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Laboratory measurements show temperature-dependent permittivity of lunar regolith simulants


The mapping of available water–ice is a crucial step in the lunar exploration missions. Ground penetrating radars have the potential to map the subsurface structure and the existence of water–ice in terms of the electromagnetic properties, specifically, the permittivity. Slight differences in permittivity can be significantly important when applied in a dry environment, such as on the Moon and Mars. The capability of detecting a small fraction of putative water–ice depends on the permittivity changes in terms of its dependent parameters, such as the frequency, the temperature, the porosity, and the chemical composition. Our work aims at mitigating false detection or overlooking of water–ce by considering their conditions that previous researches did not cover. We measured the permittivity of different lunar regolith relevant analogue samples with a fixed 40 % porosity in the ultra-high-frequency–super-high-frequency band. We used the coaxial probe method to measure anorthosite, basalt, dunite and ilmenite at \(20\,^\circ \hbox {C}\), \(-20\,^\circ \hbox {C}\) and \(-60\,^\circ \hbox {C}\), and we find that, at \(-60\,^\circ \hbox {C}\), the permittivity decreases about 6–18 % compared with the values at \(20\,^\circ \hbox {C}\). Within this temperature range, the permittivity is quite similar to the permittivity of water–ice. We find that the conventional calculation would overestimate the permittivity in the low temperature areas, such as the permanently shadowed regions. We also find that each component in the lunar regolith has different temperature-dependent permittivity, which might be important for radar data analysis to detect lunar polar water–ice. Our results also suggest that it should be possible to estimate the water–ice content from radar measurements at different temperatures given an appropriate method.

Graphical Abstract


The existence of putative water–ice on the Moon has been a frequently debated topic for the last decades (Arnold 1979; Watson et al. 1961). Multiple observations have implied the existence of water–ice, especially in the low-temperature regions of the lunar poles in permanently shadowed regions (Colaprete et al. 2010; Feldman et al. 1998; Lawrence et al. 2006; Li et al. 2018; Nozette et al. 1996; Spudis et al. 2013; Zuber et al. 2012; Kereszturi 2020). The water–ice on the Moon has substantial scientific values and is also a vital resource for future explorations and long-term missions on the Moon. However, there is no consensus about the amount and distribution of water–ice. The estimated amount in the regolith ranges from less than 1.0 wt% (Miller et al. 2012; Pieters et al. 2009; Sanin et al. 2017) to about 30 wt% (Li et al. 2018). Moreover, the estimated distribution by different observations does not match (e.g., Fisher et al. 2017; Hayne et al. 2015; Li et al. 2018). Thus, several landing missions such as Lunar Polar Exploration (LUPEX), Volatiles Investigating Polar Exploration Rover (VIPER), and Chang’E-6 aim at gathering data about the amount and distribution of water–ice in the lunar polar region (Colaprete et al. 2019; Hoshino et al. 2020). The existence of ice could be examined through in-situ analysis of subsurface materials by drilling, which is technically possible up to a few meters (Boazman et al. 2022). In our work, we focus on obtaining information about the subsurface up to this depth and aid the selection of candidate sites.

One observational instrument that can obtain information on the lunar subsurface up to a few meters in depth and with a high resolution is the Ground-Penetrating Radar (GPR). GPRs use high-frequency radio waves to image the subsurface. Electromagnetic (EM) waves reflect or scatter at the boundary between materials with different dielectric properties. The behavior of EM waves in a medium is mainly determined by permittivity, permeability, and conductivity. For the Apollo samples, the conductivity is typically almost zero \((10^{-9} - 10^{-14}\) S/m) (Heiken et al. 1991), which means that the maximum attenuation rate is in the order of \(10^{-7}\) dB/m in the lunar regolith and can be negligible for the EM propagation through the lunar regolith. In GPRs frequency range, most minerals (except for magnetic minerals) have no ferromagnetism, so the permeability is almost the same as the magnetic constant (permeability in vacuum), and does not affect the propagation of EM waves through soils or rocks (Martinez and Byrnes 2001). Thus, permittivity is the only dominant parameter for EM propagation through lunar regolith. This physical exploration method has been conducted by the previous Chang’E missions (Xiao et al. 2015; Li et al. 2020; Zhang et al. 2020). LUPEX is also equipped with a GPR to identify regolith structures before drilling.

