The anelastic reaction of planet-forming materials is successfully described by the Andrade rheological model, which presents an extension of the simple Maxwell rheology. In addition to the instantaneous elastic deformation and the long-term viscous creep, the Andrade rheology incorporates the transient creep in metals, ices, and silicates, and is able to explain the tidal parameters of planets even in cases, where the Maxwell model requires the assumption of unrealistically low mantle viscosities. In this work, we discuss the applications of the Andrade model in planetary science, the parameters used in the literature, and their justification by material science and geodesy. We also examine the topic of relating the empirical tidal parameters to the mantle viscosity of moons and terrestrial planets and assess the limitations resulting from the uncertainties in the rheological parameters. Our study illustrates the necessity for future measurements that would help to better calibrate the rheological models to conditions relevant to the deep interiors of planets and moons.

The composition of basaltic melts in equilibrium with the mantle can be determined for several Martian meteorites and in-situ rover analyses. We use the melting model MAGMARS to reproduce these primary melts and estimate the bulk composition and temperature of the mantle regions from which they originated. We find that most mantle sources are depleted in CaO and Al2O3 relative to models of the bulk silicate Mars and likely represent melting residues or magma ocean cumulates. The concentrations of Na2O, K2O, P2O5, and TiO2 are variable and often less depleted, pointing to the re-fertilization of the sources by fluids and low-degree melts, or the incorporation of residual trapped melts during the crystallization of the magma ocean. The mantle potential temperatures of the sources are 1400-1500 ºC, regardless of the time at which they melted and within the range of the most recent predictions from thermochemical evolution models.

A document by Aymeric Fleury. Click on the document to view its contents.

Regardless of the steady increase of computing power during the last decades, 3D numerical models continue to be used in specific setups to investigate the thermochemical convection of planetary interiors, while the use of 2D geometries is still favored in most exploratory studies involving a broad range of parameters. The 2D cylindrical and the more recent 2D spherical annulus geometries are predominantly used in this context, but the extent to how well they reproduce the 3D spherical shell in comparison to each other, and in which setup, has not yet been extensively studied. Here we performed a thorough and systematic study in order to assess which 2D geometry reproduces best the 3D one. In a first set of models, we investigated the effects of the geometry on thermal convection in steady-state setups while varying a broad range of parameters. Additional thermal evolution models of three terrestrial bodies, respectively Mercury, the Moon, and Mars, which have different interior structures, were used to compare the 2D and 3D geometries. Our study shows that the spherical annulus geometry improves results compared to cylindrical geometry when reproducing 3D models. Our results can be used to determine for which setup acceptable differences are expected when using a 2D instead of a 3D geometry.

A document by Tilman Spohn. Click on the document to view its contents.

Regardless of the steady increase of computing power during the last decades, 3D numerical models continue to be used in specific setups to investigate the thermochemical convection of planetary interiors, while the use of 2D geometries is still favored in most exploratory studies involving a broad range of parameters. The 2D cylindrical and the more recent 2D spherical annulus geometries are predominantly used in this context, but the extent to how well they reproduce the 3D spherical shell in comparison to each other, and in which setup, has not yet been extensively studied. Here we performed a thorough and systematic study in order to assess which 2D geometry reproduces best the 3D one. In a first set of models, we investigated the effects of the geometry on thermal convection in steady-state setups while varying a broad range of parameters. Additional thermal evolution models of three terrestrial bodies, respectively Mercury, the Moon, and Mars, which have different interior structures, were used to compare the 2D and 3D geometries. Our study shows that the spherical annulus geometry improves results compared to cylindrical geometry when reproducing 3D models. Our results can be used to determine for which setup acceptable differences are expected when using a 2D instead of a 3D geometry.

A document by Adrien Pierre Michel Broquet. Click on the document to view its contents.

Basaltic melts are produced when convection adiabatically brings deep and hot mantle to lower pressures. Such primary melts were extracted from the mantle of Mars, crystallized near the surface and progressively built the Martian crust. This process displaced a large fraction of the heat producing elements from the mantle to the crust and created an insulating layer that slowed down further cooling of the mantle. The complex crust-mantle system controlled many aspects of the geologic history of Mars, including the development of an atmosphere and whether conditions favorable to life could have existed. Our knowledge of the mineralogy, chemical composition and physical properties of the crust of Mars is rapidly expanding. Global geodynamical models can be used to interpret the available data and constrain the processes of crust-mantle differentiation. However, existing models still treat melting in a simplified way. For example, the degree of melting is often assumed to increase linearly above the solidus temperature, while the density of the residue is assumed to decrease linearly. Calculating the density of the residual mantle more accurately is critical because the compositional buoyancy that develops during partial melting fundamentally modifies mantle dynamics. Here, we present an improved parametrization of partial melting of the Martian mantle, which will be combined with the convection code Gaia. We created a new empirical model of melting that calculates the composition of the extracted melts and, when combined to thermodynamic models (e.g., Perple_X), the density of the corresponding residual mantle. Another advantage of the new melting parametrization is that the major-element composition of partial melts can be tracked and used to constrain the petrogenesis of surface rocks. Preliminary results will be compared to available Martian rocks believed to represent primary mantle melts or melts affected by minor fractional crystallization.

