Laboratory studies on seismic and electrical properties of the moon

Laboratory measurements of seismic wave velocities and electrical properties of Apollo lunar samples and similar material of terrestrial origin are discussed in this paper. Measurements of the electrical properties show that in the frequency range above a few hundred Hz the outer region of the Moon may be considered as a low loss dielectric. This observation supports a longstanding speculation that dry, powdered rocks in which the dielectric loss tangent is frequency-independent over a wide range of frequency are present in the uppermost lunar surface layers. The surface layers of the Moon are likely to have an extremely low electrical conductivity. Thus future electromagnetic probing of the Moon to a few hundred kilometer depth is possible in the few kHz frequency range. Based on ultrasonic experiments with pressure as a variable, we next present the elastic constants and equations of state of lunar materials and characteristic dispersion of seismic wave velocities of the Moon. We find thatP andS wave velocities increase sharply within the first 30 km depth and then level off gradually. Combining this observation with lunar seismic and geophone data, we believe that the first 30 km of the Moon may be interpreted as a scattering region. If H₂O exists on the Moon, H₂O may occur at some shallow depth beneath the outermost surface layer in solid ice interlocking cracks and pores and mineral grains. The rocks in this permafrost state have relatively low seismic velocity and highQ. If permafrost does exist, we would expect a wide range of electrical conductivity and dielectric constant. Future electromagnetic probing of the Moon should yield very usefull information on the physical state of the lunar interior; when this electrical information is combined with the seismic information, we should learn much more about the internal constitution and the state of the Moon than is known today.     

Moonquakes and lunar tectonism

With the succesful installation of a geophysical station at Hadley Rille, on July 31, 1971, on the Apollo 15 mission, and the continued operation of stations 12 and 14 approximately 1100 km SW, the Apollo program for the first time achieved a network of seismic stations on the lunar surface. A network of at least three stations is essential for the location of natural events on the Moon. Thus, the establishment of this network was one of the most important milestones in the geophysical exploration of the Moon. The major discoveries that have resulted to date from the analysis of seismic data from this network can be summarized as follows:

1. Lunar seismic signals differ greatly from typical terrestrial seismic signals. It now appears that this can be explained almost entirely by the presence of a thin dry, heterogeneous layer which blankets the Moon to a probable depth of few km with a maximum possible depth of about 20 km. Seismic waves are highly scattered in this zone. Seismic wave propagation within the lunar interior, below the scattering zone, is highly efficient. As a result, it is probable that meteoroid impact signals are being received from the entire lunar surface.
2. The Moon possesses a crust and a mantle, at least in the region of the Apollo 12 and 14 stations. The thickness of the crust is between 55 and 70 km and may consist of two layers. The contrast in elastic properties of the rocks which comprise these major structural units is at least as great as that which exists between the crust and mantle of the earth. (See Toks?zet al., p. 490, for further discussion of seismic evidence of a lunar crust.)
3. Natural lunar events detected by the Apollo seismic network are moonquakes and meteoroid impacts. The average rate of release of seismic energy from moonquakes is far below that of the Earth. Although present data do not permit a completely unambiguous interpretation, the best solution obtainable places the most active moonquake focus at a depth of 800 km; slightly deeper than any known earthquake. These moonquakes occur in monthly cycles; triggered by lunar tides. There are at least 10 zones within which the repeating moonquakes originate.
4. In addition to the repeating moonquakes, moonquake ‘swarms’ have been discovered. During periods of swarm activity, events may occur as frequently as one event every two hours over intervals lasting several days. The source of these swarms is unknown at present. The occurrence of moonquake swarms also appears to be related to lunar tides; although, it is too soon to be certain of this point.

These findings have been discussed in eight previous papers (Lathamet al., 1969, 1970, 1971) The instrument has been described by Lathamet al. (1969) and Sutton and Latham (1964). The locations of the seismic stations are shown in Figure 1.     

The lunar seismogram

The unexpected and unusual characteristics of the lunar seismogram have given rise to various speculations regarding their origin: secondary ejecta, diffusive wave propagation and wave propagation effects in a self-compacted powder layer with a linearly increasing velocity with depth. Many of the characteristics can be explained, qualitatively, by the simple theory of a self-compacting, dry powder layer for which the velocity varies as the sixth root of the depth. This gives a very low seismic velocity at the lunar surface which, in turn, allows the signal to have a long duration, a lack of correlation between horizontal and vertical displacements, a signal envelope that changes with source to receiver separation and a varying spectrum over the duration of the signal. To explain the long duration of the seismic signal quantitatively, it is necessary to include scattering of the normally incident rays at the surface by shallow surface undulations. The sixth root velocity-depth dependence is consistent with the measured variation, with pressure, of the compressibility and velocity of lunar samples.     

