic layers above and below as reflectors. This is because the
98 reflectors are detected at shallower depths than the thickness of the basaltic layers
99 estimated by crater analyses in lunar maria (De Hon, 1971; Williams and Zuber, 1998).
100 Oshigami et al. (2009) further claimed that the correlation between the surface age and
101 detection rate of the reflectors means thicker regolith layers in older regions.
102 Another correlation, which is negative though, between the detection rate and
103 surface distribution of ilmenite suggests that metals such as titanium may prevent
104 penetration of radar pulses to interfere the reflector detection (Pommerol et al., 2010;
105 Olhoeft and Strangway, 1975; Carrier et al., 1991; Shkuratov and Bondarenko, 2001).
106 The composition of the Moon’s surface was revealed by spectroscopic studies of
107 SELENE data. This means that not only the permittivity that determines the speed of 108 light in the medium in concern but also the loss tangent that is defined as the ratio of the
109 conduction current to the displacement current and plays a role in attenuation of the
110 radar pulses is important. Analyses of lunar rock samples strongly imply the
111 correlation between the loss tangent and the ilmenite content, whereas the permittivity
112 does not show significant dependence on rock composition. It has, in turn, a strong
113 correlation with rock density (Olhoeft and Strangway, 1975; Carrier et al., 1991;
114 Shkuratov and Bondarenko, 2001). The different dependence of physical properties of
115 the Moon’s surface suggests regional dependence of those properties, and thus implies
116 necessity of determination of those properties from place to place.
117 Porosity is another factor of consideration here. Although it is negligible in
118 the case of laboratory measurements, effects of bulk porosity are inevitably included in
119 the results of radar sounding as a form of bulk density. If we can also estimate
120 porosity from our LRS data, it can be another important database, since Rust et al.
121 (1999) pointed out that porosity is indicative of volcanism/tectonics of the Moon in the
122 past.
123 Ishiyama et al. (2013; 2014) performed combined analyses of the delay of 124 echoes from the subsurface reflectors and the depth of subsurface reflectors excavated
125 at the impact craters based on data from LRS, Multiband Imager (MI) and Trrain
126 Camera (TC) onboard the SELENE spacecraft, and determined the speed of the radar
127 wave in uppermost layers in several maria. Based on the speed, they also estimated bulk
128 permittivity and porosity. The estimated bulk permittivities were between 1.6 and 14.0
129 in Mare Serenitatis, and between 1.3 and 5.1 in Oceanus Procellarum. They also pointed
130 out that the estimated porosity, up to about 80 %, was much larger than that of Apollo
131 soil samples, and discussed possible contributions of intrinsic voids of lava and impact-
132 induced cracks.
133 In this study, we aim at estimation of the relative permittivity of the Moon’s
134 surface by comparison of echo intensities from the surface and subsurface reflector.
135 We will approximate the Moon by two-layer models with different permittivities and
136 electrical conductivities in each layer and determine those model parameters by
137 calculation of EM wave propagation according to the radar range equation. In the
138 course of estimation, we newly introduce correlation between the electrical conductivity
139 and the ilmenite content to resolve the non-uniqueness appeared in previous studies. 140 This study will also provide spatial dependence of the true depths to the detected
141 reflectors, which may lead to better understanding of the Moon’s subsurface structures.
142 Furthermore, those true depths can be applied to estimation of erupted lava volumes,
143 which are useful in unraveling the Moon’s volcanism in the past. Finally, the
144 estimated loss tangent and porosity contribute to the understandings of the Moon’s
145 evolution and thermal history as well.
146
147 2. Data of Lunar Radar Sounder
148 A pair of mutually orthogonal 30m dipole antennas was used for LRS. The pulse
149 width (T), sweep rate ( ) and output power of the transmitted chirp signals were 200s,
푓̇ 150 10kHz/s and 800W, respectively. Each pulse was further shaped by a sinusoidal
151 wave to minimize sidelobe effects at the time of FFT and is given by;
152 , (1) 푡 푡 푉푇푋(푡) = 푉푇푋0sin (휋 푇) 푠푖푛 (∫0 2휋(푓0 + 푓̇푡′)푑푡′) 153 where VTX0 is the amplitude of the transmitted pulse and f0 = 4MHz.
154 In general, radars are associated with a trade-off between the penetration
155 depth, which is a function of the output power, and the ranging resolution, which is a 156 function of the pulse width. However, the pulse compression technique using chirp
157 signals gives us a radar with a large output power and a narrow pulse width at the same
158 time, which improves both the penetration depth and the ranging resolution. In the
159 case of LRS, they are 5km and 75m in vacuum as mentioned before, but they are also
160 dependent on both the permittivity and the loss tangent beneath the Moon’s surface.
161 The LRS operation throughout the mission was done by 20Hz transmission for 72 days,
162 while it was operated with a transmission rate of 2.5Hz for the remaining 27 days. The
163 LRS data are now open to the public at;
164 http://darts.isas.jaxa.jp/planet/pdap/selene/,
165 and all the data used in this study were downloaded from this Japan Aerospace
166 Exploration Agency website.
167
168 2.1 A-scope Data
169 Received echoes of LRS are not original waveforms of the reflected echoes themselves
170 but resampled waveforms multiplied by a local signal, which were further transferred to
171 the Earth from the spacecraft. The observed data, therefore, are different from the 172 original waveforms of the reflected echoes.
