Mark A. Wieczorek

Major lunar crustal terranes: Surface expressions and crust‐mantle origins

In light of global remotely sensed data, the igneous crust of the Moon can no longer be viewed as a simple, globally stratified cumulus structure, composed of a flotation upper crust of anorthosite underlain by progressively more mafic rocks and a residual-melt (KREEP) sandwich horizon near the base of the lower crust. Instead, global geochemical information derived from Clementine multispectral data and Lunar Prospector gamma-ray data reveals at least three distinct provinces whose geochemistry and petrologic history make them geologically unique: (1) the Procellarum KREEP Terrane (PKT), (2) the Feldspathic High-lands Terrane (FHT), and (3) the South Pole-Aitken Terrane (SPAT). The PKT is a mafic province, coincident with the largely resurfaced area in the Procellarum-Imbrium region whose petrogenesis relates to the early differentiation of the Moon. Here, some 40% of the Th in the Moons crust is concentrated into a region that constitutes only about 10% of the crustal volume. This concentration of Th (average ∼5 ppm), and by implication the other heat producing elements, U and K, led to a fundamentally different thermal and igneous evolution within this region compared to other parts of the lunar crust. Lower-crustal materials within the PKT likely interacted with underlying mantle materials to produce hybrid magmatism, leading to the magnesian suite of lunar rocks and possibly KREEP basalt. Although rare in the Apollo sample collection, widespread mare volcanic rocks having substantial Th enrichment are indicated by the remote data and may reflect further interaction between enriched crustal residues and mantle sources. The FHT is characterized by a central anorthositic region that constitutes the remnant of an anorthositic craton resulting from early lunar differentiation. Basin impacts into this region do not excavate significantly more mafic material, suggesting a thickness of tens of kilometers of anorthositic crust. The feldspathic lunar meteorites may represent samples from the anorthositic central region of the FHT. Ejecta from deep-penetrating basin impacts outside of the central anorthositic region, however, indicate an increasingly mafic composition with depth. The SPAT, a mafic anomaly of great magnitude, may include material of the upper mantle as well as lower crust; thus it is designated a separate terrane. Whether the SPA basin impact simply uncovered lower crust such as we infer for the FHT remains to be determined.

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.

Localized gravity/topography admittance and correlation spectra on Mars: Implications for regional and global evolution

From gravity and topography data collected by the Mars Global Surveyor spacecraft we calculate gravity/topography admittances and correlations in the spectral domain and compare them to those predicted from models of lithospheric flexure. On the basis of these comparisons we estimate the thickness of the Martian elastic lithosphere (T_e) required to support the observed topographic load since the time of loading. We convert T_e to estimates of heat flux and thermal gradient in the lithosphere through a consideration of the response of an elastic/plastic shell. In regions of high topography on Mars (e.g., the Tharsis rise and associated shield volcanoes), the mass-sheet (small-amplitude) approximation for the calculation of gravity from topography is inadequate. A correction that accounts for finite-amplitude topography tends to increase the amplitude of the predicted gravity signal at spacecraft altitudes. Proper implementation of this correction requires the use of radii from the center of mass (collectively known as the planetary “shape”) in lieu of “topography” referenced to a gravitational equipotential. Anomalously dense surface layers or buried excess masses are not required to explain the observed admittances for the Tharsis Montes or Olympus Mons volcanoes when this correction is applied. Derived T_e values generally decrease with increasing age of the lithospheric load, in a manner consistent with a rapid decline of mantle heat flux during the Noachian and more modest rates of decline during subsequent epochs.