The Spectrum of Torsional Oscillations of the Moon

The diagnostic potentialities of the torsional oscillations for probing the structure of the interiors of the Moon are investigated. Models with no core, a liquid core, and a solid core are considered. The profiles of compressional and shear wave velocities V _P and V _S for the lunar interior estimated by Bills and Ferrari (1977), Goins et al. (1981), and Nakamura (1983) from the Apollo lunar seismic network are used. For all these models, the periods of torsional oscillations for n = 2–100 and four overtones have been calculated. The derivatives of the dimensionless eigenfrequency with respect to the dimensionless shear modulus and density are calculated and tabulated for use. These data can be used to determine corrections to the model density and shear modulus distributions due to their small change. The damping of torsional oscillations is studied. Several trial radial distributions of the dissipative function Q are considered.     

Non-LTE line formation in a magnetic field

Theoretical line contours calculated for fixed values of the line constants and a given model atmosphere show an increase of the Stokes parameters Q, U, and V but a decrease of I if the portion of non-coherent scattering increases. These effects increase from the centre of the solar disk to the limb. The action of scattering may be approximately simulated in LTE contours by increasing the gradient of the source function and fitting in this way theoretical contours to observed ones. There remains, however, the effect of V-reversal near the line core, which is caused by anomalous dispersion and is abnormally increased by scattering.     

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.     

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.     

A note on the physical parameters of the Moon

Using the Stokes coefficients of the Moon recommended by IERS Standards (1992), we determined the expression of lunar equipotential surface (selenoid), then calculated the parameters of best-fitting lunar ellipsoid. Moreover, we derived a set of hydrostatic values of lunar physical parameters by solving the Clairaut equation, and discussed the feature of nonhydrostatic component in the figure parameters of the Moon. Finally, we suggest that the lunar physical parameters should be divided into three kinds: primary constants, derived constants, and estimated constants (see Table III); as well that the second-degree Love number,k ₂, of the Moon should belong to the estimated constants. At present, in view of the accuracy in reductions of LLR data, a value ofk ₂ obtained from model calculations should be defined as its adopted value. For example, the value ofk ₂, 0.0266, in this paper can replace 0.0222 in IERS Standards (1992).     

Bidirectional Reflectance Spectroscopy: 5. The Coherent Backscatter Opposition Effect and Anisotropic Scattering

A model published previously by the author that describes light scattering from particulate media is modified to include several improvements: (1) a better approximation to the Ambartsumian-Chandrasekhar H-functions that is especially important for particles with single scattering albedos close to 1.00, (2) increased accuracy for anisotropically scattering particles, and (3) incorporation of coherent backscattering. The goal of the original model of being analytic and mathematically tractable is preserved. No new parameters are introduced by the first and second modifications; however, the third unavoidably adds two new parameters: the amplitude and width of the coherent backscatter opposition effect. Several examples are given in which the results of calculations using the original and new models are compared with exact numerical computations.It is shown that a medium composed of complex particles that are large compared to the wavelength can have a coherent backscatter opposition effect (CBOE) that is broad enough to be readily observable. The CBOE multiplies the entire reflectance and not just the multiply scattered component, so that a low-albedo medium, such as lunar regolith, can have a strong CBOE.     