173 Specifically, let the original waveform be;
174 , (2) 푡−휏푅푋 푡−휏푅푋 푉푅푋(푡) = 푉푅푋0sin (휋 푇 ) 푠푖푛 (∫0 2휋(푓0 + 푓̇푡′)푑푡′) 175 where VRX0 is the amplitude of the reflected echo and RX is a two-way travel time of
176 the echo, by which the apparent depth to the reflector, dA, can be given by;
177 . (3) 푐0휏푅푋 푑퐴 = 2 178 where c0 is the speed of light in vacuum. In chirp radars, the received echoes are
179 further mixed with a local signal typically given by the following formula;
180 , (4) 푡−휏퐿푂 푉퐿푂(푡) = 푉퐿푂0푠푖푛 (∫0 2휋(푓0 + 푓̇푡′)푑푡′) 181 where VLO0 is the amplitude of the local signal and LO is the time of the mixing onset.
182 The waveform after mixing becomes:
183 푡−휏푅푋 푡−휏푅푋 푉푅푋(푡) × 푉퐿푂(푡) = 푉푅푋0푉퐿푂0sin (휋 푇 ) 푠푖푛 (∫0 2휋(푓0 + 푓̇푡′)푑푡′) × 184 푡−휏퐿푂 푡−휏푅푋 푠푖푛 (∫0 2휋(푓0 + 푓̇푡′)푑푡′) = 푉푅푋0푉퐿푂0sin (휋 푇 ) 푠푖푛 [2휋 {푓0(푡−휏푅푋) + 185 . (5) 1 2 1 2 2 푓̇(푡−휏푅푋) }] × 푠푖푛 [2휋 {푓0(푡−휏퐿푂) + 2 푓̇(푡−휏퐿푂) }] 186 Using a formula for the trigonometric functions, Eq. (5) can be further modified into a
187 sum of the high frequency part and the low frequency part as: 188 1 푡−휏푅푋 푉푅푋(푡) × 푉퐿푂(푡) = − 2 푉푅푋0푉퐿푂0sin (휋 푇 ) × (푐표푠 [2휋 {푓0(2푡−휏푅푋 −휏퐿푂) + 189 1 2 2 2 2 푓̇(푡 +휏푅푋 − 2(휏푅푋 +휏퐿푂)푡+휏퐿푂 )}] − 푐표푠 [2휋 {푓̇(휏푅푋 −휏퐿푂)푡 + 푓0(휏푅푋 − 190 . (6) 1 2 2 휏퐿푂) − 2 푓̇(휏푅푋 −휏퐿푂 )}]) 191 Equation (6) is then low-pass filtered with a cut-off frequency of 2MHz to eliminate the
192 first term in L.H.S. and resampled for 2048 points with a sampling frequency of
193 6.25MHz. Figure 1 shows a sample plot of thus processed and transferred to the Earth.
194 Although filtered and resampled, the waveforms of the reflected echoes
195 preserve the information of the two-way travel times in the form of frequency.
196 Namely, if one makes Fourie transforms of the echoes and finds specific frequencies,
197 fIF’s, for each peak reflection, then the following relation holds:
198 . (7)
푓퐼퐹 = 푓̇(휏푅푋 −휏퐿푂) 199 Equations (3) and (7) are combined to give:
200 . (8) 푐0휏푅푋 푐0휏퐿푂 푐0푓퐼퐹 푑퐴 = 2 = 2 + 2푓 201 The first term on R.H.S. of Eq. (8) is called the ‘altitude origin for ranging’ and
202 recorded in the LRS data together with the received waveform itself, the time stamp, the
203 selenographic latitude/longitude and the spacecraft’s altitude. Figure 2(a) shows 204 Fourier transforms of the reflected echo shown in Fig.1. Plots of this kind are called
205 ‘A-scope’. In Fig. 2(b), three echoes are evident, one is from the Moon’s surface and
206 the other two from the subsurface reflectors.
207
208 2.2 B-scan Data
209 B-scan is a sort of dynamic spectrum using A-scope with echo intensity in color, and is
210 called ‘radargram’, a pseudo section of the Moon’s subsurface structure. Figure 3(a)
211 shows a B-scan image over Mare Imbrium. The height of the steps seen on the
212 Moon’s surface is approximately 75m, which is in good harmony with the ranging
213 resolution of LRS in vacuum.
214 Reflected echoes do not always come from the nadir direction. If there is
215 significant undulation of the Moon’s surface, the subsurface reflectors are possibly
216 masked by strong reflected echoes on the surface. Figure 3(b) shows a typical
217 example of the surface echoes, which have clear parabolic shapes because the distance
218 between the spacecraft and the reflection points on the Moon’s surface can vary with
219 time as the spacecraft maneuvers along its orbit. 220 Taking running means on the B-scan images is known to give a better
221 protection against the surface echoes (Ono et al., 2010), provided that the subsurface
222 reflectors are horizontal. It is also desirable to compare the running means of adjacent
223 orbits so as to confirm the echoes coming from not ‘surface’ but ‘subsurface’. Figure
224 3(c) shows a B-scan image by a running mean width of 21. It is noteworthy that the
225 continuity of the subsurface reflectors is much clearer than Fig. 3(a).
226
227 3. Methods
228 3.1 Two-layer Model
229 Because the regions with two subsurface reflectors like the one shown in Fig. 3(c) were
230 very limited, we decided to model the majority of the LRS data by two layers, into
231 which the transmitted waves entered normal to the surface. Figure 4 shows a
232 schematic diagram of the assumed model. Using the radar range equation (e.g.,
233 Phillips, 1973b), the reflected powers, Prs and Prss, are respectively given by;
234 , (9) 2 2 푃푡퐺 휆 2 푃푟푠(휀1) = 4(4휋푅) 푟01 235 and 236 , (10) 2 2 푅푑 푡 1 푃 퐺 휆 −2휔 푐1 푡푎푛훿 2 푃푟푠푠(휀1, 휀2, 휎2) = 4[4휋(푅+푅푑)] 푒 푡01푟12푡10 237 where G, , , tan 1, and Rd are the gain of the antenna, the wavelength and angular
238 frequency of the transmitted wave, the loss tangent of the first layer and the true
239 thickness of the first layer, respectively. c1 is the speed of light in the first layer and
240 given by;
241 , (11) 1 푐0 1 푐 = √휀1휀0휇0 = √휀1 242 where 0 and 0 are the permittivity and magnetic permeability in vacuum, respectively.
