Lunar structure and dynamics - results from the apollo passive seismic experiment

Analysis of seismic signals from man-made impacts, moonquakes, and meteoroid impacts has established the presence of a lunar crust, approximately 60 km thick in the region of the Apollo seismic network; an underlying zone of nearly constant seismic velocity extending to a depth of about 1000 km, referred to as the mantle; and a lunar core, beginning at a depth of about 1000 km, in which shear waves are highly attenuated suggesting the presence of appreciable melting. Seismic velocitites in the crust reach 7 km s^–1 beneath the lower-velocity surface zone. This velocity corresponds to that expected for the gabbroic anorthosites found to predominate in the highlands, suggesting that rock of this composition is the major constituent of the lunar crust. The upper mantle velocity of about 8 km s^–1 for compressional waves corresponds to those of terrestrial olivines, pyroxenites and peridotites. The deep zone of melting may simply represent the depth at which solidus temperatures are exceeded in the lower mantle. If a silicate interior is assumed, as seems most plausible, minimum temperatures of between 1450°C and 1600°C at a depth of 1000 km are implied. The generation of deep moonquakes, which appear to be concentrated in a zone between 600 km and 1000 km deep, may now be explained as a consequence of the presence of fluids which facilitate dislocation. The preliminary estimate of meteoroid flux, based upon the statistics of seismic signals recorded from lunar impacts, is between one and three orders of magnitude lower than previous estimates from Earth-based measurements.Paper dedicated to Professor Harold C. Urey on the occasion of his 80th birthday on 29 April, 1973.     

Lunar velocity structure and compositional and thermal inferences

Seismic data from the Apollo Passive Seismic Network stations are analyzed to determine the velocity structure and to infer the composition and physical properties of the lunar interior. Data from artificial impacts (S-IVB booster and LM ascent stage) cover a distance range of 70–1100 km. Travel times and amplitudes, as well as theoretical seismograms, are used to derive a velocity model for the outer 150 km of the Moon. TheP wave velocity model confirms our earlier report of a lunar crust in the eastern part of Oceanus Procellarum.The crust is about 60 km thick and may consist of two layers in the mare regions. Possible values for theP-wave velocity in the uppermost mantle are between 7.7 km s^–1 and 9.0 km s^–1. The 9 km s^–1 velocity cannot extend below a depth of about 100 km and must decrease below this depth. The elastic properties of the deep interior as inferred from the seismograms of natural events (meteoroid impacts and moonquakes) occurring at great distance indicate that there is an increase in attenuation and a possible decrease of velocity at depths below about 1000 km. This verifies the high temperatures calculated for the deep lunar interior by thermal history models.Paper presented at the Lunar Science Institute Conference on Geophysical and Geochemical Exploration of the Moon and Planets, January 10–12, 1973.     

Visual and radiometric photometry of 1580 Betulia

We obtained broadband visual and 10.6-μm photometry of 1580 Betulia during its close approach to Earth in May 1976. We analyzed our photometry by using the “radiometric method” to derive the radius (2.10 ± 0.40 km) and albedo (0.108 ± 0.012) of Betulia. Radar and polarimetric results indicate a radius greater than 3.0 km and a geometric albedo of about 0.05. To be compatible with these results we also modeled Betulia as having a surface with the thermal characteristics of bare rock rather than those of the “lunar” regolith model used for previous analysis of radiometry of other asteroids. A 3.7-km radius and a geometric albedo of ～0.04 are compatible with all available observations. Betulia is the first Mars-crossing asteroid found to have such a low albedo, which may be indicative of carbonaceous surface material.     

