Effects of subsurface volume scattering on the lunar microwave brightness temperature spectrum

The effects of volume scattering on the lunar microwave brightness temperature spectrum are evaluated for a broad range of plausible scattering fragment populations. Mie-scattering phase functions and the radiative transfer method are utilized. Results indicate that emission darkening of ～1–7°K is to be expected over the wavelength range 3–30 cm, dependent on the total volume fraction of centimeter-sized and larger fragments. Spectral variations can occur if the size distribution of scatterers is nonuniform in a power law sense. For mare regions representative of the Surveyor III, V, and VI sites, an increase in brightness temperature with wavelength is predicted which is smaller than the predicted spectral variation due to planetary heat flow. The amplitude of lunation variation in brightness temperature is particularly sensitive to the fraction of fragments in the upper 10-cm diurnal layer. Deductions of electrical loss based on purely absorptive models can overestimate loss tangent values by a factor of 1.5 or more if scattering effects are not accounted for. The absence of anomalies exceeding ～2°K in lunar night-time γ3.55-cm brightness temperature maps requires a remarkable uniformity of the surface layer (upper 10 cm) scattering properties on a 250-km scale.     

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.     

Interpretation of the lunar microwave brightness temperature spectrum: Feasibility of orbital heat flow mapping

A detailed model of the lunar regolith is analyzed to examine the feasibility of an orbital mapping of heat flow using microwave radiometers. For regolith thermal and electrical properties which are representative of Apollo findings, brightness temperature observations in the bandλ = 5–30 cm would be required for heat flow analysis. Spectral variations shortward of 5 cm are controlled primarily by the temperature dependencies of the thermal conductivity and electrical absorption within the diurnal-varying layer. For wavelengths longer than 30 cm, unwanted emission from high impedance subregolith layers can be significant and size limitations on spacecraft radiometers is a factor. Over the 5- to 30-cm band, lunation-averaged brightness temperature increases of 2–10°K are predicted for heat flow values representative of the Apollo measurements. The magnitude of this increase depends directly on the value of regolith microwave absorption. For absorption values consistent with Apollo laboratory measurements, a spectral increase of 5°K is predicted. This value is considered marginally sufficient for an orbital heat flow measurement. However, important non-heat flow effects must be accounted for. Spectral variations can occur due to surface topography and subsurface scattering. For nadir viewing, surface roughness effects are not expected to be significant and topographic effects are nearly constant with wavelength for λ > 5cm. Volume scattering due to subsurface rock fragments can cause emission darkening of 1–6°K. However, spectral variations will not be large unless the distribution of scatterer sizes is sharply skewed. For the Moon, the most serious spurious effect appears to be emissivity variations due to the near-surface density gradient. A brightness temperature decrease of 10°K is predicted from centimeter to decameter wavelengths. If the transition from porous surface fines to compacted regolith soil occurs rapidly (within the upper 3–5 cm), most of the emissivity decrease will occur in the 5- to 30-cm wavelength band. It is recommended that complementary radar measurements be utilized to augment constraints on regolith emissivity and scattering properties.     

Broadband submillimeter measurements of the full Moon center brightness temperature and application to a lunar eclipse

We report on observations of the full Moon brightness temperature covering the frequency range of 300-950 GHz, and also on observations of the lunar eclipse of July 16, 2000, though only covering the frequency range of 165-365 GHz due to poor atmospheric transmission at higher frequencies. All observations were performed from the summit of Mauna Kea (HI) using a Fourier Transform Spectrometer mounted on the Caltech Submillimeter Observatory and supplemented by measurements of the atmospheric opacity using a 183 GHz Water Vapor Monitor. The telescope was pointed to the center of the lunar disk (with a footprint of ∼45-15 km on the Moon at 300 through 900 GHz). In order to obtain the correct values of the Moon brightness temperatures at all frequencies we carefully corrected for the atmospheric absorption, which varies across the submillimeter domain. This correction is fully described. The measured pre-eclipse brightness temperature is around 337 K in the 165-365 GHz range. This temperature slightly increases with frequency to reach ∼353 K at 950 GHz, according to previous broader band data. The magnitude of the temperature drop observed during the eclipse at 265 GHz (central frequency of the band covered) was about ∼70 K, in very good agreement with previous millimeter-wave measurements of other lunar eclipses. We detected, in addition, a clear frequency trend in the temperature drop that has been compared to a thermal and microwave emission model of the lunar regolith, with the result of a good match of the relative flux drop at different frequencies between model and measurements.     