243 The loss tangent in the first layer can be written by;
244 , (12) 휎1 푡푎푛훿1 = 휔휀0휀1 245 as well. rij and tij (i, j = 0, 1, 2) denote the reflection and transmission coefficients at
246 each interface and satisfy the following relation according to the Fresnel equations;
247 , (13) √휀1 01 10 2 푡 = 푡 = (1+√휀1) 248 , (14) 2 1−√휀1 01 푟 = (1+√휀1) 249 . (15) 2 √휀1−√휀2 12 푟 = (√휀1+√휀2) 250 Equation (15) allows solutions of both and . However, if one takes
휀1 > 휀2 휀1 < 휀2 251 , it yields , which is incompatible with the results of the Moon rock
휀1 > 휀2 1 < 휀2 < 2 252 analyses (e.g., Olhoeft and Strangway, 1975). It, therefore, is assumed
휀1 < 휀2 253 throughout this study.
254
255 3.2 Correlation among Physical Properties
256 The previous analyses of the lunar rock samples (Shkuratov and Bondarenko, 2001;
257 Olhoeft and Strangway, 1975) revealed correlation among the physical properties of the
258 rocks such as density, bulk permittivity, titanium content and loss tangent. In short,
259 they are expressed by the following formulae;
260 , (16) 1−푝 −4 2 휌푔푟푎푖푛(푆)+0.085푆 푡푎푛훿 = 8.8 × 10 푒 261 , (17)
휌푔푟푎푖푛(푆) = 0.0165푆 + 2.616 262 , (18) 휌푏푢푙푘 휀푏푢푙푘 = 1.919 263 where S, p and are the total content of titanium and iron [wt%], porosity and density,
264 respectively. The subscritps, grain and bulk, denote the properties of the sample itself
265 and those corrected for the porosity. The porosity, therefore, is defined by:
266 . (19)
휌푏푢푙푘 = 휌푔푟푎푖푛(1 − 푝) 267 From Eqs. (18) and (19), the permittivity of the sample also reads: 268 . (20) 휌푔푟푎푖푛 휀푔푟푎푖푛 = 1.919 269
270 3.3 Flow of Data Analysis
271 First, the following quantities are considered as constants: Pt = 800W, = 0.06km for
272 the center frequency (5MHz) for a range of 4-6MHz and G = 1.64 from the theoretical
273 value of the dipole antenna. It follows from Eqs. (9), (14) and observed (Prs, Prss) that
274 1 can be determined. Equation (18) allows us to convert thus obtained 1 to bulk.
275 Lawrence et al. (2002) analyzed the spectroscopic data by Lunar Prospector to
276 yield 5o by 5o grid data of the surface content of iron and titanium as:
277 http://pds-geosciences.wustl.edu/lunar/lp-l-grs-5-elem-abundance-
278 v1/lp_9001/data/lpgrs_high1_elem_abundance_5deg.tab
279 Substitution of the above iron and titanium contents (S) into Eq. (17) gives grain.
280 Once bulk and grain are known, the porosity, p, can be estimated using Eq. (19). The
281 remaining model parameters, 1 and 2, can be determined using Eqs. (10), (12) and
282 (16) as shown in the flow chart (Fig. 5).
283 In this analysis, we need absolute values of the echo powers in unit of W. 284 They are determined based on the prelaunch calibration of the LRS's receiver. Of
285 course, it was not confirmed by the end-to-end calibration including extended antenna
286 and spacecraft because such test was quite difficult to perform on the ground. So, we
287 roughly check validity of the absolute calibration of the echo powers used in this study
288 by comparison between bulk permittivities estimated in Ishiyama et al. (2013; 2014)
289 and those in this study (see Section 5.1).
290
291 4. Results
292 4.1 Analyzed Regions
293 We analyzed four lunar maria, viz., Mare Serenitatis, Oceanus Procellarum, Mare
294 Imbrium, and Mare Crisium. This is partly because clear subsurface reflectors were
295 recognized by radargrams of several adjacent orbits in those lunar maria, and partly
296 because it is difficult to completely eliminate the effect of surface echoes, which are
297 especially intense in the highland areas of the Moon. Figure 6 shows the four target
298 regions of this study.
299 300 4.2 Mare Serenitatis
301 Figures 7(a) and 7(b) show radargrams of this region. For 20 – 25oN, S = 15.36wt%
-3 -2 302 was adopted to give 1,grain of 6.49; 6.0% < p < 36.4%, 8.09 x 10 < tan1 < 1.25 x 10 ,
-6 -5 303 7.39 x 10 S/m < 1 < 2.02 x 10 S/m using the observed range of 1,bulk: 3.29 < 1,bulk <
304 5.81. The derived 1,bulk are within a range between 1.6 and 14.0 reported in Ishiyama
305 et al. (2013; 2014). The average of the observed apparent depths of this region, 350m,
306 was cast into a range of true depths from 145m to 193m.
o 307 For 25 – 30 N, S = 13.95wt% was adopted to give 1,grain of 6.39, which
-3 308 sequentially yields the following ranges; 5.8% < p < 39.6%, 6.80 x 10 < tan1 < 1.10 x
-2 -6 -5 309 10 , and 5.80 x 10 S/m < 1 < 1.76 x 10 S/m based on the observed range for 1,bulk:
310 3.06 < 1,bulk < 5.74. The observed apparent depth of 350m is equivalent to a range of
311 true depths from 146m to 200m. Figures 8(a) and 8(b) summarize the estimated 1 in
312 this region.
