Multispectral polarimetry as a tool to investigate texture and chemistry of lunar regolith particles

We report results of telescope polarimetric imaging of the Moon with a CCD LineScan Camera at large phase angles, near 88°. This allows measurements of the polarization degree with an absolute accuracy better than 0.3% and detection of features with polarization contrast as small as 0.1%. The measurements are carried out in two spectral bands centered near 0.65 and 0.42 μm. We suggest characterizing the lunar regolith with the parameter a(Pmax)A, where Pmax,A, and a are the degree of maximum polarization, albedo, and the parameter describing the linear regression of the correlation Pmax-A. The parameter bears significant information on the particle characteristic size and packing density of the lunar regolith. We also suggest characterizing the lunar regolith with color-ratio images obtained with a polarization filter at large phase angles. We here consider the color-ratios C||(0.65/0.42 μm) and C_⊥(0.65/0.42 μm). Using light scattering model calculations we show that the color-ratio images obtained with a polarization filter at large phase angles suggest a new tool to study the lunar surface. In particular, it turns out that the color-ratios C||(0.65/0.42 μm) and C_⊥(0.65/0.42 μm) are sensitive to somewhat different thicknesses of the surfaces of regolith particles. We consider the applicability of the Hubble Space Telescope, the Very Large Telescope (ESO), and a spacecraft on a lunar polar orbit for polarimetric observations of the lunar surface.     

Mercury's albedo from Mariner 10: Implications for the presence of ferrous iron

Mariner 10 clear filter (490 nm) images of Mercury were recalibrated and photometrically normalized to produce a mosaic of nearly an entire hemisphere of the planet. Albedo contrasts are slightly larger than seen in the lunar highlands (excluding maria). Variegations indicative of compositional differences include diffuse low albedo units often overlain by smooth plains, the high albedo smooth plains of Borealis Planitia, and high-albedo enigmatic crater floor deposits. A higher level of contrast between immature crater ejecta and average mature material on Mercury compared to the Moon is consistent with a more intense space weathering environment on Mercury that results in a more mature regolith. Immature lunar highlands materials are ∼1.5 times higher in reflectance than analogous immature mercurian materials. Immature materials of the same composition would have the same reflectance on both bodies, thus this observation requires that Mercury's crust contains a significant darkening agent, either opaque minerals or ferrous iron bearing silicates, in abundances significantly higher than those of the lunar highlands. If the darkening agent is opaque minerals (e.g. ilmenite or ulvospinel) Mercury's crust may contain significant ferrous iron and yet not exhibit a 1-μm absorption band.     

Properties of the Hermean regolith: IV. Photometric parameters of Mercury and the Moon contrasted with Hapke modelling

A comparison of the photometric properties of Mercury and the Moon is performed, based on their integral phase curves and disk-resolved image data of Mercury obtained with the Swedish Vacuum Solar Telescope. Proper absolute calibration of integral V-band magnitude observations reveals that the near-side of the Moon is 10-15% brighter than average Mercury, and 0-5% brighter for the “bolometric” wavelength range 400-1000 nm. As shown, this is supported by recent estimates of their geometric albedos. Hapke photometric parameters of their surfaces are derived from identical approaches, allowing a contrasting study between their surface properties to be performed. Compared to the average near-side Moon, Mercury has a slightly lower single-scattering albedo, an opposition surge with smaller width and of marginally smaller amplitude, and a somewhat smoother surface with similar porosity. The width of the lobes of the single-particle scattering function are smaller for Mercury, and the backward scattering anisotropy is stronger. In terms of the double Henyey-Greenstein b-c parameter plot, the scattering properties of an average particle on Mercury is closer to the properties of lunar maria than highlands, indicating a higher density of internal scatterers than that of lunar particles. The photometric roughness of Mercury is well constrained by the recent study of Mallama et al. (2002, Icarus 155, 253-264) to a value of about 8°, suggesting that the surfaces sampled by the highest phase angle observations (Borealis, Susei, and Sobkou Planitia) are lunar mare-like in their textural properties. However, Mariner 10 disk brightness profiles obtained at intermediate phase angles indicate a surface roughness of about twice this value. The photometric parameters of the Moon are more difficult to constrain due to limited phase angle coverage, but the best Hapke fits are provided by rather small surface roughnesses. Better-calibrated, multiple-wavelength observations of the integral and disk-resolved brightnesses of both bodies, and obtained at higher phase angle values in the case of the Moon, are urgently needed to arrive at a more consistent picture of the contrasting light scattering properties of their surfaces.     