Lunar Prospector measurements of secondary electron emission from lunar regolith

We present the first in situ measurements of the secondary electron emission efficiency of lunar regolith, utilizing Lunar Prospector measurements of secondary electrons emitted from the negatively charged night side and accelerated upward by surface electric fields. By comparing measurements of secondary currents emitted from the surface and incident primary electron currents, we find that the secondary yield of lunar regolith is a factor of ∼3 lower than that measured for samples in the laboratory. This lower yield significantly affects current balance at the lunar surface and the resulting equilibrium surface potentials. This information must be folded into models of the near-surface plasma sheath, in order to predict the effects on dust and other components of the lunar environment, and ultimately determine the importance for surface exploration and scientific investigations on the Moon.     

On the depth of the lunar regolith

The aim of this paper is to point out that if the sinuous rilles on the Moon represent trenches in the mare ground in which they meander, the existence of a great number of individual boulders on their slopes - as discovered on the high-resolution photographs taken by US Lunar Orbiters 4 and 5 in 1967 - suggests that the solid substrate of the lunar globe is covered by broken-up debris produced by cosmic abrasion - and hereafter referred to as lunar regolith - of thickness comparable with the depth of the respective rilles - at least of those lacking flat floors; which is generally in the order of 200–300 m. This depth is much greater than that indicated previously by other methods possessing more limited depth in range; and need not apply uniformly all over the Moon. In point of fact, marial regions abounding in sinuous rilles may represent loci where the lunar regolith has developed its maximum depth.     

Volatiles in lunar regolith samples: A survey

A summary is given of the literature data on the content of volatiles in the lunar regolith, the characterization of the likely sources of the volatiles, and the possible processes of their migration and burial. The main sources of volatiles in the regolith are the solar wind, small Solar System bodies (comets and meteorites), and the lunar interior. Different sources are the leading ones for different volatiles. Water and other volatiles can accumulate on the surface and in the near-surface layers of the Moon only in the so-called cold traps in polar basins, where other volatiles, as well as water ice, including highly toxic elements such as mercury and cadmium must be accumulated. The content of volatiles in the lunar interior is comparable to that in terrestrial rocks. Water could have played an important role in the early stages of the Moon’s history, e.g., in the formation of mare basalts. The isotopic composition of the lunar juvenile water is similar to that on the Earth, which suggests a common origin of the terrestrial and lunar water.     

Constraints on the depth and variability of the lunar regolith

Abstract— Knowledge of regolith depth structure is important for a variety of studies of the Moon and other bodies such as Mercury and asteroids. Lunar regolith depths have been estimated using morphological techniques (i.e., Quaide and Oberbeck 1968; Shoemaker and Morris 1969), crater counting techniques (Shoemaker et al. 1969), and seismic studies (i.e., Watkins and Kovach 1973; Cooper et al. 1974). These diverse methods provide good first order estimates of regolith depths across large distances (tens to hundreds of kilometers), but may not clearly elucidate the variability of regolith depth locally (100 m to km scale). In order to better constrain the regional average depth and local variability of the regolith, we investigate several techniques. First, we find that the apparent equilibrium diameter of a crater population increases with an increasing solar incidence angle, and this affects the inferred regolith depth by increasing the range of predicted depths (from ～7–15 m depth at 100 m equilibrium diameter to ～8–40 m at 300 m equilibrium diameter). Second, we examine the frequency and distribution of blocky craters in selected lunar mare areas and find a range of regolith depths (8–31 m) that compares favorably with results from the equilibrium diameter method (8–33 m) for areas of similar age (～2.5 billion years). Finally, we examine the utility of using Clementine optical maturity parameter images (Lucey et al. 2000) to determine regolith depth. The resolution of Clementine images (100 m/pixel) prohibits determination of absolute depths, but this method has the potential to give relative depths, and if higher resolution spectral data were available could yield absolute depths.     

Long-term variations in the microwave brightness temperature of the Uranus atmosphere

We present a self-consistent, 36-year record of the disk-averaged radio brightness of Uranus at wavelengths near 3.5 cm. It covers nearly half a uranian year, and includes both equatorial and polar viewing geometries (corresponding to equinox and solstice, respectively). We find large (greater than 30 K) changes over this time span. In agreement with analyses made of more limited microwave data sets, our observations suggest the changes are not caused by geometric effects alone, and that temporal variations may exist in the deep uranian troposphere down to pressures of tens of bars. Our data also support an earlier suggestion that a rapid, planetary-scale change may have occurred in late 1993 and early 1994. The seasonal record presented here will be useful for constraining dynamical models of the deep atmosphere, and for interpreting observations made during Uranus' 2007 equinox passage. As part of a multi-wavelength observing campaign for this event, the Goldstone-Apple Valley Radio Telescope (GAVRT) project will continue to make frequent, single-dish observations near 3.5 cm.     

