Lunar mascons: another model and its implications

A mascon model is proposed in which the mass excess of the mare basalts in the circular maria is supported isostatically by mass deficits at depth. The model predicts the observed positive gravity anomalies surrounded by negative ring anomalies and explains the absence of gravity anomalies over the irregular maria. The model implies that mare basalts were derived by partial melting of a source region at depth due to pressure relief resulting from the excavation of the circular mare basins, and that the crystalline residuum in the source region is of lower density than the original source rock. The trace element enrichment and near cotectic character of Apollo 11 and 12 lavas reported by some investigators may be caused by extensive magma fractionation enroute from an origin in the circular maria to the final, distant emplacement sites.     

Evidence for isostasy in the lunar mascon Maria

The pronounced positive gravity anomalies in the lunar circular maria imply lack of isostatic compensation of the lunar mascons. This lack of isostasy is hard to reconcile with the rheological properties of the lunar crust. Analysis of the negative ring anomalies that appear to surround the major positive gravity peaks indicates that associated with each mascon is a mass deficit of approximately the same size. In view of the lunar rheology these mass deficits most probably represent compensating mass deficits beneath the lunar mascon maria. Consequently, most lunar mascons appear to be near isostatic equilibrium, and the observed gravity anomalies may be essentially the superposition of positive gravity peaks due to the basaltic mare fill, and less pronounced, broader gravity lows due to the compensating mass deficits at depth.     

Gravity: Mare humorum

Global tracking coverage of the Apollo 15 subsatellite has provided gravity measurements from 50 km altitudes over the entire Humorum basin. An estimate of surface mass points at 2 degree intervals, which best fit the data reveals a mass distribution having a lesser mass excess for the very central area. When two different profiles were fit using a 2 disk model it was again found for each profile that the smaller central disk decreased the central mass by approximately 30%. The mass distribution per unit area however for the major portion of the mascon is still consistent with the other mascons (Crisium, Nectaris and Serenitatis) of approximately 800-900 kg cm^–2. The surface mass point solution seems to correlate somewhat with the dark areas on Whitaker's IR-UV map.Paper dedicated to Prof. Harold C. Urey on the occasion of his 80th birthday on 29 April 1973.This paper represents the results of one phase of research carried out at the Jet Propulsion Laboratory, California Institute of Technology under Contract No. NAS 7-100, sponsored by the National Aeronautics and Space Administration.     

Venus gravity: Analysis of Beta Regio

Radio tracking data acquired over Beta Regio were analyzed to obtain a surface mass distribution from which a detailed vertical gravity field was derived. In addition, a corresponding vertical gravity field was evaluated solely from the topography of the Beta region. A comparison of these two maps confirms the strong correlation between gravity and topography which was previously seen in line-of-sight gravity maps. It also demonstrates that the observed gravity is a significant fraction of that predicted from the topography alone. The effective depth of complete isostatic compensation for the Beta region is estimated to be 330 km, which is somewhat deeper than that found for other areas of Venus.     

GRAVITY RECONNAISSANCE AT THREE MAURITANIAN CRATERS OF EXPLOSIVE ORIGIN

We have carried out reconnaissance gravity surveys across three Mauritanian craters: Aouelloul, an undoubted meteorite crater; Tenoumer, a probable meteorite crater with a unique array of concentric dikes on its outer rim flanks containing xenoliths of country rock showing abundant shock artifacts; and Temimichat Ghallaman, a crater of possible meteorite impact origin. All three have residual negative gravity anomalies associated with their interiors. In all cases the gravity values return to “normal” immediately outside their rims. At Tenoumer the anomaly has the form and magnitude expected for a meteorite crater which has been subsequently in-filled with unconsolidated sediments to the level of the surrounding country. Maximum depth from the present crater floor to the bottom of the sedimentary fill (top of the original crater floor) is at least 750 feet. With a rim-rim diameter of 6,300 feet, the origin depth/diameter ratio of about 1:8 is virtually identical with that of Meteor Crater, Arizona. Temimichat, with a rim-rim diameter of 2,100 to 2,400 feet, is somewhat larger than has been previously reported. If it is meteoritic in origin the gravity data dictate a surprisingly shallow structure, with a depth from the present floor to the original crater floor of 150 feet maximum and an original depth/diameter ratio of 1:15. No positive evidence for an impact origin has yet been found for Temimichat. Aouelloul is also larger than generally reported, with a rim-rim diameter averaging 1,275 feet. As for Temimichat the gravity data dictate a remarkably shallow structure having a depth/diameter ratio of about 1:13. The combination of a shallow depth and a reasonably high rim apparently requires a scaled depth of burst for the impact event substantially in excess of 0.50, a value previously considered a maximum for explosive impacts. The morphological resemblance between Temimichat and Aouelloul is striking but, without additional evidence, this fact alone cannot be used to infer a similar origin.     

