Frank G. Lemoine

Mars Orbiter Laser Altimeter: Experiment summary after the first year of global mapping of Mars

The Mars Orbiter Laser Altimeter (MOLA), an instrument on the Mars Global Surveyor spacecraft, has measured the topography, surface roughness, and 1.064-μm reflectivity of Mars and the heights of volatile and dust clouds. This paper discusses the function of the MOLA instrument and the acquisition, processing, and correction of observations to produce global data sets. The altimeter measurements have been converted to both gridded and spherical harmonic models for the topography and shape of Mars that have vertical and radial accuracies of ~1 m with respect to the planets center of mass. The current global topographic grid has a resolution of 1/64° in latitude × 1/32° in longitude (1 × 2 km^2 at the equator). Reconstruction of the locations of incident laser pulses on the Martian surface appears to be at the 100-m spatial accuracy level and results in 2 orders of magnitude improvement in the global geodetic grid of Mars. Global maps of optical pulse width indicative of 100-m-scale surface roughness and 1.064-μm reflectivity with an accuracy of 5% have also been obtained.

The Crust of the Moon as Seen by GRAIL

The Holy GRAIL? The gravity field of a planet provides a view of its interior and thermal history by revealing areas of different density. GRAIL, a pair of satellites that act as a highly sensitive gravimeter, began mapping the Moons gravity in early 2012. Three papers highlight some of the results from the primary mission. Zuber et al. (p. 668, published online 6 December) discuss the overall gravity field, which reveals several new tectonic and geologic features of the Moon. Impacts have worked to homogenize the density structure of the Moons upper crust while fracturing it extensively. Wieczorek et al. (p. 671, published online 6 December) show that the upper crust is 35 to 40 kilometers thick and less dense—and thus more porous—than previously thought. Finally, Andrews-Hanna et al. (p. 675, published online 6 December) show that the crust is cut by widespread magmatic dikes that may reflect a period of expansion early in the Moons history. The Moons gravity field shows that the lunar crust is less dense and more porous than was thought. High-resolution gravity data obtained from the dual Gravity Recovery and Interior Laboratory (GRAIL) spacecraft show that the bulk density of the Moons highlands crust is 2550 kilograms per cubic meter, substantially lower than generally assumed. When combined with remote sensing and sample data, this density implies an average crustal porosity of 12% to depths of at least a few kilometers. Lateral variations in crustal porosity correlate with the largest impact basins, whereas lateral variations in crustal density correlate with crustal composition. The low-bulk crustal density allows construction of a global crustal thickness model that satisfies the Apollo seismic constraints, and with an average crustal thickness between 34 and 43 kilometers, the bulk refractory element composition of the Moon is not required to be enriched with respect to that of Earth.

Recent Greenland ice mass loss by drainage system from satellite gravity observations.

Mass changes of the Greenland Ice Sheet resolved by drainage system regions were derived from a local mass concentration analysis of NASA–Deutsches Zentrum für Luftund Raumfahrt Gravity Recovery and Climate Experiment (GRACE mission) observations. From 2003 to 2005, the ice sheet lost 101 ± 16 gigaton/year, with a gain of 54 gigaton/year above 2000 meters and a loss of 155 gigaton/year at lower elevations. The lower elevations show a large seasonal cycle, with mass losses during summer melting followed by gains from fall through spring. The overall rate of loss reflects a considerable change in trend (–113 ± 17 gigaton/year) from a near balance during the 1990s but is smaller than some other recent estimates.

The shape and internal structure of the moon from the clementine mission.

Global topographic and gravitational field models derived from data collected by the Clementine spacecraft reveal a new picture of the shape and internal structure of the moon. The moon exhibits a 16-kilometer range of elevation, with the greatest topographic excursions occurring on the far side. Lunar highlands are in a state of near-isostatic compensation, whereas impact basins display a wide range of compensation states that do not correlate simply with basin size or age. A global crustal thickness map reveals crustal thinning under all resolvable lunar basins. The results indicate that the structure and thermal history of the moon are more complex than was previously believed.