On the original igneous source of Martian fines

The composition of the silicate portion of Martian regolith fines indicates derivation of the fines from mafic to ultramafic igneous rocks, probably rich in pyroxene. Rock types similar in chemical and mineralogical composition include terrestrial Archean basalts and certain achondrite meteorites. If these igneous rocks weathered nearly isochemically, the nontronitic clays proposed earlier as an analog to Martian fines could be formed. Flood basalts of pyroxenitic lavas may be widespread and characteristic of early volcanism on Mars, analogous to maria flood basalts on the Moon and early Precambrian basaltic komatiites on Earth. Compositional differences between lunar, terrestrial, and Martian flood basalts may be related to differences in planetary sizes and mantle compositions of the respective planetary objects.     

Volatile emission on the moon; Possible sources and release mechanisms

Evidence for very recent emission of volatiles on the Moon is primarily of four types: (1) transient lunar optical events observed by Earth-based astronomers; (2) excursions on Apollo SIDE and mass spectrometer instruments; (3) localized Rn²²²/Po²¹⁰ enhancements on the lunar surface detected by Apollo 15 and 16 orbital alpha spectrometers; (4) presence in lunar fines of retrapped Ar⁴⁰ and other volatiles. Available evidence indicates that the release rate of volatile substances into the lunar atmosphere is not steady, but instead sporadic and episodic. Rn²²²/Po²¹⁰ anomalies are at locations that are among those from which transient events have most often been reported (edges of maria, certain specific craters), and are probably related to them. Volatiles emitted at maria rims may originate in the Moon's fluid core, reaching the surface through deep cylindrical fault systems that ring the maria borders. The sources of volatiles emitted at craters such as Aristarchus or Tsiolkovsky, which possess floors which are cracked or filled with dark lava and possess central peaks, are more likely to be local pockets of magma or trapped gas at shallower depths. The volatiles are produced directly by radioactive decay (He⁴, Ar⁴⁰, Rn) and by heating (other volatiles). The release by heating can occur either during melting or by ‘bakeout’ of unmelted materials. Release of gas into the lunar atmosphere is probably triggered by buildup of its own pressure. This may be assisted by tidal forces exerted on the Moon by the Earth. In addition to independent release, volatile emission is also expected to accompany other lunar activity, such as ash flows, if any lunar volcanism is presently active.

     

The Structure of the Surface of Mercury's Regolith from Remote Sensing Data

Long experience of ground-based and cosmic studies of the Moon has shown that space-weathering processes play a key role in the formation of the surface layers of atmosphereless bodies. Undoubtedly, the surface of Mercury, which is subjected to the same processes, is covered by a mantle of shattered rocks—the regolith. The structure of the reflecting layer determines the photometric and polarization characteristics of the surface of a planetary body. Despite the general similarity of the integral optical properties of the surfaces of Mercury and the Moon, specific characteristics of the media of these celestial bodies manifest themselves as certain differences in the details of the measured parameters. Moreover, the similarity to the Moon permits in-depth interpretation of the results of remote observations of Mercury, such as integral polarimetry and integral spectropolarimetry. The data obtained suggest that the general structure of the surface layer of the Mercurian regolith is very similar to the structure of the lunar soil, although it is somewhat smoother and probably has a greater amount of the fine-grained fraction. The soil maturity matches the content of about 80% of the secondary particles. At the same time, the exposure age of the soil, which has the same degree of maturity, is less than the age of the soil formed under lunar conditions.     

Vitrification darkening of rock powders: implications for optical properties of the lunar surface

Laboratory experiments show that albedoes as low as those on the Moon can be produced by vacuum vitrification and associated chemical fractionation of ordinary terrestrial basaltic material. Vitrification is established as an unequivocal process that can account for the low albedo and apparent local darkening with age of the lunar surface. The spectral reflectance curves of glass powders are significantly different than those of the parent rock mineralogy; thus, the presence of ubiquitous glass in lunar surface material complicates compositional determinations by interpretation of spectral reflectance curves. Vitrification of rocks on the Moon may highly modify the chemical composition of the resulting glass; thus, glass fragments found in lunar fines cannot be assumed to represent bulk parent rock material. Progressive impact vitrification of lunar surface material throughout the Moon's history may have led to a fine-grain, opaque, refractory-rich material we call ultimate glass. This unidentified and, at this point, hypothetical component may exist in dark regolith material; if found, it may be a useful indicator of regolith maturity.Paper dedicated to Prof. Harold C. Urey on the occasion of his 80th birthday on 29 April 1973.     