313 In Mare Serenitatis, 634 and 345 subsurface echoes were identified for 20 –
o o 314 25 N and 25 – 30 N, respectively. Estimates of 2,bulk were obtained using the
315 corresponding 1,bulk for 6 continuous reflectors each and shown in Figs. 9(a) and 9(b). o 316 The ranges for 2,bulk were determined as 6.13 – 13.35 for 20 – 25 N and 5.78 – 13.59
317 for 25 – 30oN.
318
319 4.3 Oceanus Procellarum
320 Figures 10(a) and 10(b) show radargrams of this region. For 40 – 45oN, S = 14.26wt%
321 was adopted to give 1,grain of 6.41, which gives the following ranges, provided that we
o -2 -2 322 exclude a value at 44.5 N; 9.5% < p < 32.8%, 0.77 x 10 < tan1 < 1.07 x 10 , 0.75 x
-5 -5 323 10 S/m < 1 < 1.61 x 10 S/m based on the observed range of 1,bulk: 3.49 < 1,bulk <
324 5.38. The derived 1,bulk are almost in a range between 1.3 and 5.1 reported in Ishiyama
325 et al. (2013; 2014). The average of the observed apparent depth to the subsurface
326 reflector of this region, 400m, is then cast to a range of true depths from 172m to 214m.
o 327 For 45 – 50 N, S = 12.41wt% was adopted to give 1,grain of 6.29, which
-2 328 sequentially yields the following ranges: 17.7% < p < 41.1%, 0.81 x 10 < tan1 < 0.58
-2 -5 -5 329 x 10 , 0.48 x 10 S/m < 1 < 1.02 x 10 S/m corresponding to the observed range for
330 1,bulk: 2.96 < 1,bulk < 4.54. The observed apparent depth of 400m can be converted into
331 a range of true depths from 288m to 233m. Figures 11(a) and 11(b) show the 332 estimated 1 in this region.
333 In Oceanus Procellarum, 586 and 427 subsurface echoes were identified for
334 40 – 45oN and 45 – 50oN, respectively. For 7 and 8 continuous reflectors, estimates of
335 2,bulk were obtained using the corresponding 1,bulk as shown in Figs. 12(a) and 12(b).
o 336 The ranges for 2,bulk were determined as 6.17 – 15.44 for 40 – 45 N and 4.84 – 12.26
337 for 45 – 50oN.
338
339 4.3 Mare Imbrium
340 Figures 13(a) and 13(b) show radargrams of this region. Because reflected echoes
341 from the Moon’s surface were observed everywhere, the bulk permittivity of the first
342 layer, 1, were estimated using Eq. (9) every 371 shots, which were approximately
343 equivalent to one selenographic latitude. Figures 14(a) and 14(b) show 1 (= 1,bulk) and
344 grain (= 1,grain) thus derived. 1,grain was estimated using Eqs. (17), (20) and the iron-
345 titanium content of this region by Lawrence et al. (2002).
o 346 For 35 – 40 N, S = 16.86wt% was adopted to give 1,grain of 6.60, which
347 sequentially yields the following ranges for the associated physical properties as 1.8% < -2 -2 -5 -5 348 p < 27.8%, 1.05 x 10 < tan1 < 1.53 x 10 , 1.14 x 10 S/m < 1 < 2.71 x 10 S/m based
349 on the observed range for 1,bulk, viz., 3.91 < 1,bulk < 6.37. Those ranges project the
350 average of the observed apparent depth to the subsurface reflector, 500m, into a range
351 of true depths from 198m to 253m.
o 352 For 40 – 45 N, S = 16.31wt% was adopted to give 1,grain of 6.56, which
353 sequentially yields the following ranges for the associated physical properties as 9.1% <
-2 -2 -5 -5 354 p < 25.7%, 1.03 x 10 < tan1 < 1.31 x 10 , 1.16 x 10 S/m < 1 < 2.01 x 10 S/m based
355 on the observed range for 1,bulk, viz., 4.04 < 1,bulk < 5.53. Those ranges project the
356 average of the observed apparent depth to the subsurface reflector, 500m, into a range
357 of true depths from 213m to 249m.
358 Unlike the surface echoes, the subsurface echoes were not always detected.
359 To circumvent this, 21 stacks of A-scope were taken using the surface echo as a
360 reference. Figure 15 shows an example of the stacked A-scope. 221 subsurface
361 echoes were identified for 35 – 40oN, while 162 were found in 40 – 45oN. Using
362 running means of those echoes, 9 and 7 estimates of 2,bulk were obtained in the
363 respective latitudinal ranges using the estimated 1,bulk and Eq. (10). Figure 16(a) and 364 16(b) show the 2,bulk thus derived together with 1,bulk used. The ranges for 2,bulk
365 were determined as 6.81 – 21.28 for 35 – 40oN and 7.81 – 14.61 for 40 – 45oN, if we
366 eliminate a value with the large error bar at 35.6oN.