Lunar gravity via the Apollo 15 and 16 subsatellites

Dense Doppler tracking coverage of the Apollo 15 and 16 subsatellites over ten and eighteen day periods when periapsis altitudes were 15–50 km has provided detailed gravity mapping of the lunar frontside. Many new gravity features are revealed including one that does not correlate with any visible topographic structure. All unfilled craters sampled are negative anomalies. The mascons consistently produce gravity highs that load the surface with ≈800 kg cm^?2 excess mass. The Orientale region is represented with a solution grid of 177 point masses that clearly show the ringed structure. The eastern limb is also displayed with a solution grid of point masses. The gravity variations over the central portion of the frontface are shown as line-of-sight acceleration contours in milligals.     

Lunar gravity: Apollo 17

Gravity results are displayed as a band of contours ≈60 km wide spanning 140° of frontside longitude. The contours traverse Grimaldi, Mare Procellarum, Copernicus, Apennines, Mare Serenitatis, Littrow, and Mare Crisium. Redundant gravity area previously mapped by Apollos 14, 15, 16, and the Apollo subsatellites are tabulated and show excellent consistency. Modeling of Grimaldi reveals a loading more than the known mascons and thus makes Grimaldi the smallest known mascon feature. Copernicus' gravity profile is best modeled with a mass defect for the basin and a mass excess for the rim. Mare Serenitatis has an irregular mass distribution with central gravity highs shifted approximately 3° in latitude.     

A crater and its ejecta: An interpretation of Deep Impact

We apply recently updated scaling laws for impact cratering and ejecta to interpret observations of the Deep Impact event. An important question is whether the cratering event was gravity or strength-dominated; the answer gives important clues about the properties of the surface material of Tempel 1. Gravity scaling was assumed in pre-event calculations and has been asserted in initial studies of the mission results. Because the gravity field of Tempel 1 is extremely weak, a gravity-dominated event necessarily implies a surface with essentially zero strength. The conclusion of gravity scaling was based mainly on the interpretation that the impact ejecta plume remained attached to the comet during its evolution. We address that feature here, and conclude that even strength-dominated craters would result in a plume that appeared to remain attached to the surface. We then calculate the plume characteristics from scaling laws for a variety of material types, and for gravity and strength-dominated cases. We find that no model of cratering alone can match the reported observation of plume mass and brightness history. Instead, comet-like acceleration mechanisms such as expanding vapor clouds are required to move the ejected mass to the far field in a few-hour time frame. With such mechanisms, and to within the large uncertainties, either gravity or strength craters can provide the levels of estimated observed mass. Thus, the observations are unlikely to answer the questions about the mechanical nature of the Tempel 1 surface.     

Mass and energy flow near sunspots

Sunspots block the flow of energy to the solar surface. The blocked energy heats the volume beneath the spot, producing a pressure excess which drives an outflow of mass. Linear numerical models of the mass and energy flow around spots were constructed to estimate the predictions of this physical picture against the observed properties of sunspot bright rings and moat flows. The width of the bright ring and moat are predicted to be proportional to the depth of the spot penumbra, in conflict with the observed proportionally of the moat width to the spot diameter. Postulating that spot depths are proportional to spot diameters would bury the moat flow too deeply to be observed, because the radial velocity at the surface is found to be inversely proportional to the depth of the spot penumbra. The radial velocity at the surface is of order a few hundred meters per second after 1 day, in agreement with the observed excess of moat velocities over supergranule velocities.     

Venus gravity west of Beta Regio

Doppler tracking data from the Pioneer Venus Orbiter (PVO) have been used to estimate the anomalous gravity field in the region of Venus west of Beta Regio. The analysis invokes a Kalman filter-smoother to solve the nonlinear spacecraft state estimation problem and a linear Bayesian estimator to perform the geophysical inversion. The topographic map for this region, derived from the PVO radar, has been filtered to have the same distortions and degree of smoothing as the gravity map. The undulations of the gravity are about 0.2 times as large as expected from the topography on the assumption that the latter is uncompensated. A comparison of the gravity and topography by means of the spectral admittance is consistent with Airy compensation at a depth of 50 km if the surface material has a density of 2.6 g/cm³. However, this is not a unique interpretation.     

