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.     

Electrophysical Model of the Moon’s Soil

Solar System Research - Based on the analysis of the data available in the literature on laboratory measurements of the dielectric characteristics of the lunar soil samples delivered to the Earth...     

A Study of the Lunar Soil in Regions with Temperature Anomalies

Based on a large body of observational data on radio emission from the Moon, we study the dependence of lunar radio temperature variations on illumination conditions. The data were obtained with the RATAN-600 radio telescope with a high sensitivity and resolution, which has not yet been used to construct radio images of the Moon. The harmonic parameters (amplitudes and phase angles) were determined both for the average Moon and for regions with temperature anomalies revealed by the RATAN-600 observations. These parameters allow the physical properties of the lunar soil to be investigated. The distribution of the loss-angle tangent (tan ), one of the characteristics of the lunar material, over the Moon was determined. The loss-angle tangent is related to the content of ilmenite, a rock containing oxygen, iron, and titanium, in the lunar soil. Studies of the ilmenite distribution on the Moon are particularly important in view of the prospects for building a habitable lunar base that needs oxygen. It is relatively easy and cheap to extract oxygen, iron, and titanium from ilmenite.     

The deconvolution of lunar brightness temperature based on the maximum entropy method using Chang’e-2 microwave data

A passive and multi-channel microwave sounder onboard the Chang’e-2orbiter has successfully acquired microwave observations of the lunar surface and subsurface structure. Compared with the Chang’e-1 orbiter, the Chang’e-2 orbiter obtained more accurate and comprehensive microwave brightness temperature data,which are helpful for further research. Since there is a close relationship between microwave brightness temperature data and some related properties of the lunar regolith,such as the thickness, temperature and dielectric constant, precise and high resolution brightness temperature data are necessary for such research. However, through the detection mechanism of the microwave sounder, the brightness temperature data acquired from the microwave sounder are weighted by the antenna radiation pattern, so the data are the convolution of the antenna radiation pattern with the lunar brightness temperature. In order to obtain the real lunar brightness temperature, a deconvolution method is needed. The aim of this paper is to solve the problem associated with performing deconvolution of the lunar brightness temperature. In this study, we introduce the maximum entropy method(MEM) to process the brightness temperature data and achieve excellent results. The paper mainly includes the following aspects: first, we introduce the principle of the MEM; second, through a series of simulations, the MEM has been verified as an efficient deconvolution method; and third, the MEM is used to process the Chang’e-2 microwave data and the results are significant.     

Thermal emission spectra of silicates from planetary nebulae

Calculations of the grain equilibrium temperature and of the expected infrared spectra of IC 418, BD+30° 3639, NGC 6572 and NGC 7027 have been performed using dielectric constants of lunar silicates. The results have been compared with previous work on pure graphite and ice-mantle grains. Lα heating of dust followed by thermal re-emission is consistent with the large infrared excesses detected in planetary nebulae. An extra source of heating is, nevertheless, necessary to fit correctly the experimental results. It appears from the calculations that, for each object, it is possible to define theoretically the most probable nature of the emitting dust.     

Lunar heat flow and regolith structure inferred from interferometric observations at a wavelength of 49.3 cm