The Development of the NASA GSFC and NIMA Joint Geopotential Model

The NASA Goddard Space Flight Center, the National Imagery and Mapping Agency (NIMA; formerly the Defense Mapping Agency or DMA) and The Ohio State University have collaborated to produce EGM96, an improved degree 360 spherical harmonic model representing the Earth’s gravitational potential. This model was developed using: (1) satellite tracking data from more than 20 satellites, including new data from GPS and TDRSS, as well as altimeter data from TOPEX, GEOSAT and ERS-1. (2) 30’ x 30’ terrestrial gravity data from NIMA’s comprehensive archives, including new measurements from areas such as the former Soviet Union, South America, Africa, Greenland, and elsewhere. (3) 30’ x 30’ gravity anomalies derived from the GEOSAT Geodetic Mission altimeter data, as well as altimeter derived anomalies derived from ERS-1 by KMS (Kort and Matrikelstyrelsen, Denmark) in regions outside the GEOSAT coverage. The high degree solutions were developed using two different model estimation techniques: quadrature, and block diagonal. The final model is a composite solution consisting a combination solution to degree 70, a block diagonal solution to degree 359, and the quadrature model at degree 360. This new model will be used to define an undulation model that will be the basis for an update of the WGS-84 geoid. In addition, the model will contribute to oceanographic studies by improving the modeling of the ocean geoid and to geodetic positioning using the Global Positioning System (GPS).

Initial observations from the Lunar Orbiter Laser Altimeter (LOLA)

As of June 19, 2010, the Lunar Orbiter Laser Altimeter, an instrument on the Lunar Reconnaissance Orbiter, has collected over 2.0 × 10^9 measurements of elevation that collectively represent the highest resolution global model of lunar topography yet produced. These altimetric observations have been used to improve the lunar geodetic grid to ~10 m radial and ~100 m spatial accuracy with respect to the Moons center of mass. LOLA has also provided the highest resolution global maps yet produced of slopes, roughness and the 1064-nm reflectance of the lunar surface. Regional topography of the lunar polar regions allows precise characterization of present and past illumination conditions. LOLAs initial global data sets as well as the first high-resolution digital elevation models (DEMs) of polar topography are described herein.

Topography of the Moon from the Clementine lidar

Range measurements from the lidar instrument carried aboard the Clementine spacecraft have been used to produce an accurate global topographic model of the Moon. This paper discusses the function of the lidar; the acquisition, processing, and filtering of observations to produce a global topographic model; and the determination of parameters that define the fundamental shape of the Moon. Our topographic model; a 72nd degree and order spherical harmonic expansion of lunar radii, is designated Goddard Lunar Topography Model 2 (GLTM 2). This topographic field has an absolute vertical accuracy of approximately 100 m and a spatial resolution of 2.5°. The field shows that the Moon can be described as a sphere with maximum positive and negative deviations of ∼8 km, both occurring on the farside, in the areas of the Korolev and South Pole-Aitken (S.P.-Aitken) basins. The amplitude spectrum of the topography shows more power at longer wavelengths as compared to previous models, owing to more complete sampling of the surface, particularly the farside. A comparison of elevations derived from the Clementine lidar to control point elevations from the Apollo laser altimeters indicates that measured relative topographic heights generally agree to within -200 m over the maria. While the major axis of the lunar gravity field is aligned in the Earth-Moon direction, the major axis of topography is displaced from this line by approximately 10° to the east and intersects the farside 24° north of the equator. The magnitude of impact basin topography is greater than the lunar flattening (∼2 km) and equatorial ellipticity (-800 m), which imposes a significant challenge to interpreting the lunar figure. The floors of mare basins are shown to lie close to an equipotential surface, while the floors of unflooded large basins, except for S.P.-Aitken, lie above this equipotential. The radii of basin floors are thus consistent with a hydrostatic mechanism for the absence of significant farside maria except for S.P.-Aitken, whose depth and lack of mare require significant internal compositional and/or thermal heterogeneity. A macroscale surface roughness map shows that roughness at length scales of 10 1 -10 2 km correlates with elevation and surface age.