Facular models and the sunspot energy deficit

The problem of the energy deficit in a sunspot is shown to be critically related to the depth of a given sunspot model. Recent facular models are discussed and a new model is derived from recent data using a two-dimensional radiative transfer analysis. The excess non-radiative energy required by this and other models is evaluated and it is shown that in some models this may account for a considerable fraction of the sunspot energy deficit. For these models the Alfvén energy travelling along the closed flux loops from the sunspot is insufficient to supply the requirements of the faculae and it is suggested that excess energy flux from below the faculae is also required. These results provide further support for deep as opposed to shallow sunspot models.     

Local harmonic analysis of planetary Doppler gravity data

Planetary gravity fields represented in terms of spherical harmonics or surface mass distributions\ do not have the necessary resolution to permit gravity analysis of local features. Doppler gravity maps representing residual line-of-sight (LOS) accelerations have much greater resolution but cannot be used for conventional geophysical analysis due to the geometric distortions inherent in LOS gravity patterns and lack of normalization of LOS data. However, LOS gravity data may be converted to vertical gravity anomalies by expressing the anomalous local gravitational potential over small rectangular areas in terms of a modified double Fourier series constrained by local Doppler gravity data. The vertical derivative of the resulting potential yields the vertical gravity components at desired altitudes. The resolution of the resulting normalized free air anomaly maps is limited only by that of the original Doppler gravity data. Extended gravity maps may be constructed this way using a moving window approach. It is anticipated that much of the lunar frontside can be mapped at resolutions ranging from 1 to 4 deg of arc.     

Apollo 15 gravity analysis from theS-band transponder experiment

TheS-Band Transponder experiment used precision doppler tracking data of the command and service module, the lunar module and the subsatellite to provide detailed information about the near side gravity field. No special instruments are required other than the existingS-Band transponder used for real time navigation. The data consists of variations in the spacecraft speed as measured by the earth-based radio tracking system, which has a resolution of 0.65 mm/s.Initial data reduction has been concentrated on the low altitude CSM data ( 20 km) which provides new detailed gravity profiles of the Serenitatis and Crisium mascons. The results are in good agreement with Apollo 14 analysis and strongly suggest that the mascons are near surface features with a mass distribution per unit area of approximately 800 kg/cm². The Apennines reveal themselves as a local gravity high of 85 mgal and Marius Hills likewise have a gravity high of 62 mgal.The subsatellite data is too sparse at present to definitely determine new gravity anomaly locations. The spacecraft is functioning well and a dense data block is being obtained, which will provide a new gravity map from ±95° longitude to ±30 latitude. Since periapsis altitudes are following relatively close to predicted altitudes, it seems fairly safe at this point to believe the subsatellite lifetime will be at least one year.     

Mean rates of the orbital elements of a satellite perturbed by a lens shaped mass concentration

Long arc gravity analysis of lunar orbiter tracking data in the past has been carried out with the help of averaged equations of motion, in which short period effects have been suppressed. This procedure has required that the harmonic terms in the gravity potential be averaged over an orbital period. In the present paper, we extend this technique to mass points and mass discs in the gravity field. This required the evaluation of expressions for the mean rates of the orbit elements for a satellite perturbed by a lens shaped mass concentration. Corresponding expressions for the perturbations due to a mass point are obtained in the limit as the lens radius goes to zero. The derived equations have been programmed on the UNIVAC 1108 computer, and the results checked by numerical differencing.     

Geoid and Gravity in Earth Sciences – An Overview

Precise global geoid and gravity anomaly information serves essentially three different kinds of applications in Earth sciences: gravity and geoid anomalies reflect density anomalies in oceanic and continental lithosphere and the mantle; dynamic ocean topography as derived from the combination of satellite altimetry and a global geoid model can be directly transformed into a global map of ocean surface circulation; any redistribution or exchange of mass in Earth system results in temporal gravity and geoid changes. After completion of the dedicated gravity satellite missions GRACE and GOCE a high standard of global gravity determination, both of the static and of the time varying field will be attained. Thus, it is the right time to investigate the future needs for improvements in the various fields of Earth sciences and to define the right strategy for future gravity field satellite missions.     