We discuss observations of the Moon at a wavelength of 49.3 cm made with the Owens Valley Radio Observatory Interferometer. These observations have been fit to models in order to estimate the lunar dielectric constant, the equatorial subsurface temperature, the latitude dependence of the subsurface temperature, and the subsurface temperature gradient. The models are most consistent with a dielectric constant of 2.52 ± 0.01 (formal errors), an equatorial subsurface temperature of 249_?5⁺⁸K, and a change in the subsurface temperature with latitude (ψ), which is proportional to cos^0.38ψ. Since the temperature of the Moon has been measured by the Apollo Lunar Heat Flow Experiment, we have been able to use our determination of the equatorial temperature to estimate the error in the flux density calibration scale at 49.3cm (608 MHz). This results in a correction factor of 1.03 ± 0.04, which must be applied to the flux density scale. This factor is much different from 1.21 ± 0.09 estimated by Muhleman et al. (1973) from the brightness temperature of Venus and apparently indicates that the observed decrease in the brightness temperature of Venus at long wavelengths is a real effect.The estimates of the temperature gradient, which are based on the measurement of limb darkening, are small and negative (temperature decreases with depth) and may be insignificantly different from zero since they are only as large as their formal errors. We estimate that a temperature gradient in excess of 0.6K/m at 10m depth would have been observed. Thus, a temperature gradient like that measured in situ at the Apollo 15 and 17 landing sites in the upper 2m of the regolith is not typical of the entire lunar frontside at the 10m depths where the 49.3 cm wavelength emission originates. This result may indicate that the mean lunar heat flow is lower than that measured at the Apollo landing sites, that the thermal conductivity is greater at 10m depth than it is at 2m depth, or that the radio opacity is greater at 10m depth than at 2m depth. The negative estimates of the temperature gradient indicate that the Moon appeared limb bright and might be explained by scattering of the emission from boulders or an interface with solid rock. The presence of solid rock at 10m depths will probably cause heat flows like those measured by Apollo to be unobservable by our interferometric method at long wavelengths, since it will cause both the thermal conductivity and radio opacity of the regolith to increase. Thus, our data may be most consistent with a change in the physical properties of the regolith to those of solid rock or a mixture of rock and soil at depths of 7 to 16m. Our results show that future radio measurements for heat flow determinations must utilize wavelengths considerably shorter than 50 cm (25 cm or less) to avoid the rock regions below the regolith.     

Lunar polarization studies at 3.1mm wavelength

Observations of the distribution of linearly polarized lunar thermal emission were made at a wavelength of 3.1 mm with The University of Texas 4.88 m parabolic reflector (0.042° HPBW). A shadow corrected, rough surface, thermal emission model for a homogeneous Moon was leastsquares-fitted to the polarization data. Results indicate an effective lunar dielectric constant of 1.34 ±0.04 with surface roughness characterized by a standard deviation of 17° ± 5° for surface slopes with a normal probability density, independent of lunar phase. A comparison of these results with published values at other wavelengths suggests that the effective lunar dielectric constant, as obtained by lunar emission measurements, decreases with decreasing wavelength of observation. This wavelength dependence may be interpreted in terms of an inhomogeneous surface and/or a surface that possesses intermediate scale surface roughness.This work was supported in part by NASA Grant NGL 44-012-006.     

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.     

Physical and mechanical properties of the lunar soil (a review)

We review the data on the physical and mechanical properties of the lunar soil that were acquired in the direct investigations on the lunar surface carried out in the manned and automatic missions and in the laboratory examination of the lunar samples returned to the Earth. In justice to the American manned program Apollo, we show that a large volume of the data on the properties of the lunar soil was also obtained in the Soviet automatic program Lunokhod and with the automatic space stations Luna-16, -20, and -24 that returned the lunar soil samples to the Earth. We consider all of the main physical and mechanical properties of the lunar soil, such as the granulometric composition, density and porosity, cohesion and adhesion, angle of internal friction, shear strength of loose soil, deformation characteristics (the deformation modulus and Poisson ratio), compressibility, and the bearing capacity, and show the change of some properties versus the depth. In most cases, the analytical dependence of the main parameters is presented, which is required in developing reliable engineering models of the lunar soil. The main physical and mechanical properties are listed in the summarizing table, and the currently available models and simulants of the lunar soil are reviewed.     

Boulder tracks and nature of lunar soil

Boulder tracks from 19 different locations on the Moon, observable in Lunar Orbiter photographs, have been examined. Measurements of the track width indicate that some of the boulders sank considerably deeper than others. It is suggested that lunar surface materials vary from place to place; the state of compaction (density of lunar soil) is probably one of the significant variables. Using bearing capacity theory, modified to be applicable to the rolling boulder problem by theoretical studies and extensive testing, the friction angle of the lunar soil was estimated. Most of the results were between 24 and 47 degrees with an arithmetic average of 37 degrees. These values suggest corresponding density variations of 1.25 to 2.00 g/cm³.     