Whole-disk spectrophotometric properties of Mercury: Synthesis of MESSENGER and ground-based observations

Disk-integrated and disk-resolved measurements of Mercury’s surface obtained by both the Mercury Dual Imaging System (MDIS) and the Mercury Atmospheric and Surface Composition Spectrometer (MASCS) onboard the MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) spacecraft were analyzed and compared with previous ground-based observations of Mercury at 11 wavelengths. The spectra show no definitive absorption features and display a red spectral slope (increasing reflectance with increasing wavelength) typical of space-weathered rocky surfaces. The MDIS spectra show evidence of phase reddening, which is not observed in the MASCS spectra. The MDIS spectra are commensurate with ground-based observations to within 10%, whereas the MASCS spectra display greater discrepancies with ground-based observations at near-infrared wavelengths. The derived photometric calibrations provide corrections within 10% for observations taken at phase angles less than ∼100°. The derived photometric properties are indicative of a more compact regolith than that of the lunar surface or of average S-type asteroids. The photometric roughness of the surface is also much smoother than the Moon’s. The calculated geometric albedo (reflectance at zero phase) is higher than lunar values. The lower reflectance of immature units on Mercury compared with immature units on the Moon, in conjunction with the higher geometric albedo, is indicative of more complicated grain structures within Mercury’s regolith.     

The negative polarization parameters of the light scattered by the lunar surface: Mapping

The images of the southwestern part of the lunar disk showing the distributions of the negative polarization parameters of the light scattered by the lunar surface are presented. The distributions of the negative polarization minimum P _min, the inversion angle α_inv, and the polarization slope at the inversion point h significantly differ from the albedo image. This testifies to the fact that polarimetry yields independent information on the structure and optical properties of the lunar regolith.     

An analysis of the Mariner 10 color ratio map of mercury

The results of a geological analysis of the Mariner 10 orange/UV color ratio man of Mercury (B. Hapke, C. Christman, B. Rava, and J. Mosher, Proc. Lunar Planet Sci. Conf. 11th 1980, pp. 817–822) are given. Certain errors that occured in reproducing the published version of the 1980 map are pointed out. The relationships between color and terrain are distinctly nonlunar. There is no correlation between color boundaries and the smooth plains on Mercury, in contrast to the strong correlation between color and maria-highlands contacts on the Moon. There are no large exposures of low-albedo, blue material that could be considered to be Mercurian analogs of high-FeTi lunar maria basalts on any part of Mercury imaged by Mariner 10. Three lines of evidence imply that the crust is low in Fe²⁺ and Ti⁴⁺: rays and ejecta blankets are bluer than most areas on Mercury; the Fe²⁺ band in Mercury's reflectance spectrum is very weak or nonexistent and the albedo contrasts are smaller than those on the Moon. There is no evidence in the spectral or albedo data that a lunar type of second wave of melting ever occured on Mercury; rather, the observations are most consistent with the hypothesis that the smooth plains are extrusive landforms derived from local material, possibly mobilized by the Caloris event. In several places correlations between color and topography can be explained if older, redder, higher-Fe materials underlie younger, bluer, lower-Fe surfaces. There is some evidence of late Fe-rich pyroclastic-like activity.     

Crater size-shape profiles for the moon and mercury: Terrain effects and interplanetary comparisons

New crater size-shape data were compiled for 221 fresh lunar craters and 152 youthful mercurian craters. Terraces and central peaks develop initially in fresh craters on the Moon in the 0–10 km diameter interval. Above a diameter of 65 km all craters are terraced and have central peaks. Swirl floor texture is most common in craters in the size range 20–30 km, but it occurs less frequently as terraces become a dominant feature of crater interiors. For the Moon there is a correlation between crater shape and geomorphic terrain type. For example, craters on the maria are more complex in terms of central peak and terrace detail at any given crater diameter than are craters in the highlands. These crater data suggest that there are significant differences in substrate and/or target properties between maria and highlands. Size-shape profiles for Mercury show that central peak and terrace onset is in the 10–20 km diameter interval; all craters are terraced at 65 km, and all have central peaks at 45 km. The crater data for Mercury show no clear cut terrain correlation. Comparison of lunar and mercurian data indicates that both central peaks and terraces are more abundant in craters in the diameter range 5–75 km on Mercury. Differences in crater shape between Mercury and the Moon may be due to differences in planetary gravitational acceleration (gMercury=2.3gMoon). Also differences between Mercury and the Moon in target and substrate and in modal impact velocity may contribute to affect crater shape.     