Model for radon diffusion through the lunar regolith

A model for radon diffusion through the lunar regolith is proposed in which the atom migrates by random walk. The regolith is represented by a system of randomly oriented baffles in which the mean distanced which the atom travels between two collisions takes on the role of a mean free path. The effective mean time between two collisions depends on two entities: the actual mean time-of-flight and the mean sticking time on grain surfaces for one collision. The latter depends strongly on the temperature and the heat of adsorption of radon on regolith materials. Bothd (mean free path) as well asQ (heat of adsorption) are either poorly known or unknown for the lunar regolith; hence these quantities are treated as free parameters. Because of the greatly different mean lifetimes against radioactive decay of²¹⁹Rn,²²⁰Rn, and²²²Rn, the regolith acts as a powerful filter for these species.²²²Rn escape is significant (32%) even ford = 1µ,Q = 7.0 kcal/mole and a regolith depth of 4 m. Calculations of radon escape from a 4 m thick regolith, usingd = 1, 10 and 80µ andQ = 4.0, 5.2 and 7.0 kcal/mole show that the²²²Rn/²²⁰Rn escape ratio can be as small as 7.7 and as large as, or larger than 47. The small value of 7.7 is of particular interest, because it is nearly equal to the escape ratio inferred by Turkevichet al. from their Surveyor 5 results.     

Ultraviolet ion chamber measurements of the solar minimum brightness temperature

The solar ultraviolet flux in the wavelength bands 1580–1640 Å and 1430–1470 Å (FWHM) has been measured using photon ion chambers carried on the satellite WRESAT I (1967-118A). These observations of the integrated ultraviolet flux from the entire disk indicate a value of (4570 ± 50) K for the solar temperature minimum. The results are compared with other estimates of the minimum value of the solar brightness temperature.Died August, 1971.     

Echo simulation of lunar penetrating radar: based on a model of inhomogeneous multilayer lunar regolith structure

Lunar Penetrating Radar(LPR) based on the time domain Ultra-Wideband(UWB) technique onboard China's Chang'e-3(CE-3) rover, has the goal of investigating the lunar subsurface structure and detecting the depth of lunar regolith. An inhomogeneous multi-layer microwave transfer inverse-model is established. The dielectric constant of the lunar regolith, the velocity of propagation, the reflection, refraction and transmission at interfaces, and the resolution are discussed. The model is further used to numerically simulate and analyze temporal variations in the echo obtained from the LPR attached on CE-3's rover, to reveal the location and structure of lunar regolith. The thickness of the lunar regolith is calculated by a comparison between the simulated radar B-scan images based on the model and the detected result taken from the CE-3 lunar mission. The potential scientific return from LPR echoes taken from the landing region is also discussed.     

Identification of magnetite in lunar regolith breccia 60016: Evidence for oxidized conditions at the lunar surface

Lunar regolith breccias are temporal archives of magmatic and impact bombardment processes on the Moon. Apollo 16 sample 60016 is an “ancient” feldspathic regolith breccia that was converted from a soil to a rock at ~3.8 Ga. The breccia contains a small (70 × 50 μm) rock fragment composed dominantly of an Fe‐oxide phase with disseminated domains of troilite. Fragments of plagioclase (An_95‐97), pyroxene (En_74‐75, Fs_21‐22,Wo_3‐4), and olivine (Fo_66‐67) are distributed in and adjacent to the Fe‐oxide. The silicate minerals have lunar compositions that are similar to anorthosites. Mineral chemistry, synchrotron X‐ray absorption near edge spectroscopy (XANES) and X‐ray diffraction (XRD) studies demonstrate that the oxide phase is magnetite with an estimated Fe³⁺/ΣFe ratio of ~0.45. The presence of magnetite in 60016 indicates that oxygen fugacity during formation was equilibrated at, or above, the Fe‐magnetite or wüstite–magnetite oxygen buffer. This discovery provides direct evidence for oxidized conditions on the Moon. Thermodynamic modeling shows that magnetite could have been formed from oxidization‐driven mineral replacement of Fe‐metal or desulphurisation from Fe‐sulfides (troilite) at low temperatures (<570 °C) in equilibrium with H₂O steam/liquid or CO₂ gas. Oxidizing conditions may have arisen from vapor transport during degassing of a magmatic source region, or from a hybrid endogenic–exogenic process when gases were released during an impacting asteroid or comet impact.     

Multidimensional radiative transfer: Applications to planetary coronae

A numerical solution to the integral equation for radiative transfer by resonance reradiation in an isothermal spherical atmosphere is described. The method presented is 100 times more efficient than earlier spherical radiative transfer models. The new model can accommodate density variations in the full three dimensional space and includes effects due to the presence of pure absorbers. Complete frequency redistribution is assumed for photon scattering. Applications of this model to the problem of solar photons scattered by atomic hydrogen in the atmospheres of Venus, Earth and Mars are described, and limb and disk profiles, as well as equivalent mean disk intensities for Venus, Earth and Mars, are presented.     

