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.     

Viscous damping of surface magnetohydrodynamic waves on magnetic interface in cold plasmas

Surface magnetohydrodynamic wave propagation on a magnetic interface in a cold plasma is studied. The anisotropic ion viscosity is taken into account. Only long waves damping weakly in a wave period are considered. The dispersion equation is obtained. This equation is shown always to have exactly one root if there is no viscosity. The dependences of phase velocity, penetration depth and damping decrement of waves on the parameters of undisturbed plasma and wave propagation direction are investigated. The resulting application for describing of surface wave damping in the solar corona is discussed.     

Velocity structure and properties of the lunar crust

Lunar seismic data from three Apollo seismometers are interpreted to determine the structure of the Moon's interior to a depth of about 100 km. The travel times and amplitudes ofP arrivals from Saturn IV B and LM impacts are interpreted in terms of a compressional velocity profile. The most outstanding feature of the model is that, in the Fra Mauro region of Oceanus Procellarum, the Moon has a 65 km thick layered crust. Other features of the model are: (i) rapid increase of velocity near the surface due to pressure effects on dry rocks, (ii) a discontinuity at a depth of about 25 km, (iii) near constant velocity (6.8 km/s) between 25 and 65 km deep, (iv) a major discontinuity at 65 km marking the base of the lunar crust, and (v) very high velocity (about 9 km/s) in the lunar mantle below the crust. Velocities in the upper layer of the crust match those of lunar basalts while those in the lower layer fall in the range of terrestrial gabbroic and anorthositic rocks.Lamant-Doherty Geological Observatory Contribution No. 1768.     

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.     

Shallow lunar structure determined from the passive seismic experiment

Data relevant to the shallow structure of the Moon obtained at the Apollo seismic stations are compared with previously published results of the active seismic experiments. It is concluded that the lunar surface is covered by a layer of low seismic velocity (V _p ? 100 m s^?1), which appears to be equivalent to the lunar regolith defined previously by geological observations. This layer is underlain by a zone of distinctly higher seismic velocity at all of the Apollo landing sites. The regolith thicknesses at the Apollo 11, 12, and 15 sites are estimated from the shear-wave resonance to be 4.4, 3.7, and 4.4 m, respectively. These thicknesses and those determined at the other Apollo sites by the active seismic experiments appear to be correlated with the age determinations and the abundances of extralunar components at the sites.     

Optimisation of seismic network design: Application to a geophysical international lunar network

Fundamental scientific questions concerning the internal structure and dynamics of the Moon, and their implications on the Earth-Moon System, are driving the deployment of a new broadband seismological network on the surface of the Moon. Informations about lunar seismicity and seismic subsurface models from the Apollo missions are used as a priori information in this study to optimise the geometry of future lunar seismic networks in order to best resolve the seismic interior structure of the Moon. Deep moonquake events and simulated meteoroid impacts are the assumed seismic sources. Synthetic P and S wave arrivals computed in a radial seismic model of the Moon are the assumed seismic data. The linearised estimates of resolution and covariance of radial seismic velocity perturbations can be computed for a particular seismic network geometry. The non-linear inverse problem relating the seismic station positions to the linearised estimates of covariance and resolution of radial seismic velocity perturbations is written and solved by the Neighbourhood Algorithm. This optimisation study favours near side seismic station positions at southern latitudes in order to constrain the deep mantle structure from deep moonquake data at large epicentral distances. The addition of a far side station allows to divide by two the size of the error bar on the seismic velocity model. The monitoring of lunar impact flashes from the Earth allows to improve the radial seismic model in the top of the mantle by adding much more meteor impact data at short epicentral distances due to the high accuracy of the space/time location of these seismic sources. Such meteor impact detections may be necessary to investigate the 3D structure of the lunar crust.     

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.     

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.     

Q and structure

An acoustic energy flow through a heterogeneous medium is characterized by transfer equations involving both scattering and real loss coefficients. Different values of seismicQ may be obtained from measurements of different portions of a seismic record, indicating a separation of the effects on energy propagation of scattering and real loss parameters. In cases in which these parameters can be separated, they can then be used in seismic modeling. As an example, a model is presented in which scattering occurs to a depth of about 10 km below the volcanic ridge in the Tonga-Fiji region. The case of the lunar maria is discussed in terms of the relation of measured seismicQ, scattering parameters, and direct ray propagation parameters. The results indicate that a fairly simple jointed bedrock model is compatible with observed lunar seismic data.Publication No. 1037 of the Institute of Geophysics and Planetary Physics, University of California, Los Angeles 90024, U.S.A.     

The analogy between sunquakes and water waves

To investigate the seismic waves generated at the surface of the convection zone by a sunquake, the solar convection zone is modeled as an incompressible fluid layer of finite depth which is excited by a pressure pulse just above the solar surface. Solutions for the surface displacement ζ as a function of time are obtained by solving the linearized Euler equations for wave propagation in an inviscid, incompressible fluid. Approximate solutions are derived using the method of stationary phase and formulas are obtained for the position of the wave crests versus time and the decay of the wave amplitude versus distance. Despite the very simple nature of the model, the resulting time–distance relation is found to exhibit the correct order of magnitude when compared to the observations of the flare initiated sunquake of 9 July 1996. However, the water wave model cannot fully explain the observations because, for one thing, the distance in between successive wave crests is greater than that seen in the observations. One may conclude that the sunquake is probably composed primarily of acoustic waves, that is, p modes and not f modes.     