Seismic effects from major basin formations on the moon and mercury

Grooved and hilly terrains occur at the antipode of major basins on the Moon (Imbrium, Orientale) and Mercury (Caloris). Such terrains may represent extensive landslides and surface disruption produced by impact-generatedP-waves and antipodal convergence of surface waves. Order-of-magnitude calculations for an Imbrium-size impact (10³⁴ erg) on the Moon indicateP-wave-induced surface displacements of 10 m at the basin antipode that would arrive prior to secondary ejecta. Comparable surface waves would arrive subsequent to secondary ejecta impacts beyond 10³ km and would increase in magnitude as they converge at the antipode. Other seismically induced surface features include: subdued, furrowed crater walls produced by landslides and concomitant secondary impacts; emplacement and leveling of light plains units owing to seismically induced ‘fluidization’ of slide material; knobby, pitted terrain around old basins from enhancement of seismic waves in ancient ejecta blankets; and perhaps the production and enhancement of deep-seated fractures that led to the concentration of farside lunar maria in the Apollo-Ingenii region.     

Apollo 12 Lunar Module exhaust plume impingement on Lunar Surveyor III

Understanding plume impingement by retrorockets on the surface of the Moon is paramount for safe lunar outpost design in NASA’s planned return to the Moon for the Constellation Program. Visual inspection, Scanning Electron Microscopy, and surface scanned topology have been used to investigate the damage to the Lunar Surveyor III spacecraft that was caused by the Apollo 12 Lunar Module’s close proximity landing. Two parts of the Surveyor III craft returned by the Apollo 12 astronauts, Coupons 2050 and 2051, which faced the Apollo 12 landing site, show that a fine layer of lunar regolith coated the materials and was subsequently removed by the Apollo 12 Lunar Module landing rocket. The coupons were also pitted by the impact of larger soil particles with an average of 103 pits/cm². The average entry size of the pits was 83.7 μm (major diameter) × 74.5 μm (minor diameter) and the average estimated penetration depth was 88.4 μm. Pitting in the surface of the coupons correlates to removal of lunar fines and is likely a signature of lunar material imparting localized momentum/energy sufficient to cause cracking of the paint. Comparison with the lunar soil particle size distribution and the optical density of blowing soil during lunar landings indicates that the Surveyor III spacecraft was not exposed to the direct spray of the landing Lunar Module, but instead experienced only the fringes of the spray of soil. Had Surveyor III been exposed to the direct spray, the damage would have been orders of magnitude higher.     

Polarimetric mapping of the Moon at a phase angle near the polarization minimum

At small phase angles the light scattered by the Moon reveals a negative polarization branch whose average amplitude is 1%. We present results of polarimetric mappings of the Moon in Pmin at a phase angle near 11°. The observations were carried out with the Kharkov 50-cm telescope at the Maidanak Observatory (Middle Asia) using a polarizing filter. A thorough calibration of the camera array allows for the reliable detection of significant variations of |Pmin| over the lunar surface, from 0.2 to 1.6%, at a wavelength of 0.52 μm. The smallest |Pmin| are characteristic of young bright craters, while the |Pmin| are the highest for the lunar highland and bright mare areas. The horse-shoe shape of the correlation dependence Pmin (albedo) is treated with data of our laboratory measurements of powdered surfaces and computer modeling of light scattering by small particles with the DDA (discrete dipole approximation) technique.     

The diameter and thermal inertia of 433 Eros

Radiometry of Eros at 10 and 20 μm demonstrates that the thermal conductivity of the upper centimeter of the surface is approximately as low as that of the Moon, suggesting that the asteroid has a regolith of highly porous rocky material. When combined with photoelectric photometry, these infrared measurements yield an effective diameter of Eros at maximum light of D₀ = 22 ± 2 km and a geometric albedo of p_v = 0.18 ± 0.03.     

