Zeros of orthogonal polynomials

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 Moon's 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.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/1999JE001103

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

High-resolution gravity data obtained from the dual Gravity Recovery and Interior Laboratory (GRAIL) spacecraft show that the bulk density of the Moon's 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.

/pdf/the-crust-of-the-moon-as-seen-by-grail-1glf8bzv6k.pdf

The Crust of the Moon as Seen by GRAIL

Lunar sourcebook. A user's guide to the moon

http://www.geo.arizona.edu/%7Ereiners/Leeetal2009.pdf

Constraints on the depths and temperatures of basaltic magma generation on Earth and other terrestrial planets using new thermobarometers for mafic magmas

Mars’ tidally forced nutation can be resonantly amplified owing to a rotational normal mode called the Free Core Nutation (FCN) which exists because the mantle and fluid part of the core can have a relative rotational motion [1]. The period of the FCN and the amplitude of the nutation depend on the moments of inertia of the mantle and core, as well as on the deformation of the planet due to rotation rate variations and tidal forcing. One of the goals of the RISE experiment on InSight [2] and of the future LaRa experiment on ExoMars 2020 is to infer the core radius of Mars by measuring nutation. Precise core radius determination from the FCN period requires knowledge of the core shape. Here we study how non-hydrostatic core shape models affect the FCN and discuss to what extent the shape of the core could be inferred if its radius were known.

/pdf/non-hydrostatic-effects-on-mars-nutation-3n7jjovtz7.pdf

Non-hydrostatic effects on Mars' nutation

In the past decades, numerous efforts have been made to estimate planetary heat flows [1]. Planetary cooling is what drives the evolution of a planet, and the measured heat flow constrains models of both thermal evolution and planetary bulk composition. As part of the Apollo program, heat flow experiments were carried out during Apollo 15 and 17 missions. These experiments measured both surface and subsurface temperatures, and analysis of the 4 years of data provided estimates of the near surface temperature gradient, thermal diffusivity, thermal conductivity and heat flow [2]. A striking result was the large difference in measures between the two experiments: 21 and 16 mWm−2 at Apollo 15 and 17 landing site, respectively. This variation has been explained by differences in radioactive elements abundance between the two regions. Unfortunately, both landing sites are on the edge of an anomalous thorium-rich geochemical province, the Procellarum KREEP terrane, and this has made estimation of the Moon’s global heat flow difficult [3]. Langseth and coworkers analyzed the heat flow experiment data in two steps [2]. First, the thermal diffusivity was calculated from the attenuation of the annual thermal wave’s amplitude with depth. Density and thermal capacity from returned samples were then used to deduce the thermal conductivity. The annual signal, due to the eccentricity of the Earth’s orbit about the Sun, and the daily thermal waves were then subtracted from the temperature profile to estimate the mean temperature gradient, and the heat flow was finally calculated by multiplying the mean thermal gradient and thermal conductivity. As an example, it can be seen from Figure 1 that the Apollo time series appear to possess a modulation of the annual signal that was not considered in the original analysis. As shown below, this is likely a result of the 18.6 years precession of the lunar nodes which has previously been neglected. A long-term temperature increase is also observed in the data that is still not well understood. Here we deal with the question of whether or not this long term increase could be a result of the 18.6 year precessional signal. Furthermore, whether the modulation of the annual signal seen in Figure 1 affects the estimation of the thermal diffusivity or not will be investigated. To do so, we use a thermal model of the lunar regolith that takes into account both thermal conduction and the radiative transport of energy [4]. Figure 1: Apollo 15 surface temperature evolution during the complete span of the mission. Plotted are the maximum temperatures encountered during each lunation as inferred from the thermocouples suspended about the lunar surface. We can see an increase of 2K in the amplitude of the annual thermal wave during this three years period.