The overturn of mantle cumulates following the crystallization of the lunar magma ocean – particularly the sinking of ilmenite-bearing cumulates (IBC) – provides an explanation for several aspects of the Moon’s evolution. However, the growth of a stagnant lid due to the temperature dependence of the viscosity tends to prevent IBC from sinking. Here, we investigate the dynamics of the overturn based on a composition-dependent rheology coupling diffusion and dislocation creep of major lunar mantle minerals via three alternative mixing models: isostrain, isostress and Minimized Power Geometric (MPG). The pre-overturn structure is obtained from a fractional crystallization model of the lunar magma ocean, which predicts the formation of a 36-km-thick IBC layer. The possibility of overturning this layer strongly depends on the choice of the rheological mixing model. The isostress model allows for a rapid and complete overturn, while the isostrain and the experiment-based MPG models do not allow IBC to sink. If IBC started sinking and mixing with the underlying mantle during magma ocean solidification, IBC could be initially distributed across a layer with a thickness of up to 150 km, whose partial overturn is always possible, independent of the rheological model. These results highlight the importance of improving rheological models for relevant lunar materials. In all cases, the overturn occurs via small-scale instabilities.

Understanding the processes that led Venus to its current state and will drive its future evolution is one of the main challenges of the next generation of space missions. In this work we analyze the retrieval of the spin vector, the tidal response and the moment of inertia of Venus with VERITAS, a Discovery-class mission proposed to NASA. By simulating the joint analysis of Doppler tracking data and tie points provided by the onboard synthetic aperture radar, we show that VERITAS would provide strong constraints on the interior structure of the planet. In particular we show that VERITAS would provide accuracies in the estimates of the tidal Love number k2 to 3.9×10-4, its tidal phase lag to 0.04o, and the moment of inertia factor to 1.4×10-3 (0.4% of the expected value).

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 recorded Mars’ seismic activity, and a list of the seismic events is available in the InSight Marsquake Service catalog [4]. In this study, we predict present-day seismic velocities in the Martian interior using the 3D thermal evolution models of [5]. We then use the 3D velocity distributions to interpret seismic observations recorded by InSight. Our analysis is focused on the two high quality events S0173a and S0235b. Both have distinguishable P- and S-wave arrivals and are thought to originate in Cerberus Fossae [6], a potentially active fault system [7]. Our results show that models with a crust containing more than half of the total amount of heat producing elements (HPE) of the bulk of Mars lead to large variations of the seismic velocities in the lithosphere. A seismic velocity pattern similar to the crustal thickness structure is observed at depths larger than 400 km for cases with cold and thick lithospheres. Models, with less than 20% of the total HPE in the crust have thinner lithospheres with shallower but more prominent low velocity zones. The latter, lead to shadow zones that are incompatible with the observed P- and S-wave arrivals of seismic events occurring in Cerberus Fossae, in 20° - 40° epicentral distance. We therefore expect that future high-quality seismic events have the potential to further constrain the amount of HPE in the Martian crust. Future work will combine the seismic velocities distribution calculated in this study with modeling of seismic wave propagation [8, 9]. This will help to assess the effects of a 3D thermal structure on the waveforms and provide a powerful framework for the interpretation of InSight’s seismic data. [1] Banerdt et al., Nat. Geo. 2020; [2] Golombek et al., Nat. Comm. 2020, [3] Lognnoné et al., Nat. Geo. 2020, [4] InSight MQS, Mars Seismic Catalogue, InSight Mission V3, 2020, https://doi.org/10.12686/A8, [5] Plesa et al., GRL 2018, [6] Giardini et al., Nat. Geo. 2020, [7] Taylor et al., JGR 2013, [8] Bozdag et al., SSR 2017, [9] Komatitsch & Tromp, GJI 2002.

The martian surface is predominantly covered by FeO-rich basalts and their alteration products. Several samples, either analyzed in situ by rovers or recovered as meteorites, might represent primitive (i.e. near-primary) basaltic melts that can shed light on the mineralogy, the bulk composition, and the temperature of their mantle sources. We recently developed a new melting model, called MAGMARS, that can predict the melt compositions of FeO-rich mantles and the martian mantle in particular (Collinet et al., submitted to JGR:P). It represents a more accurate alternative to pMELTS (Ghiorso et al., 2002, G3), which systematically overestimates the FeO and MgO content of martian melts and underestimates the SiO2 content (by up to 8 wt.%). MAGMARS can simulate near-fractional and batch melting of various mantle compositions. For example, MAGMARS can produce melts identical to the Adirondack-class basalts by near-fractional melting, between 2.3 and 1.7 GPa, of a depleted mantle with a potential temperature (Tp) of 1390°C (~7 wt.% melt fraction). For this study, MAGMARS is applied to all other martian basalts from which the primary melt compositions can be inferred in order to constrain their mantle sources: the Columbia hills basalts, igneous rocks from Gale crater, shergottites, nakhlites and Northwest Africa (NWA) 7034/7533. We find that a few basaltic clasts in the pre-Noachian polymict regolith breccia NWA 7034/7533 are the only samples with bulk compositions that could represent melts derived from a primitive mantle. The Columbia hills basalts (Gusev crater), alkali-rich rocks from Gale crater, nakhlites and enriched shergottites are most easily reproduced by melting depleted mantle reservoirs that were re-fertilized to different degrees in alkalis by fluids or melts (i.e. metasomatized sources). Most martian basalts, with the exception of depleted shergottites, can be produced from martian mantle reservoirs with Mg# comprised between 75 and 81. From this sample set, the melting conditions of the martian mantle seem to remain relatively stable through time (Tp = 1400 ± 100 ºC and P = 2 ± 0.5 GPa) but the depleted nature of all mantle sources sampled after the pre-Noachian points towards an early crust-mantle differentiation.