367
368 4.4 Mare Crisium
369 Figures 17(a) and 17(b) show radargrams of this region. For 10 – 15oN, S = 10.61wt%
370 was adopted to give 1,grain of 6.17, which gives the following ranges, provided that
371 values with large error bars around 13.5oN and 14.5oN in addition to the one near
372 10.7oN where topographic echoes were dominant, were excluded; 29.6% < p < 35.6%,
-3 -3 -6 -6 373 5.32 x 10 < tan1 < 5.70 x 10 , 4.78 x 10 S/m < 1 < 5.80 x 10 S/m based on the
374 observed range of 1,bulk: 3.23 < 1,bulk < 3.60. The average of the observed apparent
375 depths of this region, 300m, can be projected into a range of true depths from 158m to
376 167m.
o 377 For 15 – 20 N, S = 12.50wt% was adopted to give 1,grain of 6.29, which
-3 378 sequentially gives the following ranges: 19.8% < p < 37.7%, 6.13 x 10 < tan1 < 7.90
-3 -6 -6 379 x 10 , 5.37 x 10 S/m < 1 < 9.60 x 10 S/m based on the observed range for 1,bulk: 380 3.15 < 1,bulk < 4.37. The observed apparent depth of 300m is equivalent to a range of
381 true depths from 158m to 167m. Figures 18(a) and 18(b) summarize the estimated 1
382 in this region.
383 In Mare Crisium, 1025 and 1274 subsurface echoes were identified for 10 –
o o 384 15 N and 15 – 20 N, respectively. Estimates of 2,bulk were obtained using the
385 corresponding 1,bulk for 7 and 6 continuous reflectors and shown in Figs. 19(a) and
o 386 19(b). The ranges for 2,bulk were determined as 4.25 – 12.52 for 10 – 15 N excluding
387 a value with a very large error bar at 11.3oN, and 6.55 – 9.63 for 15 – 20oN.
388
389 4.6 Summary of Data Analyses
390 All results described in this section are summarized in Table 1 along with estimated
391 ages of the lunar maria determined by crater density (Hiesinger et al., 2000; 2003;
392 2011). Values of the bulk permittivity show correlation with S. Table 1 also shows
393 that each tabulated value has small spatial variation in the latitude range of 5o to 10o.
394 Figure 20 was created from Table 1, which shows a clear positive correlation of the
395 bulk permittivity, 1,bulk, derived in this study with the reported Fe and Ti content, S 396 (Lawrence et al., 2002). The bulk permittivity can be expressed by 1,bulk = 0.297 S +
397 0.0107 with a correlation coefficient of R² = 0.881.
398
399 5. Discussion
400 5.1 Validity of Applied Methods
401 Because many of A-scope data showed peaks of a single subsurface reflector that can be
402 identified on adjacent orbits as well, it is reasonable to assume two-layer models for the
403 LRS data. However, the analyzed results show that there exist regions of anomalously
404 large errors for bulk permittivity. It is very difficult to consider those errors due to
405 actual spatial variations of the physical quantity. It can be rather interpreted as a result
406 of scattering of surface echoes by rugged topography. The radargrams over the large
407 error regions suggest that those regions are characterized by combinations of intense
408 and weak echoes. In this study, relatively flat regions were selected to yield
409 radargrams by taking running means for better protection against rugged topography.
410 However, the results showed that it is not sufficient for all regions. It, therefore, will
411 be desirable to do more accurate numerical simulations of EM wave propagation by 412 incorporating known topography on the Moon’s surface, so as to estimate more precise
413 bulk permittivity over broader regions in the future.
414 As confirmed in Subsections 4.2 and 4.3, the bulk permittivities derived in
415 Mare Serenitatis and Oceanus Procellarum in this study were almost in the range
416 reported in Ishiyama et al. (2013; 2014). The agreement suggests that the absolute
417 calibration of the echo powers used in this study was not extremely deviated from
418 correct calibration.
419
420 5.2 Bulk Permittivity
421 The derived bulk permittivity of the lunar uppermost layer was in a range
422 from 2.96 (at Mare Imbrium) to 6.37 (at Oceanus Procellarum), which supports the
423 actual depth to the reflectors in those maria to be around 200 m.
424 Olhoeft and Strangway (1975), and Carrier et al. (1991) reported that the bulk
425 permittivity of the Moon rock samples shows values ranging from 1.1 to 11, majority of
426 which falls between 4 and 9. However, this study yields somewhat smaller bulk
427 permittivity not only in Mare Serenitatis and Oceanus Procellarum, which was already 428 reported by Ishiyama et al. (2013; 2014), but also in Mare Imbrium and Mare Crisium.
429 This can be partly attributed to the effect of porosity as discussed by Ishiyama et al.
430 (2013, 2014) but also explained by the effect of composition, i.e., titanium content.
431 Olhoeft and Strangway (1975) showed that the bulk permittivity is primarily a
432 strong function of bulk density. This means that the bulk permittivity depends on not
433 only how porous the medium in concern is, but also how dense and dielectric the rest of
434 the medium other than cavity is. Titanium bearing minerals such as ilmenite is typical
435 of those that have both large density and high permittivity. The good correlation
436 between the bulk permittivity derived in this study and the known titanium content of
437 the lunar maria surface shown in Fig. 20 can be regarded as possible presence of
438 enriched titanium bearing minerals in each lunar mare such as Mare Imbrium.
439 The analysis method used in this study enabled us to derive bulk permittivity
440 and porosity in wide area of multiple maria. A new suggestion brought by the
441 comparison of porosity in multiple maria in this study will be described in the next
442 subsection. The estimates of showed larger shot-by-shot scatter than . It was
휀2 휀1 443 assumed throughout this study that in applying the two-layer models.
휀1 < 휀2 444 However, its validity for multiple layer models should be examined in the future.
445
446 5.3 Porosity
447 Based on the bulk permittivity from 2.96 to 6.37, the porosity takes the values between
448 1.8% to 41.1%. Porosity of the Moon rock samples is less than 10% in most cases, and
449 hence samples with porosity larger than 20% are rare (Olhoeft and Strangway, 1975).
450 However, this study yielded large porosity, which possibly represents macroscopic
451 (bulk) porosity rather than microscopic as was pointed out by Ishiyama et al. (2013).