/pdf/the-heat-flow-of-the-moon-influence-of-long-term-orbital-23pfr2152z.pdf

The heat flow of the Moon: influence of long term orbital signals

The InSight mission [1] landed in November 2018 in the Elysium Planitia region [2] bringing the first geophysical observatory to Mars. Since February 2019 the seismometer SEIS [3] has continuously ...

/pdf/seismic-velocities-distribution-in-a-3d-mantle-implications-3dyquenzm9.pdf

Seismic Velocities Distribution in a 3D Mantle: Implications for InSight Measurements

Over the past decades, global geodynamic models have been used to investigate the thermal evolution of terrestrial planets. With the increase of computational power and improvement of numerical techniques, these models have become more complex, and simulations are now able to use a high resolution 3D spherical shell geometry and to account for strongly varying viscosity, as appropriate for mantle materials. In this study we review global 3D geodynamic models that have been used to study the thermal evolution and interior dynamics of Mars. We discuss how these models can be combined with local and global observations to constrain the planet’s thermal history. In particular, we use the recent InSight estimates of the crustal thickness, upper mantle structure, and core size to show how these constraints can be combined with 3D geodynamic models to improve our understanding of the interior dynamics, present-day thermal state and temperature variations in the interior of Mars. Our results show that the crustal thickness variations control the surface heat ﬂow and the elastic thickness pattern, as well as the location of melting zones in the present-day martian mantle. The lithospheric temperature and the seismic velocities pattern in the shallow mantle reﬂect the crustal thickness pattern. The large size of the martian core leads to a smaller scale convection pattern in the mantle than previously suggested. Strong mantle plumes that produce melt up to recent times become focused in Tharsis and Elysium, while weaker plumes are distributed throughout the mantle. The thickness of the seismogenic layer, where seismic events can occur, can be used to discriminate between geodynamic models, if the source depth and location of seismic events is known. Furthermore model predictions of present-day martian seismicity can be compared to the values measured by InSight. Future models need to consider recent estimates from the present-day elastic lithosphere thickness at the north pole of Mars, the eﬀects of lateral variations of seismic velocities on waves propagation through the mantle and lithosphere, and to test the spatial distribution of seismicity by comparing model predictions to observations.

Interior Dynamics and Thermal Evolution of Mars -- a Geodynamic Perspective

The shallowest intracrustal layer (extending to 8 ± 2 km depth) beneath the Mars InSight Lander site exhibits low seismic wave velocity, which is likely related to a combination of high porosity and other lithological factors. The SsPp phase, an SV‐ to P‐wave reflection on the receiver side, is naturally suited for constraining the seismic structure of this top crustal layer since its prominent signal makes it observable with a single station without the need for stacking. We have analyzed six broadband and low‐frequency seismic events recorded on Mars and made the first coherent detection of the SsPp phase on the red planet. The timing and amplitude of SsPp confirm the existence of the ∼8 km interface in the crust and the large wave speed (or impedance) contrast across it. With our new constraints from the SsPp phase, we determined that the average P‐wave speed in the top crustal layer is between 2.5 and 3.2 km/s, which is a more precise and robust estimate than the previous range of 2.0–3.5 km/s obtained by receiver function analysis. The low velocity of Layer 1 likely results from the presence of relatively low‐density lithified sedimentary rocks and/or aqueously altered igneous rocks that also have a significant amount of porosity, possibly as much as 22%–30% by volume (assuming an aspect ratio of 0.1 for the pore space). These porosities and average P‐wave speeds are compatible with our current understanding of the upper crustal stratigraphy beneath the InSight Lander site.

Mark A. Wieczorek

Papers

Non-hydrostatic effects on Mars' nutation

The heat flow of the Moon: influence of long term orbital signals

Seismic Velocities Distribution in a 3D Mantle: Implications for InSight Measurements

Interior Dynamics and Thermal Evolution of Mars -- a Geodynamic Perspective

Crustal Structure Constraints From the Detection of the SsPp Phase on Mars