Optical measurements of the Moon as a tool to study its surface

This survey is a general overview of modern optical studies of the Moon and their diagnostic meaning. It includes three united parts: phase photometry, spectrophotometry, and polarimetry. The first one is devoted to the progress in the photometry of the Moon, which includes absolute albedo determination to refine the albedo scale (e.g., to connect lunar observations and the data of lunar sample measurements) and mapping the parameters of a lunar photometric function (e.g., the phase-angle ratios method) with the aim of making qualitative estimates of regolith structure variations. This part also includes observations of the lunar opposition effect as well as photogrammetry and photoclinometry techniques. In particular, available data show that because of the low albedo of the lunar surface, the coherent backscattering enhancement hardly influences the lunar opposition spike, with the exception of the brightest lunar areas measured in the NIR. The second part is devoted to chemical/mineral mapping of the Moon's surface using spectrophotometric measurements. This section also includes analyses related to the detection of water ice or hydroxyl, prognoses of maturity, and helium-3 abundance mapping. In particular, we examine the relationship between superficial OH/H₂O compounds spectrally detected recently and bulk “water ice” found earlier by the Lunar Prospector GRS and LRO LEND, assuming that the compounds are delivered to cold traps (permanently shadowed regions) with electrostatically levitated dust saturated by solar wind hydrogen. Significant problems arise with the determination of TiO₂ content, as the correlation between this parameter and the color ratio C(750/415 nm) is very non-linear and not universal for different composition types of the lunar surface; a promising way to resolve this problem is to use color ratios in the UV spectral range. The third part is devoted to mapping of polarization parameters of the lunar surface, which enable estimates of the average size of regolith particles and their optical inhomogeneity. This includes considerations of the Umov effect and results of spectropolarimetry, negative polarization imagery, and measurements of other polarimetric parameters, including the third Stokes parameter. Although these three research divisions have not been developed equally and the numbers of proper references are very different, we try to keep a balance between them, depicting a uniform picture. It should be emphasized that many results presented in this review can be applied to other atmosphereless celestial bodies as well.     

Regolith thickness over the lunar nearside: Results from Earth-based 70-cm Arecibo radar observations

The inversion of regolith thickness over the nearside hemisphere of the Moon from newly acquired Earth-based 70-cm Arecibo radar data is investigated using a quantitative radar scattering model. The radar scattering model takes into account scattering from both the lunar surface and buried rocks in the lunar regolith, and three parameters are critically important in predicting the radar backscattering coefficient: the dielectric constant of the lunar regolith, the surface roughness, and the size and abundance of subsurface rocks. The measured dielectric properties of the Apollo regolith samples at 450 MHz are re-analyzed, and an improved relation among the complex dielectric constant, bulk density and regolith composition is obtained. The complex dielectric constant of the lunar regolith is estimated globally from this relation using the regolith composition derived from Lunar Prospector gamma-ray spectrometer data. To constrain the lunar surface roughness and abundance of subsurface rocks from radar data, nine regions are selected as calibration sites where the regolith thickness has been estimated using independent analysis techniques. For these sites, scattering from the lunar surface and buried rocks cannot be perfectly distinguished, and a tradeoff relationship exists between the size and abundance of buried rocks and surface roughness. Using these tradeoff relations as guidelines for globally representative parameters, the regolith thickness of four regions over the lunar nearside is inverted, and the inversion uncertainties caused by calibration errors of the radar data and model input parameters are analyzed. The regolith thickness of the maria is generally smaller than that of highlands, and older surfaces have thicker regolith thicknesses. Our approach cannot be applied to regions where the surface roughness is very high, such as with young rocky craters and regions in the highly rugged highlands.     

The great-circle pattern of large circular maria: product of an earth-moon encounter

The circular maria - Orientale, Imbrium, Serenitatis, Crisium, Smythii, and Tsiolkovsky -lie nearly on a lunar great circle. This pattern can be considered the result of a very close, non-capture encounter between Moon and Earth early in solar-system history. Of critical importance in analyzing the effects of such an encounter is the position of the weightlessness limit of the Earth-Moon System which is located at about 1.63R _e, measured from the center of Earth to center of Moon. Within this weightlessness limit, material can be pulled from the lunar surface and interior by Earth's gravity and either escape from the Moon or be redistributed onto the lunar surface. In the case of an encounter with a non-spinning Moon, backfalling materials would be distributed along a lunar great circle. However, if the Moon is rotating during the encounter, the backfall pattern will deviate from the great circle, the amount depending on the rate and direction of spin. Such a close encounter model may be related to the pattern of circular maria if materials departing from the source region are visualized as spheroids of molten lunar upper mantle basalt. These spheroids, then, would impact onto the lunar surface to form a pattern of lava lakes. Radiometric dates from mare rocks are consistent with this model of mare formation if the older mare rock dates are considered to date the encounter and younger dates are considered to date subsequent volcanic eruptions on a structurally weakened Moon.     