In-situ observations have been conducted to estimate lunar regolith permittivity (e.g., Dong et al. 2017, 2021; Ishiyama et al. 2013; Su et al. 2022), but the accuracy is limited, which makes laboratory measurements to be one of the best methods to estimate permittivity. A reliable data set was compiled from the Apollo missions measured under dry conditions at various temperatures (e.g., Chung and Westphal 1973; Frisillo et al. 1975; Gold et al. 1976; Olhoeft and Strangway 1975; Heiken et al. 1991). The relative permittivity is associated with the bulk density and FeO+\(\hbox {TiO}_2\) content (e.g., Heiken et al. 1991; Olhoeft and Strangway 1975), and more recent results came from the JSC-1A (Johnson Space Center) lunar regolith simulant measurements (Calla and Rathore 2012) and the Chang’E-5 mission (Su et al. 2022).

Although these studies help us understand the lunar subsurface, it is still challenging to predict the permittivity of future exploration sites. This is because the permittivity is dependent on various parameters such as applied frequency, water content, chemical composition, and temperature (Campbell and Ulrichs 1969; Hansen 1973; Heiken et al. 1991; Jones and Friedman 2000; Shkuratov and Bondarenko 2001; Topp et al. 1980), that is, the permittivity should be treated with the constraints of these parameters. Future GPRs also use a higher frequency band than previous in-situ observations to acquire higher resolution, so it is unclear whether the permittivity at other frequencies can be applied to the analysis of GPRs. In addition, the chemical composition of lunar rocks and regolith has a wide range (e.g., Heiken et al. 1991; Lemelin et al. 2022). Thus, it is not easy to estimate the permittivity at different landing sites from only the measurement of returned samples. Although the measurement of permittivity of simulants is helpful for this purpose, the chemical composition is adjusted to be similar to Apollo samples and the variation has less. Although the effect of temperature on the permittivity is also significant, especially in the low temperature regions such as the permanently shadowed regions, few previous researches have considered the effect in the frequency band for GPR. Calla and Rathore (2012) reported on the temperature dependence of permittivity by measuring the JSC-1A simulant, which is partly very useful to consider the permittivity under the low-temperature environment on the Moon. However, the JSC-1A simulant is manufactured to represent Mare region, not highland and polar region. Thus, the permittivity of highland and polar region at low temperatures has been unclear. Furthermore, the permittivity of water–ice is about 3.1–3.2 (Fujita et al. 2000), which is very close to that of the lunar subsurface. This means that it is unreliable to analyse water–ice existence from the roughly estimated permittivity. To gain useful results for near-future lunar missions, we need to precisely estimate the permittivity at landing sites with various chemical compositions.

In this letter, we focus not on the mixture of lunar simulant, but the typical lunar regolith end-members covering the whole lunar surface of mare, highland, and polar regions (useful for arbitrary mixture permittivity estimations), and report permittivity measurements on different frequencies, which are useful for the GPR data analysis. We simulate the lunar surface/subsurface environment of the polar regions and measure the permittivity with high accuracy in the UHF–SHF band. Knowing the permittivity of several lunar simulants as the end-member of lunar regolith has an advantage to enable us to estimate the bulk permittivity of regolith with an arbitrary composition in the future. Our results highlight the importance of keeping the temperature dependence of various minerals in mind when studying radar data, because other basic lunar regolith materials could be mistaken for water–ice content. The new water–ice hunting lunar missions already on their way to the Moon, working or planned to start in the next years make our results a timely addition to the field.