452 One of the main causes for large bulk porosity is cracks by degassing at the
453 time of volcanic eruptions, by quenching of lavas or by meteorite impacts. Sizes of the
454 Moon rock samples are of the order of centimeter, while the spatial resolution of LRS is
455 at most a few tens of meters. This means that the LRS data are subject to be affected
456 by large-scale cracks. It, therefore, can be speculated that if the maximum porosity
457 determined by laboratory experiments is 10%, that by the LRS data can reach 20%.
458
459 5.4 Loss Tangent 460 The estimated range of loss tangent was 5.3 x 10-3 - 1.53 x 10-2 in this study. Olhoeft
461 and Strangway (1975) derived a range of 7.53 x 10-3 - 1.92 x 10-2 at (Fe + Ti wt%) = 15
462 by their laboratory experiments of the Moon rock samples. The smaller loss tangent
463 range of this study may also be attributed to the macroscopic porosity. Substitution of
464 (Fe + Ti wt%) = 15 into Eqs. (16) and (17) yields a width of 4.6 x 10-3 for the loss
465 tangent range, if porosity is changed from 0% through 30%. If the observed loss
466 tangent is corrected by this range width, the two ranges, i.e., the field and laboratory
467 ranges, agree very well. Furthermore, Bando et al. (2015) investigated the ratio
468 between the powers of echoes from subsurface reflectors at deferent depths measured
469 by LRS to yield a loss tangent range of 1.07 x 10-2 - 1.13 x 10-2, which corresponds to
470 the median value of the observed loss tangent by this study. It, therefore, can be
471 concluded that the loss tangent by this study may reflect the true loss tangent near the
472 lunar surface with possible scatter produced by macroscopic porosity.
473
474 6. Conclusions
475 Assuming incident EM waves from LRS being normal to the horizontally stratified two- 476 layer models, bulk permittivity, porosity and loss tangent near the lunar surface were
477 estimated using the observed LRS data by calculating EM wave propagation according
478 to the radar range equation. Combined use of the estimated titanium content
479 distribution by spectroscopy of the lunar surface (Lawrence et al., 2002) and the
480 empirical relations among physical quantities in concern derived from analyses of the
481 Moon rock samples (Shkuratov and Bondarenko, 2001; Olhoeft and Strangway, 1975)
482 enabled unique determination of otherwise degenerated physical quantities. The
483 results are summarized in Table 1, in which all the analyzed regions, viz., Mare
484 Imbrium, Oceanus Procellarum, Mare Crisium and Mare Serenitatis, are included. It is
485 obvious by the table that the actual depth to the subsurface reflectors of the Moon is
486 around 200m.
487 The estimates of each physical quantity do not change much within a
488 latitudinal range of 5o to 10o, whereas bulk permittivity shows a positive correlation
489 with titanium content. Since porosity, in turn, shows a negative correlation with
490 formation ages of lunar maria, it may be reflected effects of volcanic eruptions rather
491 than those of meteorite impacts. Finally, Table 1 will make a good reference for future 492 studies, because discrepancy between the field and laboratory estimates is turned out to
493 be reconciled by the effect of porosity.
494
495 Declarations
496 List of abbreviations
497 ALSE: Apollo Lunar Sounder Experiment
498 EM: electromagnetic
499 ESA: European Space Agency
500 JUICE: JUpiter ICy moon Explorer
501 LRS: Lunar Radar Sounder
502 RIME: Radar of Icy Moon Exploration
503 SELENE: SELenological and ENgineering Explorer
504 Availability of data and materials
505 The datasets used and/or analyzed during the current study are available
506 from the following links:
507 The LRS data: 508 http://l2db.selene.darts.isas.jaxa.jp/
509 The Fe and Ti content distribution:
510 http://www.mapaplanet.org/data_local/Lunar_Prospector/lp_fe_5d.asc
511 http://www.mapaplanet.org/data_local/Lunar_Prospector/lp_ti_5d.asc
512 Competing interests
513 The authors declare that they have no competing interests.
514 Funding
515 This work was partly supported by JSPS KAKENHI Grant Number
516 JP25420402.
517 Authors' contributions
518 KH carried out data processing, modelling and figure and table drawings.
519 HT supervised KH throughout this study to achieve a master degree, and
520 converted his master thesis in Japanese to the draft manuscript in
521 English. AK guided the data processing and modelling by providing
522 raw time-series of reflected echoes together with their metadata and
523 necessary information for modelling/interpretation. All authors read 524 and approved the final manuscript.
525 Acknowledgements
526 We are indebted to Professors A. Yamaji at Graduate School of Science,
527 Kyoto University and M. Yamamoto at Research Institute for Sustainable
528 Humanosphere, Kyoto University for their help that was indispensable to
529 complete this work.
530 Authors' information
531 Keigo Hongo, Division of Earth and Planetary Sciences, Graduate School
532 of Science, Kyoto University
533 Hiroaki Toh, Division of Earth and Planetary Sciences, Graduate School
534 of Science, Kyoto University
535 Atsushi Kumamoto, Department of Geophysics, Graduate School of
536 Science, Tohoku University
537 Corresponding Author: Hiroaki Toh
538
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622 Figure legends
623 Figure 1 An example of received waveforms. This 327.68s long time-series of a
624 reflected echo was received at 00:57:15.181 UTC on May 4, 2008 when SELENE
625 was flying over Mare Imbrium, i.e., (40.226N°, 345.304E°) in the selenographic
626 coordinate. It is filtered and resampled as described in the text.
627 Figure 2 (a) A-scope of the reflected echo of Fig. 1. We used the 2nd term of Eq. (8)
628 for x-axis instead of dA. (b) A zoom-in plot of Fig. 2(a). The first three
629 reflections including the Moon’s surface are clearly seen.