Martian cratering revisited: Implications for early geologic evolution

Improved crater statistics from varied Martian terrains are compared to lunar crater populations. The distribution functions for the average Martian cratered terrain and the average lunar highlands over the diameter range 8–2000 km are quite similar. The Martian population is less dense by approximately 0.70 from 8 to 256 km diameter and diverges to proportionally lower densities at greater diameters. Crater densities on Martian “pure” terra give a lower limit to the Mars/Moon integrated crater flux of 0.75 since the last stabilization of the respective planetary crusts. The crater population >8 km diameter postdating the Martian northern plains is statistically indistinguishable from that population postdating the lunar maria. Monte Carlo simulations were performed to constrain plausible mechanisms of crater obliteration. The models demonstrate that if the crater density difference between the lunar and Martian terra has been due to resurfacing processes, random intercrater plains formation cannot be the sole process. If plains preferentially form in and obliterate larger craters, then the observed Martian distribution retains its “shape” as the crater density decreases. This result is consistent with the morphology of Martian intercrater plains.     

Thermal evolution of the moon

The thermal history and current state of the lunar interior are investigated using constraints imposed by recent geological and physical data. Theoretical temperature models are computed taking into account different initial conditions, heat sources, differentiation and simulated convection. To account for the early formation of the lunar highlands, the time duration of magmatism and presentday temperatures estimated from lunar electrical conductivity profiles, it is necessary to restrict initial temperatures and abundances of radioactivie elements. Successful models require that the outer half of the Moon initially heated to melting temperatures, probably due to rapid accretion. Differentiation of radioactive heat sources toward the lunar surface occurred during the first 1.6 billion years. Temperatures in the outer 500 km are currently low, while the deep interior (radius less than 700 to 1000 km) is warmer than 1000°C, and is of primordial material. In some models there is a partially melted core. The calculated surface heat flux is between 25 and 30 erg/cm² s.Presently at the Research Triangle Institute, Research Triangle, North Carolina 27709, U.S.A.     

The velocity structure of the lunar crust

Seismic refraction data, obtained at the Apollo 14 and 16 sites, when combined with other lunar seismic data, allow a compressional wave velocity profile of the lunar near-surface and crust to be derived. The regolith, although variable in thickness over the lunar surface, possesses surprisingly similar seismic properties. Underlying the regolith at both the Apollo 14 Fra Mauro site and the Apollo 16 Descartes site is low-velocity brecciated material or impact derived debris. Key features of the lunar seismic velocity profile are: (i) velocity increases from 100–300 m s^–1 in the upper 100 m to 4 km s^–1 at 5 km depth, (ii) a more gradual increase from 4 km s^–1 to 6 km s^–1 at 25 km depth, (iii) a discontinuity at a depth of 25 km and (iv) a constant value of 7 km s^–1 at depths from 25 km to about 60 km. The exact details of the velocity variation in the upper 5 to 10 km of the Moon cannot yet be resolved but self-compression of rock powders cannot duplicate the observed magnitude of the velocity change and the steep velocity-depth gradient. Other textural or compositional changes must be important in the upper 5 km of the Moon. The only serious candidates for the lower lunar crust are anorthositic or gabbroic rocks.Paper dedicated to Professor Harold C. Urey on the occasion of his 80th birthday on 29 April, 1973.     

Thermophysical properties of lunar material returned by Apollo missions

Data on thermophysical properties measured on lunar material returned by Apollo missions are reviewed. In particular, the effects of temperature and interstitial gaseous pressure on thermal conductivity and diffusivity have been studied. For crystalline rocks, breccias and fines, the thermal conductivity and diffusivity decrease as the interstitial gaseous pressure decreases from 1 atm to 10^–4T. Below 10^–4T, these properties become insensitive to the pressure. At a pressure of 10^–4T or below, the thermal conductivity of fines is more temperature dependent than that of crystalline rocks and breccias. The bulk density also affects the thermal conductivity of the fines. An empirical relationship between thermal conductivity, bulk density and temperature derived from the study of terrestrial material is shown to be consistent with the data on lunar samples. Measurement of specific heat shows that, regardless of the differences in mineral composition, crystalline rocks and fines have almost identical specific heat in the temperature range between 100 and 340K. The thermal parameter calculated from thermal conductivity, density and specific heat shows that the thermal properties estimated by earth-based observations are those characteristic only of lunar fines and not of crystalline rocks and breccias. The rate of radioactive heat generation calculated from the content of K, Th and U in lunar samples indicates that the surface layer of the lunar highland is more heat-producing than the lunar maria. This may suggest fundamental differences between the two regions.Now at Lamont-Doherty Geological Observatory, Columbia University, Palisades, New York, U.S.A.     