Potential anomalies on a sphere: Applications to the thickness of the lunar crust

A new technique for calculating potential anomalies on a sphere due to finite amplitude relief has been developed. We show that by raising the topography to the nth power and expanding this field into spherical harmonics, potential anomalies due to topography on spherical density interfaces can be computed to arbitrary precision. Using a filter for downward continuing the Bouguer anomaly, we have computed a variety of crustal thickness maps for the Moon, assuming both a homogeneous as well as a dual-layered crust. The crustal thickness maps for the homogeneous model give plausible results, but this model is not consistent with the seismic data, petrologic evidence, and geoid to topography ratios, all of which suggest some form of crustal stratification. Several dual-layered models were investigated, and it was found that only models with both upper and lower crustal thickness variations could satisfy the gravity and topography data. These models predict that the entire upper crust has been excavated beneath the major nearside multiring basins. Additionally, significant amounts of lower crustal material was excavated from these basins, especially beneath Crisium. This model also predicts that mantle material should not have been excavated during the South-Pole Aitken basin forming event, and that lower crustal material should be exposed at the surface in this basin.

Spatiospectral Concentration on a Sphere

We pose and solve the analogue of Slepians time-frequency concentration problem on the surface of the unit sphere to determine an orthogonal family of strictly bandlimited functions that are optimally concentrated within a closed region of the sphere or, alternatively, of strictly spacelimited functions that are optimally concentrated in the spherical harmonic domain. Such a basis of simultaneously spatially and spectrally concentrated functions should be a useful data analysis and representation tool in a variety of geophysical and planetary applications, as well as in medical imaging, computer science, cosmology, and numerical analysis. The spherical Slepian functions can be found by solving either an algebraic eigenvalue problem in the spectral domain or a Fredholm integral equation in the spatial domain. The associated eigenvalues are a measure of the spatiospectral concentration. When the concentration region is an axisymmetric polar cap, the spatiospectral projection operator commutes with a Sturm--Liouville operator; this enables the eigenfunctions to be computed extremely accurately and efficiently, even when their area-bandwidth product, or Shannon number, is large. In the asymptotic limit of a small spatial region and a large spherical harmonic bandwidth, the spherical concentration problem reduces to its planar equivalent, which exhibits self-similarity when the Shannon number is kept invariant.

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.

The “Procellarum KREEP Terrane”: Implications for mare volcanism and lunar evolution

Geophysical, remote-sensing, and sample data demonstrate that the Procellarum and Imbrium regions of the Moon make up a unique geochemical crustal province (here dubbed the Procellarum KREEP Terrane). Geochemical studies of Imbriums ejecta and the crustal structure of the Imbrium and Serenitatis basins both suggest that a large portion of the lunar crust in this locale is composed of a material similar in composition to Apollo 15 KREEP basalt. KREEP basalt has about 300 times more uranium and thorium than chondrites, so this implies that a large portion of Moons heat-producing elements is located within this single crustal province. The spatial distribution of mare volcanism closely parallels the confines of the Procellarum KREEP Terrane and this suggests a causal relationship between the two phenomena. We have modeled the Moons thermal evolution using a simple thermal conduction model and show that as a result of the high abundance of heat-producing elements that are found in the Procellarum KREEP Terrane, partial melting of the underlying mantle is an inevitable outcome. Specifically, by placing a 10-km KREEP basalt layer at the base of the crust there, our model predicts that mare volcanism should span most of the Moons history and that the depth of melting should increase with time to a maximum depth of about 600 km. We suggest that the 500-km seismic discontinuity that is observed in the Apollo seismic data may represent this maximum depth of melting. Our model also predicts that the KREEP basalt layer should remain partially molten for a few billion years. Thus the Imbrium impact event most likely excavated into a partially molten KREEP basalt magma chamber. We postulate that the KREEP basalt composition is a by-product of mixing urKREEP with shallow partial melts of the underlying mantle. Since Mg-suite rocks are likely derived from crystallizing KREEP basalt, the provenance of these plutonic rocks is likely to be unique to this region of the Moon.

