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.     

Internal structure of the Moon and moonquakes

I discuss the relation between the internal structure of the Moon and the radial distribution of the moonquake foci. I believe that the important factor conditioning the radial distribution is the fact that the rigidity of the lunar material decreases with increasing depth. Using a two-layer model, solutions of the elasticity equations are found for the cases of a uniform surface load and of a uniform radial body force. The results show that when the inner sphere is less rigid than the outer shell, the maximum sheer stress is located near the boundary of the two components, thus explainning why the moonquakes are mostly deep quakes. The results also suggest that a liquid core exists in the Moon.     

Complements to Moons'1 Lunar Libration Theory

Analytical complements have been brought to Moons' lunar libration theory concerning tidal effects, direct perturbations due to the Earth's figure, and indirect non periodic perturbations. Comparisons to JPL numerical integrations DE245 and DE403 have been performed and the residuals treated by frequency analysis, allowing the determination of fitted free libration parameters and numerical complements. This revised version was published online in July 2006 with corrections to the Cover Date.     

Tides in a body librating about a spin–orbit resonance: generalisation of the Darwin–Kaula theory

The Darwin-Kaula theory of bodily tides is intended for celestial bodies rotating without libration. We demonstrate that this theory, in its customary form, is inapplicable to a librating body. Specifically, in the presence of libration in longitude, the actual spectrum of Fourier tidal modes differs from the conventional spectrum rendered by the Darwin–Kaula theory for a nonlibrating celestial object. This necessitates derivation of formulae for the tidal torque and the tidal heating rate, that are applicable under libration. We derive the tidal spectrum for longitudinal forced libration with one and two main frequencies, generalisation to more main frequencies being straightforward. (By main frequencies we understand those emerging due to the triaxiality of the librating body.) Separately, we consider a case of free libration at one frequency (once again, generalisation to more frequencies being straightforward). We also calculate the tidal torque. This torque provides correction to the triaxiality-caused physical libration. Our theory is not self-consistent: we assume that the tidal torque is much smaller than the permanent-triaxiality-caused torque, so the additional libration due to tides is much weaker than the main libration due to the permanent triaxiality. Finally, we calculate the tidal dissipation rate in a body experiencing forced libration at the main mode, or free libration at one frequency, or superimposed forced and free librations.     

A correlation between large-scale asymmetry of the Moon and the foci of moonquakes

Some evidence is produced to show that the Moon is asymmetric on the large scale as regards its figure, structure, composition, the distribution of tidal force, natural remnant magnetism and magnetic anomaly. This asymmetry produces the state of stress in the Moon, causing most foci of moonquakes to be located in the nearside of the Moon.     

Effects of the physical libration of the moon on lunar orbiters

Lunar physical libration, which is true oscillation of lunar equator in the space, alters the lunar gravitational field in the space coordinate system and affects the orbiting motion of lunar orbiters (hereafter called as lunar satellites) correspondingly. The effect is very similar to that of the precession and nutation on the earth satellites, and a similar treatment can be used. The variations in the gravitational force and in the orbit perturbation solution are clearly given in this paper together with numerical illustrations.     

月球物理天平动对环月轨道器运动的影响

月球物理天平动是月球赤道在空间真实的摆动，会导致月球引力场在空间坐标系中的变化，从而引起环月轨道器(以下称为月球卫星)的轨道变化，这与地球的岁差章动现象对地球卫星轨道的影响类似．采用类似对地球岁差章动的处理方法，讨论月球物理天平动对月球卫星轨道的影响，给出相应的引力位的变化及卫星轨道的摄动解，清楚地表明了月球卫星轨道的变化规律，并和数值解进行了比对，从定性和定量方面作一讨论．     

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.     

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.     

Strike-slip fault patterns on Europa: Obliquity or polar wander?