Experiment methodology

We measure the permittivity of four samples, including rocks and a pure mineral, that typically exist on the Moon (Additional file 1: Fig. S1 and Additional file 3: Table S1): anorthosite, basalt, dunite and ilmenite. Anorthosite, mainly composed of plagioclase accompanying several types of mafic minerals, is distributed widely on the lunar highland and is considered as a representative material for a primitive crust. According to the data from the Kaguya Spectral Profiler measurement, the polar regions can be characterized by a mixture of homogeneous plagioclase (up to 90 wt%) and FeO (<15 wt%) content (Lemelin et al. 2022). Thus, the permittivity of anorthosite is crucial for interpreting the data of the radar observations by LUPEX and Chang’E, while basalt is typically found in Mare regions. Using the permittivity of anorthosite and basalt we can roughly estimate the bulk permittivity in almost all lunar regions. Besides, as mafic materials, we measured the permittivity of dunite (mainly composed of olivine, located in the region where the crust is relatively thin), which exists on the floor of the SPA basin, and its permittivity should be significant for the analysis of the Lunar Penetrating Radar (LPR) data on Chang’E-4 Yutu-2 rover. In addition, the bulk permittivity of the lunar surface and subsurface could be affected by a small fraction of other materials, especially with high concentrations of Fe and/or Ti (Heiken et al. 1991; Olhoeft and Strangway 1975), and thus, we also measure the permittivity of ilmenite. The chemical composition of the geological samples is measured by X-Ray Fluorescence (XRF) to consider the adequacy of samples for the simulated lunar materials. The measurement is conducted using ZSX Primus II (Rigaku) at 50 kV. Additional file 3: Table S2. shows the chemical composition of each sample. We also checked the modal composition of anorthosite to conduct the point counting method, and confirmed that the anorthosite consistes of mostly Ca-rich plagioclase (92 vol% at most) and with minor pyroxene and olivine, which is consistent with the Apollo sample from highland (Heiken et al. 1991). The bulk composition of basalt is within the chemical composition of the Apollo samples except for \(\hbox {TiO}_2\) and FeO, which may result from the lack of ilmenite. The grain density of each sample is also measured using a 25 mL Gay–Lussac pycnometer. As in the case of the ilmenite, the grain density is the ideal one (Holden 1921).

Sample preparation

The coaxial probe method requires uniformly mixed samples for accurate permittivity measurements, so we crushed the solid samples into fine powders to exclude heterogeneity (Additional file 1: Fig. S1). A few to tens of centimetre-sized samples are first crushed with the hammer and jaw crusher (CR-200B; Marubishi Scientific Instrument Meg. CO., LTD) into smaller than 10 mm, then crushed further with the stamp mill made of stainless steel (ANS-143PS; NITTO KAGAKU CO., LTD). We then sieved the powders with 46 \(\mu\)m with JIS standard sieves. The grain size of ilmenite is about hundreds micrometers, and the basalt is sieved with 500 \(\mu\)m because this sample has a mineral dependence on the particle size and the sieving would exclude some minerals arbitrarily. We then baked the samples at 95 \(^\circ \hbox {C}\) for a day or more in the oven to get rid of the water content because the lunar regolith is mostly dry (at the polar regions it is more complex as ice might exist under dry regolith), and the existence of water could affect the bulk permittivity of the samples (Olhoeft and Strangway 1975; Topp et al. 1980). To remove the effect of porosity on the permittivity, which is one of the most effective parameters on the permittivity, we carefully arranged each sample to have the same porosity of 40 %, which is relevant for the top cm–dm layer although at 1 m below the porosity is much smaller. The porosity can change with tapping so we treated the samples carefully, minimising vibrations before the measurement. This preparation makes it possible to measure the permittivity depending on only the difference of materials under the constrained environment.

Permittivity measurement

Various methods are proposed to measure the permittivity (Venkatesh and Raghavan 2005), but coaxial probe method is the most accurate with high reproducibility at the UHF–SHF band. The method utilises the reflection caused by the impedance mismatch between the probe and the samples (Wang et al. 2020). The reflection is measured at a single network port as the \(S_{11}\) parameter which describes the ratio of input to output power in an electrical instrument. We used the coaxial probe and cable (85070E Dielectric Probe Kit; Keysight) and the vector network analyzer (VNA; 8753ES S-parameter Network Analyzer; Keysight) (Additional file 2: Fig. S2), with frequency between 1 MHz to 6 GHz in 1601 points (the frequency resolution is \(\sim\)3.7 MHz). To make the measurement stable, we warm up the vector network analyzer for 60 minutes before measurements. For the calibration, air, short, and pure water are used, which is the standard method for using the coaxial probe method (Blackham and Pollard 1997). We include the numerical results of the room temperature (\(20\,^\circ \hbox {C}\)),\(-20\,^\circ \hbox {C}\), and \(-60\,^\circ \hbox {C}\) deep freezer experiments in this Letter as we use these to determine the permittivity of an arbitrary mixture.


To quantify the measurement error of the developed experimental system, we measured the permittivity of air and pure water after calibration, before and after the room temperature experiments. The permittivity values and standard errors of air and pure water measurements are in Additional file 3: Tables S3 and S4 comparing with Barthel et al. (1991). The maximum relative error of air is 2.8 % at 1 GHz and \(\le\) 1.0 % above 2 GHz, while that of pure water is 1.3 % at 1.7 GHz and \(\le\) 0.8 % above 2.05 GHz. As the maximum relative error is more prominent at 1 GHz than at frequencies higher than 2 GHz, we show the measurement results of the permittivity of geological samples between 2 GHz and 6 GHz.