Dynamical History of the Earth–Moon System

Differential equations describing the tidal evolution of the earth's rotation and of the lunar orbital motion are presented in a simple close form. The equations differ in form for orbits fixed to the terrestrial equator and for orbits with the nodes precessing along the ecliptic due to solar perturbations. Analytical considerations show that if the contemporary lunar orbit were equatorial the evolution would develop from an unstable geosynchronous orbit of the period about 4.42 h (in the past) to a stable geosynchronous orbit of the period about 44.8 days (in the future). It is also demonstrated that at the contemporary epoch the orbital plane of the fictitious equatorial moon would be unstable in the Liapunov's sense, being asymptotically stable at early stages of the evolution. Evolution of the currently near-ecliptical lunar orbit and of the terrestrial rotation is traced backward in time by numerical integration of the evolutional equations. It is confirmed that about 1.8 billion years ago a critical phase of the evolution took place when the equatorial inclination of the moon reached small values and the moon was in a near vicinity of the earth. Before the critical epoch t _cr two types of the evolution are possible, which at present cannot be unambiguously distinguished with the help of the purely dynamical considerations. In the scenario that seems to be the most realistic from the physical point of view, the evolution also has started from a geosynchronous equatorial lunar orbit of the period 4.19 h. At t < t _cr the lunar orbit has been fixed to the precessing terrestrial equator by strong perturbations from the earth's flattening and by tidal effects; at the critical epoch the solar perturbations begin to dominate and transfer the moon to its contemporary near-ecliptical orbit which evolves now to the stable geosynchronous state. Probably this scenario is in favour of the Darwin's hypothesis about originating the moon by its separation from the earth. Too much short time scale of the evolution in this model might be enlarged if the dissipative Q factor had somewhat larger values in the past than in the present epoch. Values of the length of day and the length of month, estimated from paleontological data, are confronted with the results of the developed model.     

Evidence for the deficiency of short cosmic ray pathlengths and a physically realistic explanation — The no-near-sources model

From our recent observations of the charge and energy spectra of cosmic-ray nuclei we have constructed secondary-to-primary charge ratios at the two ends of the charge spectrum. These ratios are found to be inconsistent with thead hoc leaky-box model of cosmic-ray propagation which leads to an exponential pathlength distribution. Models for which the pathlength distribution function is deficient in short pathlengths provide a more consistent picture. Several of these models are investigated, bothad hoc and physical. The physical model considered here is one for which detailed galactic propagation parameters and boundary conditions are used and for which there exists no near sources of cosmic rays over a time interval corresponding to a few times the cosmic-ray age.     

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.     

Light scattering by complex particles in the Moon's exosphere: Toward a taxonomy of models for the realistic simulation of the scattering behavior of lunar dust

It is suspected that the lunar exosphere has a dusty component dispersed above the surface by various physical mechanisms. Most of the evidence for this phenomenon comes from observations of “lunar horizon glow” (LHG), which is thought to be produced by the scattering of sunlight by this exospheric dust. The characterization of exospheric dust populations at the Moon is key to furthering our understanding of fundamental surface processes, as well as a necessary requirement for the planning of future robotic and human exploration.We present a model to simulate the scattering of sunlight by complex lunar dust grains (i.e. grains that are non-spherical and can be inhomogeneous in composition) to be used in the interpretation of remote sensing data from current and future lunar missions. We numerically model lunar dust grains with several different morphologies and compositions and compute their individual scattering signatures using the Discrete Dipole Approximation (DDA). These scattering properties are then used in a radiative transfer code to simulate the light scattering due to a dust size distribution, as would likely be observed in the lunar exosphere at high altitudes 10's of km. We demonstrate the usefulness and relevance of our model by examining mode: irregular grains, aggregate of spherical monomers and spherical grains with nano-phase iron inclusions. We subsequently simulate the scattering by two grain size distributions (0.1 and radius), and show the results normalized per-grain. A similar methodology can also be applied to the analysis of the LHG observations, which are believed to be produced by scattering from larger dust grains within about a meter of the surface.As expected, significant differences in scattering properties are shown between the analyses employing the widely used Mie theory and our more realistic grain geometries. These differences include large variations in intensity as well as a positive polarization of scattered sunlight caused by non-spherical grains. Positive polarization occurs even when the grain size is small compared to the wavelength of incident sunlight, thus confirming that the interpretation of LHG based on Mie theory could lead to large errors in estimating the distribution and abundances of exospheric dust.     

Density within the moon and implications for lunar composition

Density models for the Moon, including the effects of temperature and pressure, can satisfy the mass and moment of inertia of the Moon and the presence of a low density crust indicated by the seismic refraction results only if the lunar mantle is chemically or mineralogically inhomogeneous. IfC/MR ² exceeds 0.400, the inferred density of the upper mantle must be greater than that of the lower mantle at similar conditions by at least 0.1 g cm^–3 for any of the temperature profiles proposed for the lunar interior. The average mantle density lies between 3.4 and 3.5 g cm^–3, though the density of the upper mantle may be greater. The suggested density inversion is gravitationally unstable, but the implied deviatoric stresses in the mantle need be no larger than those associated with lunar gravity anomalies. UsingC/MR ³=0.400 and the recent seismic evidence suggesting a thin, high density zone beneath the crust and a partially molten core, successful density models can be found for a range of temperature profiles. Temperature distributions as cool as several inferred from the lunar electrical conductivity profile would be excluded. The density and probable seismic velocity for the bulk of the mantle are consistent with a pyroxenite composition and a 100 MgO/(MgO+FeO) molecular ratio of less than 80.Communication presented at the Lunar Science Institute Conference on Geophysical and Geochemical Exploration of the Moon and Planets, January 10–12, 1973.     