A primary analysis of microwave brightness temperature of lunar surface from Chang-E 1 multi-channel radiometer observation and inversion of regolith layer thickness

In China’s first lunar exploration project, Chang-E 1 (CE-1), a multi-channel microwave radiometer was aboard the satellite, with the purpose of measuring microwave brightness temperature (Tb) from lunar surface and surveying the global distribution of lunar regolith layer thickness. In this paper, the primary 621 tracks of swath data measured by CE-1 microwave radiometer from November 2007 to February 2008 are collected and analyzed. Using the nearest neighbor interpolation to collect the Tb data under the same Sun illumination, global distributions of microwave brightness temperature from lunar surface at lunar daytime and nighttime are constructed. Based on the three-layer media modeling (the top dust-soil, regolith and underlying rock media) for microwave thermal emission of lunar surface, the CE-1 measured Tb and its dependence upon latitude, frequency and FeO + TiO₂ content, etc. are discussed. The CE-1 Tb data at Apollo landing sites are especially chosen for validation and calibration on the basis of available ground measurements. Using the empirical dependence of physical temperature upon the latitude verified by the CE-1 multi-channel Tb data at Apollo landing sites, the global distribution of regolith layer thickness is further inverted from the CE-1 brightness temperature data at 3 GHz channel. Those inversions at Apollo landing sites and the characteristics of regolith layer thickness for lunar maria are well compared with the Apollo in situ measurements and the regolith thickness derived from the Earth-based radar data. Finally, the statistical distribution of regolith thickness is analyzed and discussed.     

Vertical-structure effects on planetary microwave brightness temperature measurements: Applications to the lunar regolith

The effects of vertical variations in density and dielectric constant on nadir-viewing microwave brightness temperatures are examined. Stratification models as well as models of a continuous increase in density with depth are analyzed. Specific applications address the vertical structure of the lunar frontside regolith, utilizing combined constraints from Apollo data, bistatic radar signatures, and Earth-based measurements of the lunar microwave brightness temperature.Results have been analyzed in terms of the effects on the zeroth and first harmonic of the lunar disk-center brightness temperature variation over a lunation, and their wavelength dependence. Lunation-mean brightness temperatures, which are diagnostic of emissivity and steady-state sub-surface temperatures, are sensitive to both near-surface soil density gradients and single high-impedance dielectric contrasts. Models of the rapid density increase in the upper 5–10 cm of the lunar regolith predict brightness temperature decreases of 2–10°K between λ₀ = 3 and 30 cm. The magnitude of this spectral variation depends upon the thickness of a postulated low-density surface coating layer, and the magnitude of the density gradient in the transition soil layer. Comparable decreases in brightness temperature can be produced by a stratified two-layer model of soil overlaying bedrock if the high-density substrate lies within 1–2 m of the surface. Multiple soil layering on a centimeter scale, such as is observed in the Apollo core samples, is not likely to induce spectral variations in mean brightness temperature due to rapid regional variations in layer depths and thicknesses.The fractional variation in disk-center brightness temperature over a lunation (first harmonic) can be altered by vertical-structure effects only for the case in which a larger and abrupt dielectric contrast exists within the upper surface layer where the significant diurnal variations in physical temperature occur. Soil density variations do not cause scattering effects sufficient to significantly alter the microwave emission weighting function within the diurnal layer. For the Moon, this layer consists of the upper 10 cm. Since no widespread rock substrate as shallow as 10 cm exists in the lunar frontside, only volume scattering effects, due to buried shallow rock fragments, can explain the apparent high electrical loss inferred from Earth-based measurements of the amplitude of lunation brightness temperature variations.Representative models of the lunar frontside vertical structure have also been examined for their effects of radar cross-section measurements and resultant inferences of bulk dielectric constant. Models of the near-surface density gradient predict a significant increase in the remotely inferred dielectric constant value from centimeter to meter wavelengths. Such a model is in general agreement with the dielectric constant spectrum inferred from Earth-based brightness temperature polarization measurements, but is difficult to reconcile with the Apollo bistatic radar results at λ₀ = 13 and 116 cm.