We list the permittivity results of each sample at \(20\,^\circ \hbox {C}\), \(-20\,^\circ \hbox {C}\), and \(-60\,^\circ \hbox {C}\) in Tables 1, 2 and 3. We measured every sample several times, with the probe positioned in various places on the surface of the samples to exclude the effects of the non-uniformity of the powdered samples (see Additional file 2: Fig. S2 in the Appendix for the experimental setup). The permittivity of the samples, with the exception of ilmenite is about 3, which is approximately consistent with the Apollo return sample results (Heiken et al. 1991). In the case of ilmenite, the permittivity is higher, about 7–8, which is consistent with previous results of the permittivity being strongly dependent on the FeO+\(\hbox {TiO}_2\) content (Heiken et al. 1991).

We found that permittivity displays a strong temperature dependence, which is different for each sample. Comparing the \(20\,^\circ \hbox {C}\) and \(-60\,^\circ \hbox {C}\) results, the permittivity of basalt changes by \(\sim\)15–18 %, the permittivity of anorthosite changes by \(\sim\)10–14 % and dunite shows only a \(\sim\)6–10 % difference. The permittivity of ilmenite also varies by about only \(\sim\)6–10 %, but the maximum absolute value change in the case of ilmenite is \(\sim\)0.9, which is larger than in the case of the other samples. The temperature dependence on the permittivity of lunar simulant has been previously reported by Calla and Rathore (2012). They described that the permittivity of JSC-1A at 2.5 GHz is about 4.13 and 4.01 at 30 \(^\circ \hbox {C}\) and − 50 \(^\circ \hbox {C}\), respectively, which indicates that the decrease is about 3.0 %. This difference is smaller than our measurement results. The theoretical research, based on the Debye model detailed in Yushkova and Kibardina (2017), reports that the permittivity decrease between \(20\,^\circ \hbox {C}\) and \(-60\,^\circ \hbox {C}\) at 1 GHz is about 13 % (see Fig. 4 in Yushkova and Kibardina 2017). Thus, our result is comparatively similar to the theoretical estimation of the permittivity at temperatures rather than the pervious measurement result of lunar simulant. At lower temperatures, such as 40–80 K (which is a typical temperature in the permanently shadowed regions), theoretical estimation of the permittivity of lunar simulants suggests that the permittivity should not decrease further after reaching a certain temperature (Yushkova and Kibardina 2017). This limit is about 200 K or less in the UHF–SHF band, so our results at \(-60\,^\circ \hbox {C}\) might be close to the lowest permittivity value (possibly somewhat larger). This should be confirmed by measuring at lower temperatures in the future work.

A simple demonstration of our results with the Looyenga–Landau–Lifshitz equation (which is one of the mixing equations of permittivity) (Looyenga 1965) would be the following: let us assume that 1) a lunar rover equipped with GPR utilising 4 GHz measured 3.0 permittivity at an anorthositic regolith site (e.g., lunar polar region), and 2) the porosity is 40 % (the relevant for the top cm–dm layer). Using the Looyenga–Landau–Lifshitz equation, the permittivity with 40 % porosity of anorthositic regolith resulting from our measurements, and the permittivity of 3.1 for water–ice (Fujita et al. 2000), we can estimate the water–ice content as 4.4 wt% at \(-20\,^\circ \hbox {C}\) and 11.2 wt% at \(-60\,^\circ \hbox {C}\). This means that because the permittivity of rock fraction is different at the two temperatures, the water–ice content estimated from the permittivity of 3.0 is different (even though the permittivity measured at the regolith site is the same). The difference between the two estimated water–ice contents indicates that for an accurate water–ice abundance estimation temperature information is also required, to consider the temperature dependent permittivity. In addition to the temperature information, the materials’ variation is also required: our results show how this temperature dependence is different for each geological sample; thus, the permittivity of lunar regolith should be estimated in the future while considering these variations. For example, if the content of ilmenite, which is one of the largest permittivity in the regolith, is not considered accurately, the higher permittivity could falsely suggest water–ice content from radar measurement. We highlight the importance to take the possibility that the measured permittivity could be a consequence of ilmenite-content into consideration. In addition, the observation of the porosity of regolith is difficult with existing method in-situ. Thus, it is required to develop the method to obtain the porosity and water–ice content with the consideration of the chemical composition of the lunar regolith at an arbitrary site. To aid this, we are developing a method to quantify the water–ice content focusing on the different temperature dependencies on the permittivity of rocks, minerals, and water–ice (Kobayashi et al., in prep.).