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

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

Characteristics of oceanic impact‐induced large water waves—Re‐evaluation of the tsunami hazard

Abstract— The potential hazard of a meteorite impact in the ocean is controversial with respect to the destructive power of generated large ocean waves (tsunamis). We used numerical modeling of hypervelocity impact to investigate the generation mechanism and the characteristics of the resulting waves up to a distance of 100–150 projectile radii. The wave signal is primarily controlled by the ratio between projectile diameter and water depth, and can be roughly classified into deep‐water and shallow‐water impacts. In the latter, the collapse of the crater rim results in a wave signal similar to solitary waves, which propagate and decay in agreement with shallow‐water wave theory. The much more likely scenario for an asteroid impact on Earth is a relatively small body (much smaller than the water depth) striking the deep sea. In this case, the collapse of the transient crater results in a significantly different and much more complex wave signal that is characterized by strong nonlinear behavior. We found that such waves decay much more rapidly than previously assumed and cannot be treated as long waves. For this reason, the shallow‐water theory is not applicable for the computation of wave propagation, and more complex models (full solution of the Boussinesq equations) are required.     

Large impacts detected by the Apollo seismometers: Impactor mass and source cutoff frequency estimations

Meteoroid impacts are important seismic sources on the Moon. As they continuously impact the Moon, they are a significant contribution to the lunar micro-seismic background noise. They also were associated with the most powerful seismic sources recorded by the Apollo seismic network. We study in this paper the largest impacts. We show that their masses can be estimated with a rather simple modeling technique and that high frequency seismic signals have reduced amplitudes due to a relatively low (about 1 s) corner frequency resulting from the duration of the impact process and the crater formation. If synthetic seismograms computed for a spherical model of the Moon are unable to match the waveforms of the observations, they nevertheless provide an approximate measure of the energy of seismic waves in the coda. The latter can then be used for an estimation of the mass of the impactors, when the velocity of the impactor is known. This method, for the artificial impacts of the LM and SIVB Apollo upper stages, allows us to retrieve the mass within 20% of relative error. The estimated mass of the largest impacts observed during the 7 years of activity of the Apollo seismic network provides an explanation for the non-detection of surface waves on the seismograms. The specifications of future Moon seismometers, in order to provide the detection of surface waves, are given in conclusion.     

SMART‐1 end of life shallow regolith impact simulations

The SMART‐1 end‐of‐life impact with the lunar surface was simulated with impacts in a two stage light‐gas gun onto inclined basalt targets with a shallow surface layer of sand. This simulated the probable impact site, where a loose regolith will have overlaid a well consolidated basaltic layer of rock. The impact angles used were at 5° and 10° from the horizontal. The impact speed was ~2 km s^?1 and the projectiles were 2.03 mm diameter aluminum spheres. The sand depth was between approximately 0.8 and 1.8 times the projectile diameter, implying a loose lunar surface regolith of similar dimensions to the SMART‐1 spacecraft. A crater in the basement rock itself was only observed in the impact at 10° incidence, and where the depth of loose surface material was less than the projectile diameter, in which case the basement rock also contained a small pit‐like crater. In all cases, the projectile ricocheted away from the impact site at a shallow angle. This implies that at the SMART‐1 impact site the crater will have a complicated structure, with exposed basement rock and some excavated rock displaced nearby, and the main spacecraft body itself will not be present at the main crater.     

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.     

Dynamic tensile strength of terrestrial rocks and application to impact cratering

Abstract— Dynamic tensile strengths and fracture strengths of 3 terrestrial rocks, San Marcos gabbro, Coconino sandstone, and Sesia eclogite were determined by carrying out flat‐plate (PMMA and aluminum) impact experiments on disc‐shaped samples in the 5 to 60 m/sec range. Tensile stresses of 125 to 300 MPa and 245 to 580 MPa were induced for gabbro and eclogite, respectively (with duration time of ?1 μs). For sandstone (porosity 25%), tensile stresses normal to bedding of ?13 to 55 MPa were induced (with duration times of 2.4 and ?1.4 μs). Tensile crack failure was detected by the onset of shock‐induced (damage) P and S wave velocity reduction. The dynamic tensile strength of gabbro determined from P and S wave velocity deficits agrees closely with the value of previously determined values by post‐impact microscopic examination (?150 MPa). Tensile strength of Coconino sandstone is 20 MPa for a 14 μs duration time and 17 MPa for a 2.4 μs duration time. For Sesia eclogite, the dynamic tensile strength is ?240 MPa. The fracture strength for gabbro is ?250 MPa, ?500 MPa for eclogite, and ?40 MPa for sandstone. Relative crack‐induced reduction of S wave velocities is less than that of post‐impact P wave velocity reductions for both gabbro and eclogite, indicating that the cracks were predominantly spall cracks. Impacts upon planetary surfaces induce tensile failure within shock‐processed rocks beneath the resulting craters. The depth of cracking beneath impact craters can be determined both by seismic refraction methods for rocks of varying water saturation and, for dry conditions (e.g., the Moon), from gravity anomalies. In principle, depth of cracking is related to the equations‐of‐state of projectile and target, projectile dimension, and impact velocity. We constructed a crack‐depth model applicable to Meteor Crater. For the observed 850 m depth of cracking, our preferred strength scaling model yields an impact velocity of 33 km/s and impactor radius of 9 m for an iron projectile.     