Thermal response properties of the Earth's ionospheric plasma

The thermal response of the Earth's ionospheric plasma is calculated for various suddenly applied electron and ion heat sources. The time-dependent coupled electron and ion energy equations are solved by a semi-automatic computational scheme that employs Newton's method for coupled vector systems of non-linear parabolic (second order) partial differential equations in one spatial dimension. First, the electron and composite ion energy equations along a geomagnetic field line are solved with respect to a variety of ionospheric heat sources that include: thermal conduction in the daytime ionosphere; heating by electric fields acting perpendicular to the geomagnetic field line; and heating within a stable auroral red are (SAR-arc). The energy equations are then extended to resolve differential temperature profiles, first for two separate ion species (H⁺, O⁺) and then for four separate ion species (H⁺, He⁺, N⁺, O⁺) in addition to the electron temperature. The electron and individual ion temperatures are calculated for conditions within a night-time SAR-arc excited by heat flowing from the magnetosphere into the ionosphere, and also for typical midlatitude daytime ionospheric conditions. It is shown that in the lower ionosphere all ion species have the same temperature; however, in the topside ionosphere above about 400 km, ion species can display differential temperatures depending upon the balance between thermal conduction, heating by collision with electrons, cooling by collisions with the neutrals, and energy transfer by inter-ion collisions. Both the time evolution and steady-state distribution of such ion temperature differentials are discussed.The results show that below 300km both the electrons and ions respond rapidly (<30s) to variations in direct thermal forcing. Above 600 km the electrons and ions display quite different times to reach steady state, depending on the electron density: when the electron density is low the electrons reach steady state temperatures in 30 s, but typically require 700 s when the density is high; the ions, on the other hand, reach steady state in 700 s when the density is high, and 1500–2500 s when the density is low. Between 300 and 600 km, a variety of thermal structures can exist, depending upon the electron density and the type of thermal forcing; however steady state is generally reached in 200–1000 s.     

Lunar heat flow experiments: Science objectives and a strategy for minimizing the effects of lander-induced perturbations

Reliable measurements of the Moon's global heat flow would serve as an important diagnostic test for models of lunar thermal evolution and would also help to constrain the Moon's bulk abundance of radioactive elements and its differentiation history. The two existing measurements of lunar heat flow are unlikely to be representative of the global heat flow. For these reasons, obtaining additional heat flow measurements has been recognized as a high priority lunar science objective. In making such measurements, it is essential that the design and deployment of the heat flow probe and of the parent spacecraft do not inadvertently modify the near-surface thermal structure of the lunar regolith and thus perturb the measured heat flow. One type of spacecraft-related perturbation is the shadow cast by the spacecraft and by thermal blankets on some instruments. The thermal effects of these shadows propagate by conduction both downward and outward from the spacecraft into the lunar regolith. Shadows cast by the spacecraft superstructure move over the surface with time and only perturb the regolith temperature in the upper 0.8 m. Permanent shadows, such as from thermal blankets covering a seismometer or other instruments, can modify the temperature to greater depth. Finite element simulations using measured values of the thermal diffusivity of lunar regolith show that the limiting factor for temperature perturbations is the need to measure the annual thermal wave for 2 or more years to measure the thermal diffusivity. The error induced by permanent spacecraft thermal shadows can be kept below 8% of the annual wave amplitude at 1 m depth if the heat flow probe is deployed at least 2.5 m away from any permanent spacecraft shadow. Deploying the heat flow probe 2 m from permanent shadows permits measuring the annual thermal wave for only one year and should be considered the science floor for a heat flow experiment on the Moon. One way to meet this separation requirement would be to deploy the heat flow and seismology experiments on opposite sides of the spacecraft. This result should be incorporated in the design of future lunar geophysics spacecraft experiments. Differences in the thermal environments of the Moon and Mars result in less restrictive separation requirements for heat flow experiments on Mars.     