Most of the previous works analysing GPR data of the Moon relies on the relationship between the permittivity of the Apollo samples and bulk density (Heiken et al. 1991; Olhoeft and Strangway 1975):

$$\begin{aligned} \epsilon =1.919^{\varrho } \end{aligned}$$

where \(\varrho\) is the bulk density in \(\hbox {g/cm}^{3}\). This empirical formula (Eq. 1) is useful as a rough average estimation of the permittivity of the lunar subsurface; however, since it was determined by fitting the permittivity measurements of the Apollo samples under various conditions, it is less accurate at specific locations. In addition, because each material showed a different temperature dependence, it is difficult to estimate the permittivity of the lunar regolith at low temperatures based on Eq. 1. We calculate the permittivity based on Eq. 1 and the density of the samples used in the measurements.

While the permittivity at \(20\,^\circ \hbox {C}\) and \(-20\,^\circ \hbox {C}\) are both larger than the value coming from Eq. 1, the permittivity at \(-60\,^\circ \hbox {C}\) is lower (Fig. 1). This indicates that GPR analysis using Eq. 1. cannot consider the temperature dependence on the permittivity, which could lead to the wrong estimation of the subsurface structure and even of the existence of water–ice. Furthermore, it is unclear whether Eq. 1 can be applied to the analysis using GPRs because of the difference in frequency range, since the equation is acquired by fitting the data measured at a lower frequency (typically 10–450 MHz). Our results in the UHF–SHF band show that while the permittivity is slightly affected by the frequency, the variation is considerably larger in the case of ilmenite (Fig. 1), which is consistent with previous studies (e.g., Stillman and Olhoeft 2008). Overall, our results indicate that though the permittivity changes with temperature change, the variation ranges widely and should be treated carefully to consider the materials present at the radar-scanned location; which makes the subsurface structure and even water–ice existence estimations possible in future missions.

Table 1 Permittivity of the samples having 40% porosity at \(20\,^\circ \hbox {C}\)
Table 2 Permittivity of the samples having 40% porosity at \(-20\,^\circ \hbox {C}\)
Table 3 Permittivity of the samples having 40 % porosity at \(-60\,^\circ \hbox {C}\)


To appropriately evaluate GPR data from previous and future lunar missions, we need to take the variations in chemical composition, temperature conditions, and porosities of the lunar regolith into consideration. We evaluated these effects individually from laboratory measurements: first, we prepared lunar representative materials, based on chemical studies of the Apollo return samples, meteorite studies and remote-sensing observations. We determined the 4 end-member rocks and minerals for radar observations, such as anorthosite, basalt, dunite, and ilmenite. We developed a system to measure the permittivity of powdered samples in the 2–6 GHz frequency range with high precision (less than 1% relative error). We prepared powdered samples of the 4 identified end-members and measured their permittivity at different temperatures (\(20\,^\circ \hbox {C}\), \(-20\,^\circ \hbox {C}\), and \(-60\,^\circ \hbox {C}\)).

We found that the permittivity of lunar simulant materials has a complex dependency on several parameters. The content of ilmenite increases the bulk permittivity of the lunar regolith, which is also strongly dependent on temperature. The permittivity decreases at lower temperatures, typically of the geological samples by 6–18% between \(-60\,^\circ \hbox {C}\) and \(20\,^\circ \hbox {C}\). Previous works did not accurately consider the temperature dependent differences of permittivity when estimating the permittivity of the lunar subsurface, thus our results fill an important knowledge gap, while being consistent with former research (e.g., Yushkova and Kibardina , 2017). While they reported the temperature dependence of the permittivity of lunar simulants, our paper reported first on the difference between temperature dependence on each lunar simulant representing lunar regolith end-members. Thus, we should consider the effect on the permittivity carefully when discussing about the existence of water–ice with radar observations at the cold polar lunar regions.