630 Figure 3 (a) B-scan over Mare Imbrium at the selenographic longitude of 345.3Eo.
631 The origin of the apparent depth is taken at the Moon’s surface assuming the
632 averaged radius of the Moon to be 1737.4km. (b) Another B-scan image at the
633 selenographic longitude of 345.0Eo. Several strong echoes of parabolic shape are
634 due to craters near by. (c) Taking running means highlighted the subsurface
635 reflectors especially for those starting from the horizontal black arrows, which 636 continue to ~42No.
637 Figure 4 The two-layer model adopted by this study. SELENE transmitted a radar
638 pulse every 0.05 (or 0.4) second with an output power of Pt [W]. Let input
639 powers of the surface and subsurface reflection be Prs [W] and Prss [W],
640 respectively. R [m] and RD [m] are respectively the altitude of the spacecraft and
641 the apparent depth to the subsurface reflector. Both relative magnetic
642 permeability and permittivity between SELENE and the Moon’s surface are
st 643 assumed to be unity, while those of the 1 layer are unity and 1. Another
st 644 physical property of the 1 layer here is the electrical conductivity, 1. The
645 remaining model parameter of this two-layer model is the bulk permittivity of the
nd 646 2 layer, 2.
647 Figure 5 The flow chart of data analysis of this study.
648 Figure 6 The topographic map of the northern hemisphere on the far side of the Moon.
649 The base map was downloaded from Geospatial Information Authority of Japan
650 ( http://gisstar.gsi.go.jp/selene/Maps/Stereo_En-800.tif.zip), which is jointly
651 operated by National Astronomical Observatory of Japan and Japan Aerospace 652 Exploration Agency. The four red ellipses denote the location of the target areas
653 of this study.
654 Figure 7 Radargrams of Mare Serenitatis for (a) 20 – 25oN and (b) 25 – 30oN.
o 655 Figure 8 Estimates of 1,bulk and 1,grain of Mare Serenitatis for (a) 20 – 25 N and (b) 25
o o 656 – 30 N. The regional representatives of 1,grain = 6.49 (for 20 – 25 N) and 6.39
657 (for 25 – 30oN) are shown by horizontal green lines. The vertical error bars for
658 1,bulk show 95% confidence intervals of each latitudinal average.
o 659 Figure 9 Estimates of 1,bulk (red) and 2,bulk (blue) of Mare Serenitatis for (a) 20 – 25 N
o 660 and (b) 25 – 30 N. Vertical error bars of 2,bulk are the 95% confidence intervals
661 determined using the observed echoes associated with each reflector, while
662 horizontal error bars denote their spatial extent.
663 Figure 10 Radargrams of Oceanus Procellarum for (a) 40 – 45oN and (b) 45 – 50oN.
o 664 Figure 11 Estimates of 1,bulk and 1,grain of Oceanus Procellarum for (a) 40 – 45 N and
o o 665 (b) 45 – 50 N. The regional representatives, i.e., 1,grain = 6.41 (for 40 – 45 N)
666 and 6.29 (for 45 – 50oN) are shown by horizontal green lines. The vertical error
667 bars for 1,bulk show 95% confidence intervals of the latitudinal averages. 668 Figure 12 Estimates of 1,bulk (red) and 2,bulk (blue) of Oceanus Procellarum for (a) 40 –
o o 669 45 N and (b) 45 – 50 N. Vertical error bars of 2,bulk are the 95% confidence
670 intervals determined using the observed echoes associated with each reflector,
671 while horizontal error bars denote the spatial extent of each reflector.
672 Figure 13 Radargrams of Mare Imbrium for (a) 35 – 40oN and (b) 40 – 45oN. 21-point
673 running means are plotted.
o 674 Figure 14 Estimates of 1,bulk and 1,grain of Mare Imbrium for (a) 35 – 40 N and (b) 40
o o o 675 – 45 N. 1,grain = 6.60 (for 35 – 40 N) and 6.56 (for 40 – 45 N) are values
676 representative of this region and determined from the known iron-titanium
677 distribution (Lawrence et al., 2002), while 1,bulk‘s are latitudinal averages. The
678 vertical error bars for 1,bulk show 95% confidence intervals of the averages.
679 Figure 15 The stacked A-scope. Prss indicates the location of the subsurface echo.
o 680 Figure 16 Estimates of 1,bulk (red) and 2,bulk (blue) of Mare Imbrium for (a) 35 – 40 N
o 681 and (b) 40 – 45 N. Vertical error bars of 2,bulk are the 95% confidence intervals
682 determined using the observed echoes associated with each reflector, while
683 horizontal error bars denote the spatial extent of each reflector. 684 Figure 17 Radargrams of Mare Crisium for (a) 10 – 15oN and (b) 15 – 20oN.
o 685 Figure 18 Estimates of 1,bulk and 1,grain of Mare Crisium for (a) 10 – 15 N and (b) 15 –
o o 686 20 N. The regional representatives of 1,grain = 6.17 (for 10 – 15 N) and 6.29 (for
o 687 15 – 20 N) are shown by horizontal green lines. The vertical error bars for 1,bulk
688 show 95% confidence intervals of each latitudinal average.
o 689 Figure 19 Estimates of 1,bulk (red) and 2,bulk (blue) of Mare Crisium for (a) 10 – 15 N
o 690 and (b) 15 – 20 N. Vertical error bars of 2,bulk are the 95% confidence intervals
691 determined using the observed echoes associated with each reflector, while
692 horizontal error bars denote the spatial extent of each reflector.