Variations in diurnal tidal stress due to Europa’s eccentric orbit have been considered as the driver of strike-slip motion along pre-existing faults, but obliquity and physical libration have not been taken into account. The first objective of this work is to examine the effects of obliquity on the predicted global pattern of fault slip directions based on a tidal-tectonic formation model. Our second objective is to test the hypothesis that incorporating obliquity can reconcile theory and observations without requiring polar wander, which was previously invoked to explain the mismatch found between the slip directions of 192 faults on Europa and the global pattern predicted using the eccentricity-only model. We compute predictions for individual, observed faults at their current latitude, longitude, and azimuth with four different tidal models: eccentricity only, eccentricity plus obliquity, eccentricity plus physical libration, and a combination of all three effects. We then determine whether longitude migration, presumably due to non-synchronous rotation, is indicated in observed faults by repeating the comparisons with and without obliquity, this time also allowing longitude translation. We find that a tidal model including an obliquity of 1.2°, along with longitude migration, can predict the slip directions of all observed features in the survey. However, all but four faults can be fit with only 1° of obliquity so the value we find may represent the maximum departure from a lower time-averaged obliquity value. Adding physical libration to the obliquity model improves the accuracy of predictions at the current locations of the faults, but fails to predict the slip directions of six faults and requires additional degrees of freedom. The obliquity model with longitude migration is therefore our preferred model. Although the polar wander interpretation cannot be ruled out from these results alone, the obliquity model accounts for all observations with a value consistent with theoretical expectations and cycloid modeling.     

Study of the transfer between libration point orbits and lunar orbits in Earth–Moon system

This paper is devoted to the study of the transfer problem from a libration point orbit of the Earth–Moon system to an orbit around the Moon. The transfer procedure analysed has two legs: the first one is an orbit of the unstable manifold of the libration orbit and the second one is a transfer orbit between a certain point on the manifold and the final lunar orbit. There are only two manoeuvres involved in the method and they are applied at the beginning and at the end of the second leg. Although the numerical results given in this paper correspond to transfers between halo orbits around the \(L_1\) point (of several amplitudes) and lunar polar orbits with altitudes varying between 100 and 500 km, the procedure we develop can be applied to any kind of lunar orbits, libration orbits around the \(L_1\) or \(L_2\) points of the Earth–Moon system, or to other similar cases with different values of the mass ratio.     

Application of two special orbits in the orbit determination of lunar satellites

Using inter-satellite range data,the combined autonomous orbit determination problem of a lunar satellite and a probe on some special orbits is studied in this paper.The problem is firstly studied in the circular restricted three-body problem,and then generalized to the real force model of the Earth-Moon system.Two kinds of special orbits are discussed:collinear libration point orbits and distant retrograde orbits.Studies show that the orbit determination accuracy in both cases can reach that of the observations.Some important properties of the system are carefully studied.These findings should be useful in the future engineering implementation of this conceptual study.     

Possible extra-Solar-System cause for certain lunar seismic events

Reanalysis of lunar seismic data collected during the Apollo program indicates that 23 of the 28 rare events known as high-frequency teleseismic (HFT) events or shallow moonquakes occurred during one-half of the sidereal month when the seismic network on the Moon's near side faced approximately towards right ascension of 12 h on the celestial sphere. Statistical analysis demonstrates that there is about a 1% probability that this pattern would occur by chance. An alternate possibility is that high-energy objects from a fixed source outside the Solar System trigger or even cause the HFT events.     

Seismic scattering and shallow structure of the moon in oceanus procellarum

Long, reverberating trains of seismic waves produced by impacts and moonquakes may be interpreted in terms of scattering in a surface layer overlying a non-scattering elastic medium. Model seismic experiments are used to qualitatively demonstrate the correctness of the interpretation. Three types of seismograms are found, near impact, far impact and moonquake. Only near impact and moonquake seismograms contain independent information. Details are given in the paper of the modelling of the scattering processes by the theory of diffusion.Interpretation of moonquake and artificial impact seismograms in two frequency bands from the Apollo 12 site indicates that the scattering layer is 25 km thick, with a Q of 5000. The mean distance between scatterers is approximately 5 km at 25 km depth and approximately 2 km at 14 km depth; the density of scatterers appears to be high near the surface, decreasing with depth. This may indicate that the scatterers are associated with cratering, or are cracks that anneal with depth. Most of the scattered energy is in the form of scattered surface waves.Communication presented at the Lunar Science Institute Conference on Geophysical and Geochemical Exploration of the Moon and Planets, January 10–12, 1973.     