While we reported that the permittivity of lunar materials depends on temperature, this is not true for water–ice (Fujita et al. 2000). This implies that by measuring lunar regolith permittivity at different temperatures (different local times), the water–ice content could be calculated from permittivity variations (Kobayashi et al., in prep). Thus we propose that using the results from our future new method the existence of even small amounts of water–ice could be detected by radar data collected at different temperatures.

Fig. 1
figure 1

Temperature dependence of the permittivity. a Anorthosite, b Basalt, c Dunite, and d Ilmenite. The circular points are the average of 10 points below and above each frequency (e.g., the average of the permittivity from 1.984–2.018  GHz in the case of 2 GHz). In the case of 6 GHz, it is averaged with the 10 points only below the frequency (i.e., the average of the permittivity from 5.966 to 6.000 GHz). The error bar shows the standard error. The colour shows the frequency (dark purple: 2 GHz, light blue: 3 GHz, green: 4 GHz, orange: 5 GHz, and dark red: 6 GHz), while the horizontal line shows the calculation result based on Eq. 1. in magenta, where appropriate. The calculation result is only shown in the case of the anorthosite and basalt, because Eq. 1 was derived from the Apollo sample and the dunite and ilmenite are minor components in the Apollo sample

Availability of data and materials

The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.



Ground-penetrating radar




Johnson Space Center


Ultra high frequency–super high frequency


Lunar Penetrating Radar


X-Ray fluorescence


Vector Network Analyzer


South Pole-Aitken


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We are grateful to Dr. Kazutaka Yasukawa for support on XRF measurements. This work is supported in part by the Ministry of Internal Affairs and Communications of Japanese Government Reiwa 4-0155-0099, by JAXA’s Feasibility Study 2022, by the University of Tokyo’s International Graduate Program for Excellence in Earth-Space Science (IGPEES), and the 164800 MÁEÖ bilateral scholarship of the Tempus Public Foundation.


This work is supported in part by the Ministry of Internal Affairs and Communications of Japanese Government Reiwa 4-0155-0099, by JAXA’s Feasibility Study 2022, by the University of Tokyo’s International Graduate Program for Excellence in Earth-Space Science (IGPEES), and the 164800 MÁEÖ bilateral scholarship of the Tempus Public Foundation.

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Authors and Affiliations



MK and HM conceived the idea of the study. MK and TN developed the measurement system. MK, TN, and TT contributed to the sample preparation. MK conducted the measurement. MK, HM, and BDP contributed to the interpretation of the results. MK, HM, and BDP drafted the original manuscript. HM supervised the conduct of this study. All authors read and approved the final manuscript.

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Correspondence to H. Miyamoto.

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Supplementary Information

Additional file 1: Figure S1.

Geological samples for our permittivity measurements. a) Anorthosite, b)Basalt, c) Dunite and d) Ilmenite

Additional file 2: Figure S2.

Experimental setup. a) The Vector Network Analyzer (VNA; 8753ES) used for our measurement. b) Appearance of our measurement system. The coaxial probe is set inside the deep freezer (up to -60 °C). To avoid the temperature change inside, the lid is closed during each measurement. c) Inside of the deep freezer. On the floor, a lab jack is set to touch the samples with probe. The coaxial probe is covered with an aluminium foil to prevent frost forming on the surface. d) Enlarged view of the sample and coaxial probe. To exclude the chemical and mineral heterogeneity on the surface of samples, the measurement was conducted by setting the probe to different places on the surface of the samples.

Additional file 3: Table S1.

Geological samples for our permittivity measurements. Anorthosite and dunite, which is aquiredas solid pieces, are crushed into microns’ size and sieved with 46 μm for stacking to the coaxial probe.The basalt has the mineral dependence on the particle size, so the sample having a broad particle sizeis used for the measurement. The grain density of ilmenite is referred from Holden [1921]. Table S2. Chemical composition of samples measured by XRF. The chemical composition of ilmenite isthe ideal one calculated based on the chemical formula. Table S3. Measured permittivity, standard error, and maximum relative error of air. Higher than 2 GHz,the maximum relative error is less than 1.0 %. Table S4. Measured permittivity, standard error, and maximum relative error of pure water comparedwith Barthel et al. (1991). Higher than 2.05 GHz, the maximum relative error is less than 1.0 %.

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Kobayashi, M., Miyamoto, H., Pál, B.D. et al. Laboratory measurements show temperature-dependent permittivity of lunar regolith simulants. Earth Planets Space 75, 8 (2023).

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