Solar-wind interactions with the moon: Role of oxygen ions

The solar-wind interacts directly with the lunar surface due to tenuous atmosphere and magnetic field. The interaction results in an almost complete absorption of the solar-wind corpuscles producing no upstream bowshock but a cavity downstream. The solar-wind oxygen ionic species induce and undergo a complex set of reactions with the elements of the lunar minerals and the solar-wind derived trapped gases. The oxygen concentration indegeneous to the lunar surface material is about 60 at.%. Some of these oxygen are displaced from their crystal lattice locations by interactions of the solar-wind corpuscles. A small fraction of these displaced oxygen is in active state. The solar-wind oxygen species flux is about 6×10⁴ cm^–2 s^–1. Besides inducing and undergoing various reactions these species become trapped as oxygen atoms in the lunar grains. Only a portion of these trapped oxygen atoms is in active state. For the contribution of oxygen atoms and molecules from the lunar surface grains to the atmosphere and their reactions with other species, the diffusion coefficients of oxygen atom and molecule should be known. However their values in the highly radiation-damaged lunar surface material are not known. The coefficients are calculated by using the apparent lifetimes of atomic and molecular oxygen in the lunar material. The atmospheric concentration of oxygen atoms and molecules near the lunar surface are found to be about 20 and 3 cm^–3, respectively. These values appear to be very reasonable in comparison with the experimental data. The Apollo 17 lunar orbital UV spectrometer data indicate the atomic oxygen concentration is <8×10¹ cm^–3. The Apollo 17 lunar surface mass spectrometer (sensitivity: 1 count=2×10² molecules cm^–3) did not detect any oxygen molecules on the dayside of the Moon, but the sunrise concentration was reported to be 1±×10³ cm^–3. At the time of the sample collection on the Moon the oxygen content in the trapped gas layer was partly as oxygen atoms and partly as oxygen molecules. At the time of sample analysis on the Earth the concentrations of these two species did not change appreciably.     

Thermal history and evolution of the moon

Possible models for the thermal evolution of the Moon are constrained by a wide assortment of lunar data. In this work, theoretical lunar temperature models are computed taking into account different initial conditions to represent possible accretion models and various abundances of heat sources to correspond to different compositions. Differentiation and convection are simulated in the numerical computational scheme.Models of the thermal evolution of the Moon that fit the chronology of igneous activity on the lunar surface, the stress history of the lunar lithosphere implied by the presence of mascons, and the surface concentrations of radioactive elements, involve extensive differentiation early in lunar history. This differentiation may be the result of rapid accretion and large-scale melting or of primary chemical layering during accretion. Differences in present-day temperatures for these two possibilities are significant only in the inner 1000 km of the Moon and are not resolvable with presently available data.If the Apollo 15 heat flow is a representative value, the average uranium concentration in the moon is 65±15 ppb. This is consistent with achondritic bulk composition (between howardites and eucrites) for the Moon.Paper dedicated to Professor Harold C. Urey on the occasion of his 80th birthday on 29 April 1973.     

The internal evolution of planetary-sized objects

The importance of ‘creep’ in controlling the internal thermal state of large objects with physical properties corresponding to a roughly homogeneous meteoritic composition is reviewed. Some results of this study are used to justify a picture of evolution as a quasistatic process. An attempt is made to show that the viscous dissipation of the motions that occur in the lifetime of such bodies formed about 4.5 × 10⁹ yr ago gives them an innate capacity to chemically differentiate if their external radius exceeds a few hundred kilometres. The capacity to differentiate increases rapidly with external radius and for objects of lunar size and greater, the process is not yet complete. During the ‘active’ stage of evolution the convective cores of these objects tend to grow smaller and hotter with time, giving a secular change in the composition of the differentiating phases. It is suggested that by a curious coincidence of dehydration curves and the horizontally averaged temperature distribution, water of dehydration can still be present at depth in the planets and is the cause of the observed seismic attenuation at the Moon's centre and in the Earth's upper mantle. It is also noted that if water is present at tenths of a percent level the temperature within objects with radii < 3000 km is kept below the Curie point of pure iron for long periods - a situation that could have significant bearing on the present magnetisation of the planetary objects in this size range.     

Size-Frequency Distribution of Small Lunar Craters: Widening with Degradation and Crater Lifetime

The review and new measurements are presented for depth/diameter ratio and slope angle evolution during small (D < 1 km) lunar impact craters aging (degradation). Comparative analysis of available data on the areal cratering density and on the crater degradation state for selected craters, dated with returned Apollo samples, in the first approximation confirms Neukum’s chronological model. The uncertainty of crater retention age due to crater degradational widening is estimated. The collected and analyzed data are discussed to be used in the future updating of mechanical models for lunar crater aging.     

Duration and extent of lunar volcanism: Comparison of 3D convection models to mare basalt ages

It is widely accepted that lunar volcanism started before the emplacement of the mare fills ( b.p.) and lasted for probably more than 3.0 Ga. While the early volcanic activity is relatively easy to understand from a thermal point of view, the late stages of volcanism are harder to explain, because a relatively small body like the Earth's Moon is expected to cool rapidly and any molten layer in the interior should solidify rather quickly. We present several thermal evolution models, in which we varied the boundary conditions at the model surface in order to evaluate the influence on the extent and lifetime of a molten layer in the lunar interior. To investigate the influence of a top insulating layer we used a fully three-dimensional spherical shell convection code for the modelling of the lunar thermal history. In all our models, a partial melt zone formed nearly immediately after the simulation started (early in lunar history), consistent with the identification of lunar cryptomare and early mare basalt volcanism on the Moon. Due to the characteristic thickening of the Moon's lithosphere the melt zone solidified from above. This suggests that the source regions of volcanic rock material proceeded to increasing depth with time. The rapid growth of a massive lithosphere kept the Moon's interior warm and prevented the melt zone from fast freezing. The lifetimes of the melt zones derived from our models are consistent with basalt ages obtained from crater chronology. We conclude that an insulating megaregolith layer is sufficient to prevent the interior from fast cooling, allowing for the thermal regime necessary for the production and eruption of young lava flows in Oceanus Procellarum.     

Post-imbrian global lunar tectonism: Evidence for an initially totally molten Moon

Evaluation of all reasonable sources of stress in the lunar crust indicates that compressional thermoelastic stresses are the only ones which have been tectonically significant on the global scale during the last 3.5×10⁹ yr of lunar history — i.e., the post-Imbrian. However, the thermoelastic stresses calculated for lunar models which have accretional heating profiles at the beginning of lunar history; i.e., a molten zone only a few hundred kilometers deep and a cool deep interior, are less than 1 kbar in the crust. Such stresses are lower than the more than 1 to 7 kbar needed to initiate thrust faulting in the outer crust according to Anderson's theory of thrust faulting. Thus such accretional models predict that no significant global thrust faulting has occurred during the post-Imbrian and that the crust should currently be seismically quiet on the global scale.In contrast, the compressional thermoelastic stresses generated in a Moon which was initially totally molten, as is the case if the Moon formed by fission, are up to 3.5 kbar in the outer few km of the crust at present. These stresses are well within the range needed to cause thrust faulting in the outer 4 km of the crust. According to this model there should be modest scale (10 km), young ( 0.5 to 1×10⁹ yr old) thrust fault scarps in the highlands.Photoselenological investigations confirm that scarps with the expected age and geometric characteristics are found in the highlands. Thus the currently available photoselenological data support the stress model derived for an initially totally molten Moon, but not one which was molten only in the outer few hundreds of km.     

Density and stress distribution in the moon

A model is presented for the lateral variations of density within the Moon. The model gives rise to a gravitational potential which is equal to the observed potential at the lunar surface, moreover, it minimizes the total shear-strain energy of the Moon. The model exhibits lateral variations of about ±0.25 g cc^–1 within 50 km depth. The variations, however, reduce to ±0.06 and ±0.008 g cc^–1 within layers at 50–135 and 135–235 km respectively, and they become negligible below this region. The associated stress differences are found to be about 50 bar within 600 km depth, having their maximum values of about 90 bars at a depth of about 250 km. On the basis of these stress differences a strength of about 100 bar is concluded for the upper 400 km of the lunar interior for the last 3.3 b.y.Paper dedicated to Professor Harold C. Urey on the occasion of his 80th birthday on 29 April, 1973.The Lunar Science Institute is operated by the Universities Space Research Association under Contract No. NSR 09-051-001 with the National Aeronautics and Space Administration. This paper is Lunar Science Institute Contribution No. 117.     