Thickness of the Martian crust: Improved constraints from geoid‐to‐topography ratios

[1] The average crustal thickness of the southern highlands of Mars was investigated by calculating geoid-to-topography ratios (GTRs) and interpreting these in terms of an Airy compensation model appropriate for a spherical planet. We show that (1) if GTRs were interpreted in terms of a Cartesian model, the recovered crustal thickness would be underestimated by a few tens of kilometers, and (2) the global geoid and topography signals associated with the loading and flexure of the Tharsis province must be removed before undertaking such a spatial analysis. Assuming a conservative range of crustal densities (2700–3100 kg m � 3 ), we constrain the average thickness of the Martian crust to lie between 33 and 81 km (or 57 ± 24 km). When combined with complementary estimates based on crustal thickness modeling, gravity/topography admittance modeling, viscous relaxation considerations, and geochemical mass balance modeling, we find that a crustal thickness between 38 and 62 km (or 50 ± 12 km) is consistent with all studies. Isotopic investigations based on Hf-W and Sm-Nd systematics suggest that Mars underwent a major silicate differentiation event early in its evolution (within the first � 30 Ma) that gave rise to an ‘‘enriched’’ crust that has since remained isotopically isolated from the ‘‘depleted’’ mantle. In comparing estimates of the thickness of this primordial crust with those obtained in this study, we find that at least one third of the Martian crust has an origin dating from the time of accretion and primary differentiation. Subsequent partial melting of the depleted mantle would have given rise to the remaining portion of the crust. While we predict that a large portion of the crust should be composed of ancient ‘‘enriched’’ materials, a representative sample of this primordial crust does not currently exist among the known Martian meteorites. INDEX TERMS: 6225 Planetology: Solar System Objects: Mars; 5417 Planetology: Solid Surface Planets: Gravitational fields (1227); 5430 Planetology: Solid Surface Planets: Interiors (8147); 1227 Geodesy and Gravity: Planetary geodesy and gravity (5420, 5714, 6019); KEYWORDS: Mars, crustal thickness, crustal evolution, geoid, topography

Gravity and Topography of the Terrestrial Planets

This chapter reviews our current knowledge of the gravity and topography of the terrestrial planets and describes the methods that are used to analyze these data. A general review of the mathematical formalism that is used in describing gravity and topography is first given. Next, the basic properties of Earth, Venus, Mars, Mercury, and the Moon are characterized. Following this, the relationship between gravity and topography is quantified, and techniques by which geophysical parameters can be constrained are detailed. Analysis methods include crustal thickness modeling, geoid/topography ratios, spectral admittance and correlation functions, and localized spectral analysis and wavelet techniques. Finally, the major results that have been obtained by modeling the gravity and topography of Earth, Venus, Mars, Mercury, and the Moon are summarized.

Correction to “Localized gravity/topography admittance and correlation spectra on Mars: Implications for regional and global evolution”

[1] In the paper ‘‘Localized gravity/topography admittance and correlation spectra on Mars: Implications for regional and global evolution’’ by Patrick J. McGovern, Sean C. Solomon, David E. Smith, Maria T. Zuber, Mark Simons, Mark A. Wieczorek, Roger J. Phillips, Gregory A. Neumann, Oded Aharonson, and James W. Head (Journal of Geophysical Research, 107(E12), 5136, doi:10.1029/ 2002JE001854, 2002), the thickness of the lithosphere and lithospheric heat flow for a number of regions of Mars and as functions of time were inferred on the basis of gravity/topography admittance spectra. Observed admittances, derived from spherical harmonic expansions localized with the scheme of Simons et al. [1997], were compared with those predicted from models for the flexural response to lithospheric loading [e.g., Turcotte et al., 1981]. Gravity was calculated according to the finite-amplitude scheme of Wieczorek and Phillips [1998]. Estimates for the thickness of the elastic lithosphere Te at the time of loading for each region were converted to equivalent thermal gradient dT/dz and heat flux q by means of an elastic-plastic stressenvelope formalism [McNutt, 1984]. Here we describe a correction required in the calculation of the modeled gravity anomalies; we report new estimates of Te, load density rl, dT/dz, and q from corrected model admittances; and we discuss the implications of the new results. [2] The source of the required correction is a difference in reference radius values. As defined by McGovern et al. [2002], the planetary shape was taken to equal the radius from the center of mass of Mars to the Martian surface expressed as a spherical harmonic expansion and referenced to the mean equatorial radius Req = 3396 km: