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The dense atmosphere of Venus and the planet’s young surface, dominated by volcanic features, bear witness to its past and potentially ongoing volcanic activity. While unique among the terrestrial planets of our Solar System, Venus is likely similar to a myriad of extrasolar worlds [1]. Thus, investigating Venus’s interior structure, thermal history, and magmatic processes may guide our understanding of the evolution and present-day state of an entire class of exoplanets.The present-day geodynamic regime of Venus’s mantle is still debated, but models agree that magmatism played a major role in shaping the atmosphere and surface that we observe today [2]. In this contribution we will summarize the evidence for recent and possibly ongoing magmatic activity in the interior of Venus and show how we can combine current and future observations with thermal evolution models to constrain the planet’s present-day interior structure, dynamics, and magmatic activity. We calculate the tidal deformation and moment of inertia in our models to provide estimates on deep interior parameters. While the tidal Love number k2, which is sensitive to the size and state of the core, has been determined from Magellan and Pioneer Venus Orbiter tracking data with large uncertainties [3], the phase lag of the deformation, whose value is particularly sensitive to the thermal state of the interior, has not yet been measured. A rough estimate of the core size of 3500 km with large (>500 km) uncertainties comes from the moment of inertia factor that was determined from Earth-based radar observations [4]. Our models address the recent volcanic activity that was suggested by several observations [e.g., 5]. In particular, we focus on investigating the constraints coming from estimates of the elastic lithosphere thickness, which is linked to the thermal state of the lithosphere at the time of the formation of geological features. Gravity and topography analyses indicate small elastic thicknesses for a variety of locations including coronae [6], steep-sided domical volcanoes [7], and crustal plateaus [8]. The young age of many surface features on Venus suggests a warm lithosphere at present-day, potentially linked to partial melting in the interior. Moreover, a recent study found that the inferred heat flux at 75 locations on Venus associated with recent volcanic and tectonic activity is similar to the values measured on Earth in areas of active extension [9]. Future measurements of the NASA VERITAS and ESA EnVision missions aim to constrain present-day volcanic and tectonic activity as well as the thickness of major layers (crust, mantle, and core) in the interior of Venus. These measurements will provide unprecedented information to address the interior structure and thermal history of our neighbor, who can teach us about the diversity of evolutionary paths that rocky planets around other stars might have followed.[1] Kane et al., 2019. [2] Rolf et al., 2022. [3] Konopliv and Yodder, 1996. [4] Margot et al., 2021. [5] Smrekar et al., 2010. [6] O’Rourke & Smrekar, 2018. [7] Borrelli et al., 2021. [8] Maia and Wieczorek, 2022. [9] Smrekar et al., 2022.

Geophysical observations will provide key information about the inner structure of the planets and satellites and understanding the internal structure is a strong constraint on the bulk composition and thermal evolution of these bodies. Thus, geophysical observations are a key to uncovering the origin and evolution of the Moon. In this article, we propose the development of an autonomous lunar geophysical experiment package, composed of a suite of instruments and a central station with standardized interface, which can be installed on various future lunar missions. By fixing the interface between instruments and the central station, it would be possible to easily configure an appropriate experiment package for different missions. We describe here a series of geophysical instruments that may be included as part of the geophysical package: a seismometer, a magnetometer, a heat flow probe, and a laser reflector. These instruments will provide mechanical, thermal, and geodetic parameters of the Moon that are strongly related to the internal structure. We discuss the functionality required for future geophysical observations of the Moon, including the development of the central station that will be used commonly by different payloads.