On the deviation of the lunar center of mass to the East. Two possible mechanisms based on evolution of the orbit and rounding off the shape of the Moon

From the observations of the gravitational field and the figure of the Moon, it is known that its center of mass (briefly COM) does not coincide with the center of figure (COF), and the line “COF/COM” is not directed to the center of the Earth, but deviates from it to the South–East. Here we study the deviation of the lunar COM to the East from the mean direction to Earth.At first, we consider the optical libration of a satellite with synchronous rotation around the planet for an observer at a point on second (empty) orbit focus. It is found that the main axis of inertia of the satellite has asymmetric nonlinear oscillations with amplitude proportional to the square of the orbit eccentricity. Given this effect, a mechanism of tidal secular evolution of the Moon’s orbit is offered that explains up to \(20\%\) of the known displacement of the lunar COM to the East. It is concluded that from the alternative—evolution of the Moon’s orbit with a decrease or increase in eccentricity—only the scenario of evolution with a monotonous increase in orbit eccentricity agrees with the displacement of lunar COM to the East. The precise calculations available confirm that now the eccentricity of the lunar orbit is actually increasing and therefore in the past it was less than its modern value, \(e = 0.0549\).To fully explain the displacement of the Moon’s COM to the East was deduced a second mechanism, which is based on the reliable effect of tidal changes in the shape of the Moon. For this purpose the differential equation which governs the process of displacement of the Moon’s COM to the East with inevitable rounding off its form in the tidal increase process of the distance between the Earth and the Moon is derived. The second mechanism not only explains the Moon’s COM displacement to the East, but it also predicts that the elongation of the lunar figure in the early epoch was significant and could reach the value \(\varepsilon\approx0.31\). Applying the theory of tidal equilibrium figures, we can estimate how close to the Earth the Moon could have formed.     

Tectonic patterns on a tidally distorted planet

Tidal deformation of the lithosphere of a synchronously rotating planet or satellite produces stresses that may result in a distinctive tectonic pattern. The lithosphereis treated as a thin elastic shell which maintains the equilibrium shape of a tidally distorted body. Stresses develop as the equilibrium shape changes during orbital evolution. E. M. Anderson's theory of faulting is used to translate this stress pattern into a tectonic pattern of faults on the planet's surface (The Dynamics of Faulting, Oliver & Boyd, Edinburgh, 1951). On a body such as the Moon, which has receded from the Earth, an originally large tidal bulge has collapsed. The predicted tectonic pattern includes N-S striking thrust faults over an area extending roughly 30° in latitude and longitude around the sub-Earth point and its antipode. The polar regions above roughly 70° latitude exhibit normal faults striking from the near side of the Moon toward the far side. Strike slip faults, with offsets consistent with east-west compression, occur near the limbs. Stress differences are largest at the equator on the limbs, and may have reached several hundreds bars over the last few billion years of the Moon's history. The existence of such a tectonic pattern on the Moon can only be resolved by photogeologic mapping. At present, there is little evidence of this pattern; however, the crucial evidence probably lies in the poorly mapped lunar polar regions. These tectonic patterns, which could provide geologic evidence for large tidal distortions, may also be present on the Galilean satellites of Jupiter.     