Possible effect of subsurface inhomogeneities on the lunar microwave spectrum

Inhomogeneities beneath the lunar surface could alter the average microwave emission spectrum of the Moon in a fashion generally consistent with observations, even in the absence of an average heat flux or density gradients with depth. The lunar subsurface was modeled as an inhomogeneous lossy dielectric with three-dimensional refractive index fluctuations characterized by independent horizontal and vertical correlation lengths. The model suggests that attempts to infer the physical properties of the Moon from the lunar microwave spectrum could be significantly inaccurate if subsurface scattering were neglected.     

The simulation of lunar micrometeorite impacts by laser pulses

Laser pulses of a finely focused beam were used to simulate micrometeorite impacts on lunar rocks and in lunar soil. The electron microscope pictures show the detailed effects so caused; it is possible to derive an estimate of the comparative amounts of erosion a given micrometeorite flux would cause in lunar rocks and lunar soil.     

Latitude effects in lunar thermal evolution

A simple analytical model is developed from which we have calculated the temperature throughout the lunar interior resulting from internal heat sources and the imposition of surface temperature boundary conditions. The surface temperature is determined almost entirely by the balance of solar heating and surface reradiation; as a consequence this temperature is latitude dependent, decreasing towards the lunar poles. The internal solution shows that the latitude effect exists almost undiminished to great depths within the Moon. It is suggested that this dependence on latitude may have a significant effect on the Moon’s thermal evolution. Using the liquefaction model the high concentration of lunar maria at low latitudes may be explained.     

Space Weathering on Mercury: Implications for Remote Sensing

By applying our understanding of lunar space weathering processes, we can predict how space weathering will effect the soil properties on Mercury. In particular, the extreme temperature range on Mercury may result in latitudinal variations in the size distribution of npFe₀, and therefore the spectral properties of the soil.     

Comment on: Constraints on the depth and variability of the lunar regolith,by B. B. Wilcox,M. S. Robinson,P. C. Thomas,and B. R. Hawke

Abstract— Any permanent presence on the Moon will require use of materials from the lunar regolith, the surface soil layer on the Moon. Thus, knowledge of the thickness of the lunar regolith is essential. It has been proposed that crater counts obtained from high Sun angle photography give larger estimates of impact crater equilibrium diameters than for low Sun angle photography, and thus deeper estimates of lunar surface regolith than were previously made using crater morphology, size of blocky rimmed craters, and equilibrium diameters determined on low Sun angle images. The purpose of this comment is to evaluate this result as a means of resolving this important question before planning for future lunar missions is undertaken     

Lunar soil grain size distribution

A comprehensive review has been made of the currently available data for lunar grain size distributions. It has been concluded that there is little or no statistical difference among the large majority of the soil samples from the Apollo 11, 12, 14, and 15 missions. The grain size distribution for these soils has reached a steady state in which the comminution processes are balanced by the aggregation processes. The median particle size for the steady-state soil is 40 to 130 µm. The predictions of lunar grain size distributions based on the Surveyor television photographs have been found to be quantitatively in error and qualitatively misleading.     

Characterization of lunar dust and a synopsis of available lunar simulants

Understanding the formation and evolution of the soil and dust of the Moon addresses the fundamental question of the interactions of space with the surface of an airless body. The physical and chemical properties of the lunar dust, the <20 μm portion of lunar soil, are key properties necessary for studies of the toxicity and the electrostatic charging of the dust. These properties have been largely overlooked until recent years. Although chemical and physical studies of the <20 μm portion of lunar soil have been the topic of several studies, there is still need for further studies, primarily of the <1 μm particles. This paper presents a review of the studies of lunar dust that have been conducted to date. As many preparations for future exploration or science activities on the Moon require testing using lunar soil/dust simulants, we also include a brief review of past and current simulants.     