Gravity Field of the Moon from the Gravity Recovery and Interior Laboratory (GRAIL) Mission

The Holy GRAIL? The gravity field of a planet provides a view of its interior and thermal history by revealing areas of different density. GRAIL, a pair of satellites that act as a highly sensitive gravimeter, began mapping the Moons gravity in early 2012. Three papers highlight some of the results from the primary mission. Zuber et al. (p. 668, published online 6 December) discuss the overall gravity field, which reveals several new tectonic and geologic features of the Moon. Impacts have worked to homogenize the density structure of the Moons upper crust while fracturing it extensively. Wieczorek et al. (p. 671, published online 6 December) show that the upper crust is 35 to 40 kilometers thick and less dense—and thus more porous—than previously thought. Finally, Andrews-Hanna et al. (p. 675, published online 6 December) show that the crust is cut by widespread magmatic dikes that may reflect a period of expansion early in the Moons history. The Moons gravity field reveals that impacts have homogenized the density of the crust and fractured it extensively. Spacecraft-to-spacecraft tracking observations from the Gravity Recovery and Interior Laboratory (GRAIL) have been used to construct a gravitational field of the Moon to spherical harmonic degree and order 420. The GRAIL field reveals features not previously resolved, including tectonic structures, volcanic landforms, basin rings, crater central peaks, and numerous simple craters. From degrees 80 through 300, over 98% of the gravitational signature is associated with topography, a result that reflects the preservation of crater relief in highly fractured crust. The remaining 2% represents fine details of subsurface structure not previously resolved. GRAIL elucidates the role of impact bombardment in homogenizing the distribution of shallow density anomalies on terrestrial planetary bodies.

An improved solution of the gravity field of Mars (GMM‐2B) from Mars Global Surveyor

A spherical harmonic solution of the Mars gravity field to degree and order 80, Goddard Mars Model 2B (GMM-2B), has been developed using X band tracking data of Mars Global Surveyor (MGS) from October 1997 to February 2000 and altimeter crossovers formed from the Mars Orbiter Laser Altimeter (MOLA) data between March and December 1999. During the mapping mission, MGS was located in a near-polar (92.9° inclination) and near-circular orbit at a mean altitude of 400 km. The tracking data from this orbit provide a detailed, global, and high resolution view of the gravity field of Mars. Mars gravity solutions are stable to 60×60 even without application of a Kaula power law constraint. The Valles Marineris is resolved distinctly with lows reaching −450 mGals. Olympus Mons and its aureole are both separately resolved, and the volcano has a peak anomaly of 2950 mGals. The global correlation of the GMM-2B gravity coefficients with MOLA-derived topography is 0.78 through degree 60, and the correlation remains above 0.6 through degree 62. The global gravity anomaly error predicted from the GMM-2B error covariance through 60×60 is 11 mGal. The global geoid error from GMM-2B through 60×60 is 1.8 m. MGS orbit quality using GMM-2B, as measured by overlapping orbital arcs, is 1 m in the radial direction and 10 m in total position.

The lunar crust: Global structure and signature of major basins

New lunar gravity and topography data from the Clementine Mission provide a global Bouguer anomaly map corrected for the gravitational attraction of mare fill in mascon basins. Most of the gravity signal remaining after corrections for the attraction of topography and mare fill can be attributed to variations in depth to the lunar Moho and therefore crustal thickness. The large range of global crustal thickness (-20-120 km) is indicative of major spatial variations in melting of the lunar exterior and/or significant impact-related redistribution. The 61-km average crustal thickness, constrained by a depth-to-Moho measured during the Apollo 12 and 14 missions, is preferentially distributed toward the farside, accounting for much of the offset in center-of-figure from the center-of-mass. While the average farside thickness is 12 km greater than the nearside, the distribution is nonuniform, with dramatic thinning beneath the farside, South Pole-Aitken basin. With the global crustal thickness map as a constraint, regional inversions of gravity and topography resolve the crustal structure of major mascon basins to half wavelengths of 150 km. In order to yield crustal thickness maps with the maximum horizontal resolution permitted by the data, the downward continuation of the Bouguer gravity is stabilized by a three- dimensional, minimum-slope and curvature algorithm. Both mare and non-mare basins are characterized by a central upwarped moho that is surrounded by rings of thickened crust lying mainly within the basin rims. The inferred relief at this density interface suggests a deep structural component to the surficial features of multiring lunar impact basins. For large (>300 km diameter) basins, moho relief appears uncorrelated with diameter, but is negatively correlated with basin age. In several cases, it appears that the multiring structures were out of isostatic equilibrium prior to mare emplacement, suggesting that the lithosphere was strong enough to maintain their state of stress to the present.