Determining parameters of Moon’s orbital and rotational motion from LLR observations using GRAIL and IERS-recommended models

The aim of this work is to combine the model of orbital and rotational motion of the Moon developed for DE430 with up-to-date astronomical, geodynamical, and geo- and selenophysical models. The parameters of the orbit and physical libration are determined in this work from lunar laser ranging (LLR) observations made at different observatories in 1970–2013. Parameters of other models are taken from solutions that were obtained independently from LLR. A new implementation of the DE430 lunar model, including the liquid core equations, was done within the EPM ephemeris. The postfit residuals of LLR observations make evident that the terrestrial models and solutions recommended by the IERS Conventions are compatible with the lunar theory. That includes: EGM2008 gravitational potential with conventional corrections and variations from solid and ocean tides; displacement of stations due to solid and ocean loading tides; and precession-nutation model. Usage of these models in the solution for LLR observations has allowed us to reduce the number of parameters to be fit. The fixed model of tidal variations of the geopotential has resulted in a lesser value of Moon’s extra eccentricity rate, as compared to the original DE430 model with two fit parameters. A mixed model of lunar gravitational potential was used, with some coefficients determined from LLR observations, and other taken from the GL660b solution obtained from the GRAIL spacecraft mission. Solutions obtain accurate positions for the ranging stations and the five retroreflectors. Station motion is derived for sites with long data spans. Dissipation is detected at the lunar fluid core-solid mantle boundary demonstrating that a fluid core is present. Tidal dissipation is strong at both Earth and Moon. Consequently, the lunar semimajor axis is expanding by 38.20 mm/yr, the tidal acceleration in mean longitude is \(-25.90 {{}^{\prime \prime }}/\mathrm{cy}^2\), and the eccentricity is increasing by \(1.48\times 10^{-11}\) each year.     

潮汐能量耗散与地月系统演化

对地月系统而言, 在很大程度上角动量守恒是正确的. 地月距离的变化主要是受到月球引起的潮汐能量耗散的影响. 根据月球的平均运动和它的长期加速度, 就可以计算出月潮能量耗散的数值. 海洋是潮汐能量耗散的主要区域. 由于潮汐的高度正比于月球对潮汐隆起的万有引力, 由此可导出总的月球潮汐摩擦力正比于月球平均运动的平方. 如果采用月球平均加速度数值-20.72$''\cdot$cy^-2, 就可以推算出35亿年来地月之间的距离以及回归年日数和朔望月日数的演化. 此理论结果与古生物钟的数据进行比对, 两者符合较好.     

On the evolution of the lunar orbit

It is generally accepted that the Earth-Moon separation is at present increasing due to tidal dissipation. Values for the corresponding lunar deceleration and the related slowing of the Earth's rotation are obtained from astronomical observations and by studies of ancient eclipses. Extrapolation of these values leads to a close approach of the Earth and Moon 1–3 b.y. BP. However, justification for such an extrapolation is required. It has been hypothesized that periodicities in the Precambrian stromatolites can be used to determine the number of solar days in a lunar month prior to 500 m.y. BP. These data combined with dynamic constraints on the number of solar days in a lunar month indicate a close approach of the Earth and Moon at 2.85 ± 0.25 b.y. BP. It is suggested that the mare volcanism on the Moon and high-temperature Archean volcanism on the Earth prior to this date were caused by tidal heating. It is also suggested that the strong tidal heating during a close approach could have contributed to the formation of the first living organisms.     

The strength of the lunar lithosphere

A self-gravitating, elastic, spherical thick shell model is used to derive the present state of the lateral variations of density and stress differences within the lunar lithosphere. The model is allowed to deform under the load of an initial surface topography and internal density distribution, such that the resulting deformed body gives rise to the observed surface topography and gravity specified by the spherical harmonics of degree up to 70. Two main models are considered, Model A and Model B, with elastic lithospheres of thickness 300 and 210 km, respectively. Model A displays density perturbations of generally less than ±200 kg/m³ within the crustal layers, reducing rapidly to less than ±20 kg/m³ at the base of the lithosphere. The density perturbations in Model B are similar in the crust and marginally higher at the base of the lithosphere. The major stress differences in the mantle are associated with the mascon basins and are found to reach maximums of 8-10 MPa within the lower lithosphere (150-270 km) of Model A and maximums of 12-16 MPa at 150 to 180 km depth for Model B. A moderate correlation exists between the modeled stress distributions and shallow moonquake epicenters. However, the overall results of this study imply that other remnant stresses, due to processes other than density perturbations, exist and play a critical role in the large shallow moonquakes.