Effects of darkening processes on surfaces of airless bodies

We find the lunar darkening process could be due neither to simple addition of impact-melted glass nor to addition of devitrified glass to crushed lunar rock. There is evidence that lunar soil grains have thin, very light-absorbing coatings that mask absorption bands, seen in the reflection spectra of freshly crushed lunar rock, in the same manner as they are masked in the spectra of lunar soils. We believe the processes that produce these coatings are (1) deposition of atoms sputtered from lunar soil grains by solar wind particles and (2) deposition of vapor species vaporized from lunar soil grains by micrometeorite impacts. Coatings produced in laboratory simulations of these processes owe their strong light-absorbing properties in large part to the presence of abundant metallic Fe grains smaller than 100 Å in diameter. Another process, which depends on implantation of solar wind protons in lunar soil grains and their later mobilization during micrometeorite impacts to produce metallic Fe in the impact glass, also seems reasonable but has not yet been demonstrated experimentally. As a result of impact vaporization the Moon would preferentially lose minor amounts of light elements, principally monatomic oxygen, and this would result in oxygen depletion in the vapor condensate. This type of fraction would be more extreme on airless bodies with lower escape velocities. Sputtering occurs at higher effective temperatures and this would cause loss of all common rock-forming elements in approximately equal amounts. There would be some bias in this process toward retention of very heavy trace elements— a characteristic that has been observed in the lunar soil. This bias would be less important for smaller airless bodies. We describe an apparent new type of fractionation that occurs during deposition of sputtered atoms. This fractionation favors retention of higher mass atoms over lower mass atoms, and appears to be a linear function of mass. This may explain observed isotopic fractionations in lunar soil, in which the heavier isotope always appears to be enriched relative to the lighter one. This “first bounce fractionation” process should operate on all airless bodies. Na and K apparently do not conform to this fractionation process and have a much greater tendency to escape. This may help explain the presence of high Na concentrations around Io.     

From regolith to rock by shock

A model for shock-lithification of terrestrial and lunar regolith is proposed that accounts for: (1) observed petrographic properties and densities of shock-lithified material from missile impact craters at White Sands, New Mexico and from Meteor Crater, Arizona; (2) observed petrographic textures of lunar soil and lunar soil analogues experimentally shocked to known pressures in laboratory experiments; (3) theoretical calculations of the behavior of air and water under shock compression; and (4) measured Hugoniot and release adiabat data on dry and wet terrestrial soils and lunar regolith. In this model it is proposed that air or an air-water mixture initially in the pores of terrestrial soil affects the behavior of the soil-air-water system under shock-loading. Shock-lithified rocks found at Meteor Crater are classified as ‘strongly lithified’ and ‘weakly lithified’ on the basis of their strength in hand specimen; only weakly lithified rocks are found at the missile impact craters. These qualitative strength properties are related to the mechanisms of bonding in the rocks. The densities of weakly lithified samples are directly related to the pressures to which they were shock-loaded. A comparison of the petrographic textures and densities of weakly lithified samples with textures and densities of ‘regolith’ shock-loaded to known pressures suggests that weakly lithified terrestrial samples formed at pressures well under 100 kb, probably under 50 kb. If terrestrial soils are shock-loaded to pressures between 100 and 200 kb by impact events of short duration, the pore pressure due to hot air or air-water mixtures exceeds the strength of the weak lithification mechanisms and fragmentation, rather than lithification, occurs. At pressures above 200 kb, lithification can occur because the formation of glass provides a lithification mechanism which has sufficient strength to withstand the pore pressure. During shock-lithification of lunar regolith at pressures below 50 kb, the material is compressed to intrinsic crystal density and remains at approximately that density upon release from the shocked state. It is proposed, however, that at pressures in excess of 50 kb, the release of trapped volatiles from lunar soil grains into fractures causes an expansion of the regolith during unloading from the shocked state.