st 693 Figure 20 Correlation between the bulk permittivity of the 1 layer, 1, and the surface
694 metal content in each lunar mare. Figures
Figure 1
An example of received waveforms. This 327.68Us long time-series of a re ected echo was received at 00:57:15.181 UTC on May 4, 2008 when SELENE was ying over Mare Imbrium, i.e., (40.226N°, 345.304E°) in the selenographic coordinate. It is ltered and resampled as described in the text. Figure 2
(a) A-scope of the re ected echo of Fig. 1. We used the 2nd term of Eq. (8) for x-axis instead of dA. (b) A zoom-in plot of Fig. 2(a). The rst three re ections including the Moon’s surface are clearly seen. Figure 3
(a) B-scan over Mare Imbrium at the selenographic longitude of 345.3Eo. The origin of the apparent depth is taken at the Moon’s surface assuming the averaged radius of the Moon to be 1737.4km. (b) Another B- scan image at the selenographic longitude of 345.0Eo. Several strong echoes of parabolic shape are due to craters near by. (c) Taking running means highlighted the subsurface re ectors especially for those starting from the horizontal black arrows, which continue to ~42No. Figure 4
The two-layer model adopted by this study. SELENE transmitted a radar pulse every 0.05 (or 0.4) second with an output power of Pt [W]. Let input powers of the surface and subsurface re ection be Prs [W] and Prss [W], respectively. R [m] and RD [m] are respectively the altitude of the spacecraft and the apparent depth to the subsurface re ector. Both relative magnetic permeability and permittivity between SELENE and the Moon’s surface are assumed to be unity, while those of the 1st layer are unity and 1. Another physical property of the 1st layer here is the electrical conductivity, E1. The remaining model parameter of this two-layer model is the bulk permittivity of the 2nd layer, e 2.
Figure 5
The ow chart of data analysis of this study. Figure 6
The topographic map of the northern hemisphere on the far side of the Moon. The base map was downloaded from Geospatial Information Authority of Japan ( http://gisstar.gsi.go.jp/selene/Maps/Stereo_En-800.tif.zip), which is jointly operated by National Astronomical Observatory of Japan and Japan Aerospace Exploration Agency. The four red ellipses denote the location of the target areas of this study. Figure 7
Radargrams of Mare Serenitatis for (a) 20 – 25oN and (b) 25 – 30oN. Figure 8
Estimates of E 1,bulk and E 1,grain of Mare Serenitatis for (a) 20 – 25oN and (b) 25 – 30oN. The regional representatives of E 1,grain = 6.49 (for 20 – 25oN) and 6.39 (for 25 – 30oN) are shown by horizontal green lines. The vertical error bars for E 1,bulk show 95% con dence intervals of each latitudinal average. Figure 9
Estimates of E1,bulk (red) and E 2,bulk (blue) of Mare Serenitatis for (a) 20 – 25oN and (b) 25 – 30oN. Vertical error bars of E 2,bulk are the 95% con dence intervals determined using the observed echoes associated with each re ector, while horizontal error bars denote their spatial extent. Figure 10
Radargrams of Oceanus Procellarum for (a) 40 – 45oN and (b) 45 – 50oN. Figure 11
Estimates of E 1,bulk and E 1,grain of Oceanus Procellarum for (a) 40 – 45oN and (b) 45 – 50oN. The regional representatives, i.e., E 1,grain = 6.41 (for 40 – 45oN) and 6.29 (for 45 – 50oN) are shown by horizontal green lines. The vertical error bars for E 1,bulk show 95% con dence intervals of the latitudinal averages. Figure 12
Estimates of E 1,bulk (red) and E 2,bulk (blue) of Oceanus Procellarum for (a) 40 – 45oN and (b) 45 – 50oN. Vertical error bars of E 2,bulk are the 95% con dence intervals determined using the observed echoes associated with each re ector, while horizontal error bars denote the spatial extent of each re ector. Figure 13
Radargrams of Mare Imbrium for (a) 35 – 40oN and (b) 40 – 45oN. 21-point running means are plotted. Figure 14
Estimates of E 1,bulk and E1,grain of Mare Imbrium for (a) 35 – 40oN and (b) 40 – 45oN. E 1, grain = 6.60 (for 35 – 40oN) and 6.56 (for 40 – 45oN) are values representative of this region and determined from the known iron-titanium distribution (Lawrence et al., 2002), while E 1, bulk‘s are latitudinal averages. The vertical error bars for E 1, bulk show 95% con dence intervals of the averages. Figure 15
The stacked A-scope. Prss indicates the location of the subsurface echo. Figure 16
Estimates of E 1,bulk (red) and E 2,bulk (blue) of Mare Imbrium for (a) 35 – 40oN and (b) 40 – 45oN. Vertical error bars of E 2,bulk are the 95% con dence intervals determined using the observed echoes associated with each re ector, while horizontal error bars denote the spatial extent of each re ector. Figure 17
Radargrams of Mare Crisium for (a) 10 – 15oN and (b) 15 – 20oN. Figure 18
Estimates of E 1,bulk and E 1,grain of Mare Crisium for (a) 10 – 15oN and (b) 15 – 20oN. The regional representatives of E 1,grain = 6.17 (for 10 – 15oN) and 6.29 (for 15 – 20oN) are shown by horizontal green lines. The vertical error bars for E 1,bulk show 95% con dence intervals of each latitudinal average. Figure 19
Estimates of E 1,bulk (red) and E 2,bulk (blue) of Mare Crisium for (a) 10 – 15oN and (b) 15 – 20oN. Vertical error bars of E 2,bulk are the 95% con dence intervals determined using the observed echoes associated with each re ector, while horizontal error bars denote the spatial extent of each re ector. Figure 20
Correlation between the bulk permittivity of the 1st layer, E1, and the surface metal content in each lunar mare.
Supplementary Files
This is a list of supplementary les associated with this preprint. Click to download.
Table1.pdf GraphicalAbs.pdf