The sign-changeable interaction between variable generalized Chaplygin gas and dark matter

In this paper, we study a cosmological model with the sign-changeable interaction between variable generalized Chaplygin gas (VGCG) and dark matter. The dynamical analysis indicates that there exists a stable scaling attractor, which can help to alleviate the coincidence problem. Furthermore, when the parameters of the model take some fixed values, the attractor corresponds to the phase w=?0.939 and the equation of state of VGCG approaches it from either w>?1 or w<?1 depending on the choice of its initial cosmic density parameter and the ratio of pressure to critical energy density. So, the phantom divide can be crossed. We find the interaction term Q can change its sign from Q<0 to Q>0 as the universe expands, which is different from the usual interaction. Also, we place constraints on the parameters from the point of view of dynamics.     

Thermal history of the Jovian satellite Io

The discovery of large volcanic eruptions on Io suggests that Io is one of the most geologically active planetary bodies. The energy source of this geologic activity is believed to be tidal heating induced by Jupiter. A number of thermal history calculations were done to investigate the effect of tidal heating on the thermal history of Io taking into account solid state convection and advective heat transfer. These simulations show that the total tidal heating energy in Io is almost equal to the advectively transferred heat, indicating that the observed heat flow from Io is nearly equal to the total tidal heating energy. Since total tidal heating energy is dependent on the radius of the liquid mantle and the internal dissipation factor (Q), the radius of the liquid mantle can be estimated for a given value of Q. Some reasonable thermal history models of Io were obtained using a model with Q ≈ 25–50 in which the magma source of Ionian volcanism is at a depth of 100–300 km. The models satisfy the heat flow data and the existence of a thick lithosphere. Using a model with Q = 25 and L = 300 km (thickness of the advective region) as the standard model (model II), we then studied the effect of convective heat transfer and the initial temperature distribution on the Ionian thermal history. In these calculations, the other parameters are the same as in the standard model (model II). These calculations show that although the temperature distribution in the central region reflects the difference in the efficiency of convective heat transfer and initial temperature distribution, the temperature distribution in the outer region does not changes appreciably.     

Mechanics of tidally driven fractures in Europa's ice shell

A fracture mechanics model is developed for the initiation and propagation of a crack through a porous ice layer of finite thickness under gravitational overburden. It is found that surface cracks generated in response to a tidally induced stress field may penetrate through the entire outer brittle layer if a subsurface ocean is present on Europa. Such penetration is found to be very unlikely in the absence of an ocean. A cycloidal crack would then form as a sequence of near instantaneous discrete failures, each extending roughly the brittle layer thickness in range, linked with a much lower apparent propagation speed set by the moving tidal stress field. The implications of this porous ice fracture model for ice-penetrating radar scattering loss and seismic activity are quantified.     

Thermal history of inter-cluster relativistic electron gas heated by quasars

The thermal evolution of an inter-cluster gas of relativistic electrons heated by quasars with redshifts up toz=3 and 4 is studied in the framework of a Friedmann-Robertson-Walker universe. The gas cools by Compton scattering with the microwave backgroud radiation and by adiabatic cooling due to the universe expansion. Power and exponential laws of cosmological evolution of the comoving density of sources are considered. The obtained temperatures are sensitive to the form of these laws and to the heating epochs. Compared to the nonrelativistic models, the results obtained in the case of the power law present strong differences. These differences decrease when the exponential law is considered. Thermalization times are compared to the characteristic time of variation of the universe energy density and to the time-scales of energy loss by bremsstrahlung radiation and by Compton scattering. It is shown that, in some cases, nonequilibrium effects may be important. The time delay effects in the propagation of electromagnetic waves in cosmic plasma are shown to be very important for the analysis of theoretical models.     

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.