A harmonic analysis of lunar topography

A global lunar topographic map has been derived from existing Earth-based and orbital observations supplemented in areas without data by a linear autocovariance predictor. Of 2592 bins, each 5° square, 1380 (64.7% by area) contain at least one measurement. A spherical harmonic analysis to degree 12 yields a mean radius of 1737.53 ± 0.03 km (formal standard error) and an offset of the center of figure of 1.98±0.06 km toward (19±2)°S, (194±1)°E. A Bouguer gravity map, derived from a 12-degree free-air gravity model and the present topography data, is presented for an elevation of 100 km above the mean surface. It is confirmed that the low-degree gravity harmonics are determined primarily by surface height variations and only secondarily by lateral density variations.     

Dynamics of Liquid Mass Spreading over a Planetary Surface

The behavior of liquid mass poured out on the surface of a rotating planet is investigated. Analysis of the numerical experiments indicates that the spreading pattern of the produced spot depends significantly on the nondimensional number Fric that describes the relationship between such parameters of the problem as the acceleration of gravity, the Coriolis parameter, the coefficient of friction, and the depth scale of the spot. In particular, for Fric < 0.1, the spot is shown to make concentric oscillations as it spreads whose origin is similar to that of Poincare waves.     

Gravity,topography, and crustal evolution of Venus

The gravity anomalies of Venus, although small by comparison with those on Mars and the Moon, are still much larger than those on Earth for large features. On Venus, even the low-degree spherical harmonic terms for Venus' gravity field indicate a close association of broad positive gravity anomalies with major topographic highs. This is striking contrast to the situation on Earth, where the broad regional gravity anomalies show little correlation with continental masses or plate tectonic features, but instead appear to be caused by deep mass anomalies.A method for estimating radial gravity anomalies from line-of-sight acceleration data, their interpolation, and use of iteration for improved radial anomaly estimates is outlined. A preliminary gravity anomaly map of Venus at spacecraft altitude prepared using first estimate values is presented. A profile across the western part of Aphrodite along longitude 85 E was analyzed using time-series techniques. An elastic plate model would require a plate thickness of about 180 to 200 km to match the general amplitude of the observed gravity anomaly (about 33 mgal): a thickness much greater than that found for earth structures and, because of high surface temperatures, unlikely for Venus. An Airy isostatic model convolved with the topography across Aphrodite, however, provides a better match between the predicted and observed gravity anomalies if the nominal crustal thickness is about 70 to 80 km. This thickness is over twice that for continental crust on the earth, and considerably greater than that of the earth's basaltic ocean crust (only 5 km). A different differentiation history for Venus than that of the earth thus is anticipated. High gravity anomalies (+110 mgal) occur over Beta Regio and over the topographic high in eastern Aphrodite; both highs are associated with regions where detected lightning is clustered, and thus the topographic features may be active volcanic constructs. The large gravity anomalies at these two sites of volcanic activity require an explanation different than that indicated for western Aphrodite.     

Reconstruction Of The Subsurface Structure Of The Marquez Impact Crater In Leon County,Texas, Usa,Based On Well‐Log And Gravity Data

Abstract— In Leon County, Texas, USA, the Marquez Dome, an approximately circular 1.2 km diameter zone of disturbed Cretaceous rocks surrounded by shallow dipping Tertiary sediments, has been interpreted by Gibson and Sharpton (1989) and Sharpton and Gibson (1990) as the surface expression of a buried complex impact crater. New gravity and magnetic anomaly data collected over the Marquez Dome have been combined with well‐log and seismic reflection information to develop a better estimate of the overall geometry of the structure. A three‐dimensional model constructed to a depth of 2000 m from all available information indicates a complex crater 13 km in diameter with an uplift in the center of at least 1120 m. The zone of deformation associated with the cratering event is limited to a depth of <1720 m. No impact breccias were recovered in drilling at two locations, 1.1 and 2 km from the center of the structure, and the central uplift may be the only prominent remnant of this impact into unconsolidated, water‐rich sediments. The magnetic anomaly field shows no correlation with the location and extent of the structure.     

Lunar surface mass distribution from dynamical point-mass solution

Combined efforts of the Jet Propulsion Laboratory and Aerospace Corporation have provided a front side lunar gravity field using the Doppler tracking data from the United States Lunar Orbiters IV and V. Data reduction was accomplished with a model which included all dynamical motion due to gravitational perturbations, as well as all tracking geometries. The field is represented as a grid of 580 surface mass points which are contoured and show correlations with various lunar surface features.This paper presents the results of one phase of research carried out at the Jet Propulsion Laboratory, California Institute of Technology, under Contract No. NAS 7-100, sponsored by the National Aeronautics and Space Administration.