A primary analysis of microwave brightness temperature of lunar surface from Chang-E 1 multi-channel radiometer observation and inversion of regolith layer thickness

In China’s first lunar exploration project, Chang-E 1 (CE-1), a multi-channel microwave radiometer was aboard the satellite, with the purpose of measuring microwave brightness temperature (Tb) from lunar surface and surveying the global distribution of lunar regolith layer thickness. In this paper, the primary 621 tracks of swath data measured by CE-1 microwave radiometer from November 2007 to February 2008 are collected and analyzed. Using the nearest neighbor interpolation to collect the Tb data under the same Sun illumination, global distributions of microwave brightness temperature from lunar surface at lunar daytime and nighttime are constructed. Based on the three-layer media modeling (the top dust-soil, regolith and underlying rock media) for microwave thermal emission of lunar surface, the CE-1 measured Tb and its dependence upon latitude, frequency and FeO + TiO₂ content, etc. are discussed. The CE-1 Tb data at Apollo landing sites are especially chosen for validation and calibration on the basis of available ground measurements. Using the empirical dependence of physical temperature upon the latitude verified by the CE-1 multi-channel Tb data at Apollo landing sites, the global distribution of regolith layer thickness is further inverted from the CE-1 brightness temperature data at 3 GHz channel. Those inversions at Apollo landing sites and the characteristics of regolith layer thickness for lunar maria are well compared with the Apollo in situ measurements and the regolith thickness derived from the Earth-based radar data. Finally, the statistical distribution of regolith thickness is analyzed and discussed.     

Magnetic waves of solar activity

An asymptotic solution of generation equations for the solar mean magnetic field is given and studied. The variation of rotational angular velocity with depth is taken from helioseismological data. Average helicity is prescribed according to the mixing length theory. It is shown that three dynamo waves of the magnetic field are excited. The first wave is generated at the surface layer and concentrates at latitudes of about 60°. Its activity becomes apparent in the poleward migration of the zone of polar faculae formation. The second more powerful wave of the field is excited in the center of the convection zone and its activity shows up in a sunspot cycle. The third wave which is similar to the first wave, is generated at the bottom of the convection zone and attenuates towards the surface. Its activity may appear as a three-fold reversal of the polar magnetic field.     

Reflection and Ducting of Gravity Waves Inside the Sun

Internal gravity waves excited by overshoot at the bottom of the convection zone can be influenced by rotation and by the strong toroidal magnetic field that is likely to be present in the solar tachocline. Using a simple Cartesian model, we show how waves with a vertical component of propagation can be reflected when traveling through a layer containing a horizontal magnetic field with a strength that varies with depth. This interaction can prevent a portion of the downward traveling wave energy flux from reaching the deep solar interior. If a highly reflecting magnetized layer is located some distance below the convection zone base, a duct or wave guide can be set up, wherein vertical propagation is restricted by successive reflections at the upper and lower boundaries. The presence of both upward and downward traveling disturbances inside the duct leads to the existence of a set of horizontally propagating modes that have significantly enhanced amplitudes. We point out that the helical structure of these waves makes them capable of generating an α-effect, and briefly consider the possibility that propagation in a shear of sufficient strength could lead to instability, the result of wave growth due to over-reflection.     

Impacts into oceans and seas

Impacts of cosmic bodies into oceans and seas lead to the formation of very high waves. Numerical simulations of 3-km and 1-km comets impacting into a 4 km depth ocean with a velocity of 20 km/sec have been conducted. For a 1-km body, depth of the interim crater in the sea bed is about 8 km below ocean level, and the height of the water wave is 10 m at a distance of 2000 km from the impact point. As the water wave runs into shallows, a huge tsunami hits the coast. The height of the wave strongly depends on the coastal and sea bed topography.If the impact occurred near the shore, the huge mass of water strikes the cliffs and the near shore mountain ridges and can cause displacement of the rocks, initiate landslides, and change the relief. Thus, impact into oceans and seas is an important geological factor.Cosmic bodies of small sizes are disrupted by aerodynamic forces. Fragments of a 100-m radius comet striking the water surface create an unstable cavity in the water of about 1 km radius. Its collapse also creates tsunami.A simple estimate has been made using the light curves from recent atmosphere explosions detected by satellites. The results of our assessment of the characteristics of meteoroids which caused these intense light flashes suggests that fragments of a 25-m stony body with initial impact velocity 15 to 20 km/sec will hit the surface. For a 75-m iron body striking the sea with a depth of 600 m, the height of the wave is 10 m at 200–300 km distance from the impact.