Solar-wind interactions with the moon: Nature and composition of nitrogen compounds

The lunar atmosphere and magnetic field are very tenuous. The solar wind, therefore, interacts directly with the lunar surface material and the dominant nature of interaction is essentially complete absorption of solar-wind particles by the surface material resulting in no upstream bowshock, but a cavity downstream. The solar-wind nitrogen ion species induce and undergo a complex set of reactions with the elements of lunar material and the solar-wind-derived trapped elements. The nitrogen concentration indigeneous to the lunar surface material is practically nil. Therefore any nitrogen and nitrogen compounds found in the lunar surface material are due to the solar-wind implantation of nitrogen ions. The flux of the solar-wind nitrogen ion species is about 6×10³ cm^–2 s^–1. Since there is no evidence for accumulation of nitrogen species in the lunar surface material, the outflux of nitrogen species from the lunar material to the atmosphere is the same as the solar-wind nitrogen ion flux. The species of the outflux are primarily NO and NH₃, and their respective concentrations in the near surface lunar atmosphere are found by calculation to be 327 and 295 cm^–3. The calculated concentration of NH₃ seems to be consistent with the sunrise concentration results of the mass spectrometer implanted on the lunar surface. This is not the case for the concentration of NO. According to the presently calculated concentration value of NO, the mass spectrometer should have detected NO at sunrise, but no report was made for its detection. There is also discrepancy about the concentration of N₂ which is explained in this paper. The concentrations of nitrogen species in the lunar material at the time of sample collection on the Moon remained about the same when the samples were analyzed on the Earth. However, no specific experiment was planned to detect the nitrogen species in the lunar material samples.     

The long-term stability of a possible aqueous ammonium sulfate ocean inside Titan

We model the thermal evolution of a subsurface ocean of aqueous ammonium sulfate inside Titan using a parameterized convection scheme. The cooling and crystallization of such an ocean depends on its heat flux balance, and is governed by the pressure-dependent melting temperatures at the top and bottom of the ocean. Using recent observations and previous experimental data, we present a nominal model which predicts the thickness of the ocean throughout the evolution of Titan; after 4.5 Ga we expect an aqueous ammonium sulfate ocean 56 km thick, overlain by a thick (176 km) heterogeneous crust of methane clathrate, ice I and ammonium sulfate. Underplating of the crust by ice I will give rise to compositional diapirs that are capable of rising through the crust and providing a mechanism for cryovolcanism at the surface. We have conducted a parameter space survey to account for possible variations in the nominal model, and find that for a wide range of plausible conditions, an ocean of aqueous ammonium sulfate can survive to the present day, which is consistent with the recent observations of Titan's spin state from Cassini radar data [Lorenz, R.D., Stiles, B.W., Kirk, R.L., Allison, M.D., del Marmo, P.P., Iess, L., Lunine, J.I., Ostro, S.J., Hensley, S., 2008. Science 319, 1649-1651].     

On constructing the general Earth’s rotation theory

In the present paper the equations of the orbital motion of the major planets and the Moon and the equations of the three–axial rigid Earth’s rotation in Euler parameters are reduced to the secular system describing the evolution of the planetary and lunar orbits (independent of the Earth’s rotation) and the evolution of the Earth’s rotation (depending on the planetary and lunar evolution). Hence, the theory of the Earth’s rotation can be presented by means of the series in powers of the evolutionary variables with quasi-periodic coefficients with respect to the planetary–lunar mean longitudes. This form of the Earth’s rotation problem is compatible with the general planetary theory involving the separation of the short–period and long–period variables and avoiding the appearance of the non–physical secular terms.