Laboratory studies into the effect of regolith on planetary X-ray fluorescence spectroscopy

In the analysis of X-ray fluorescence spectra from planetary surfaces, it is traditionally assumed that the observed surface is a plane-parallel, smooth, and homogeneous medium. The spectral and spatial resolutions of the instruments that have been used to measure X-ray emission from planetary surfaces to date have been such that this has been a reasonable assumption, but a new generation of X-ray spectrometers will provide enhanced spectral and spatial resolutions when compared with previous instrumentation. In light of these improvements in performance, it is important to assess how the requirements on the methodology of analysis of spectra may change when the surface is considered as a regolith. At other wavelengths, varying physical properties of planetary regoliths, such as the packing density, are known to have an effect on the observed signal as a function of viewing geometry. In this paper, the results from laboratory X-ray fluorescence measurements of regolith analogue materials at different viewing geometries are presented. Characteristic properties of the regolith such as particle sizes and packing density are found to affect the measured elemental line ratios. A semiempirical function is introduced as a tool for fitting fluorescent line intensity dependences as a function of viewing geometry. The importance of the results is discussed and recommendations are made for the future analysis of planetary X-ray fluorescence data.     

Lunar microwave brightness temperature observations reevaluated in the light of Apollo program findings

Remote observations of the lunar radiowave emission are reexamined in the light of physical property data accumulated through the Apollo program. It is found that thermal and electrical properties determined for a number of different landing sites yield theoretical results in good agreement with remote observations for millimeter and short centimeter wavelengths. Theoretical models incorporating reflecting layers of rock and physical property data from the Apollo program are compared to the longer wavelength (5–500 cm) observational data to estimate a disk average steady state heat flow and a mean depth of the lunar regolith. It is found that a high heat flow, comparable to the heat flows measured at the Apollo 15 and 17 sites, is required to fit the available 5–20 cm wavelength remote data, and that a lunar surface layer relatively free of large boulders within the upper 10–30 m best fits the observations of a decreasing brightness temperature with wavelength for wavelengths greater than ～ 50 cm.     

On estimating contributions of basin ejecta to regolith deposits at lunar sites

Abstract— We have developed a quantitative model for predicting characteristics of ejecta deposits that result from basin‐sized cratering events. This model is based on impact crater scaling equations (Housen, Schmitt, and Holsapple 1983; Holsapple 1993) and the concept of ballistic sedimentation (Oberbeck 1975), and takes into account the size distribution of the individual fragments ejected from the primary crater. Using the model, we can estimate, for an area centered at the chosen location of interest, the average distribution of thicknesses of basin ejecta deposits within the area and the fraction of primary ejecta contained within the deposits. Model estimates of ejecta deposit thicknesses are calibrated using those of the Orientale Basin (Moore, Hodges, and Scott 1974) and of the Ries Basin (Hörz, Ostertag, and Rainey 1983). Observed densities of secondary craters surrounding the Imbrium and Orientale Basins are much lower than the modeled densities. Similarly, crater counts for part of the northern half of the Copernicus secondary cratering field are much lower than the model predicts, and variation in crater densities with distance from Copernicus is less than expected. These results suggest that mutual obliteration erases essentially all secondary craters associated with the debris surge that arises from the impacting primary fragments during ballistic sedimentation; if so, a process other than ballistic sedimentation is needed to produce observable secondary craters. Regardless, our ejecta deposit model can be useful for suggesting provenances of sampled lunar materials, providing information complementary to photogeological and remote sensing interpretations, and as a tool for planning rover traverses (e.g., Haskin et al. 1995, 2002).     

A Monte Carlo model for the gardening of the lunar regolith

The processes of movement and turnover of the lunar regolith are described by a Monte Carlo model, which includes the effects of collisions by particles from 10^?7 g to 10¹⁰ g. The movement of material by the direct cratering process is the dominant mode, but slumping is also included for angles exceeding the static angle of repose. Using a group of interrelated computer programs a large number of properties are calculated, including topography, formation of layers, depth of the disturbed layer, nuclear track distributions, cosmogenic nuclides and others. In the most complex program, the history of a 36 point square array is followed for times up to 4 × 10⁸ yr. As expected the histories generated are complex and exhibit great variety. Because a crater covers much less area than its ejecta blanket, there is a tendency for the height change at a test point to exhibit the ‘gambler's ruin’ phenomenon: periods of slow accumulation followed by sudden excavation. In general the agreement with experiment and observation seems good. Two areas of disagreement stand out. First, the calculated surface is rougher than that observed. This problem is understood, and will not occur in a newer version of the model. Second, the observed bombardment ages, of the order of 4 × 10⁸ yr, are shorter than expected (by perhaps a factor of 5). We cannot accept Fireman's (1974) explanation; this remains an important puzzle.