This work reviews the long-term evolution of the atmosphere of Venus, and modulation of its composition by interior/exterior cycling. The formation and evolution of Venus’s atmosphere, leading to contemporary surface conditions, remain hotly debated topics, and involve questions that tie into many disciplines. We explore these various inter-related mechanisms which shaped the evolution of the atmosphere, starting with the volatile sources and sinks. Going from the deep interior to the top of the atmosphere, we describe volcanic outgassing, surface-atmosphere interactions, and atmosphere escape. Furthermore, we address more complex aspects of the history of Venus, including the role of Late Accretion impacts, how magnetic field generation is tied into long-term evolution, and the implications of geochemical and geodynamical feedback cycles for atmospheric evolution. We highlight plausible end-member evolutionary pathways that Venus could have followed, from accretion to its present-day state, based on modeling and observations. In a first scenario, the planet was desiccated by atmospheric escape during the magma ocean phase. In a second scenario, Venus could have harbored surface liquid water for long periods of time, until its temperate climate was destabilized and it entered a runaway greenhouse phase. In a third scenario, Venus’s inefficient outgassing could have kept water inside the planet, where hydrogen was trapped in the core and the mantle was oxidized. We discuss existing evidence and future observations/missions required to refine our understanding of the planet’s history and of the complex feedback cycles between the interior, surface, and atmosphere that have been operating in the past, present or future of Venus.

Fully dynamical 3D simulations that self-consistently model the evolution of mantle flow are routinely used to investigate the thermal history of the interior of rocky planets, and through their nature, they can address both global and local observations in regions of interest. Over the past years, models of the thermal evolution of Mars have been combined with crustal thickness variations derived from gravity and topography data, tidal deformation models, and calculations of the seismic velocities and seismogenic layer thickness to estimate the present-day seismicity. Recent data from the InSight mission about the crustal thickness, upper mantle structure, and core size provide the most direct constraints on the interior structure of Mars. Here we use InSight’s estimates in addition to constraints from tidal deformation, elastic lithosphere thickness, and recent volcanic activity to model the thermal history and present-day state of the interior of Mars. Similar to previous studies (Plesa et al., 2016, 2018), the geodynamical simulations include crustal thickness variations (Fig. 1a). We use the most recent global crustal thickness models of Mars (Wieczorek et al., 2022) that are derived from gravity and topography data and constrained by crustal thickness estimates at the InSight landing site from seismic observations (Knapmeyer-Endrun et al., 2021; Wieczorek et al., 2022). Fig. 1: a) crustal thickness model derived from gravity and topography data and anchored by the crustal thickness at InSight location; b) corresponding heat flow and c) elastic thickness variations at present day; d) average melt fraction and e) average melt zone depth at present day; f) seismogenic layer thickness computed using the 573 K isotherm. The present-day thermal state in the 3D geodynamical models is obtained by running the entire thermal evolution of Mars. The models assume that 55 to 70% of the bulk amount of heat producing elements are stored in the crust as suggested by Knapmeyer-Endrun et al. (2021) in order to avoid wide-spread melting in the interior of Mars at present day. The strong crustal enrichment, and thus a mantle depleted in heat sources, leads to an average present-day lithospheric thickness of about 500 km in good agreement with the thermal lithosphere thickness estimated from the analysis of seismic events (Khan et al., 2021; Duran et al., 2022). Our models show that crustal thickness variations have a first order effect on the temperature distribution in the shallow mantle. Thus, the patterns of the surface heat flow and elastic lithosphere thickness at present day correlate with the crustal thickness variations (Fig. 1b,c). The present-day elastic lithosphere thickness at the north pole of Mars is one of the strongest constraints for thermal evolution models and indicates that the mantle contains less than 45% of the total heat production and/or that the polar cap has not yet reached elastic equilibrium (Broquet et al., 2020). The radius of the core in our models has been set to 1850 km, a value that lies well within the current core radius estimates (Stähler et al., 2021). Such a large core prevents the stability of an endothermic phase transition from wadsleyite/ringwoodite to bridgmanite that was previously proposed to explain the formation of the martian crustal thickness dichotomy and Tharsis through a low degree convection pattern (Harder & Christensen, 1996, Breuer et al., 1998). Current models show a mantle characterized by several mantle plumes distributed throughout the mantle. During the evolution, strong mantle plumes that produce melt up to recent times become focused in regions covered by a thick crust, in particular in the Tharsis province (Fig. 1d,e). We compute the tidal deformation using the interior structure and present-day thermal state from the geodynamic models. For the tidal deformation calculations, we use a semi-analytical model based on the normal mode theory for radially stratified viscoelastic bodies (Sabadini & Vermeersen, 2004) and choose an Andrade rheology. Results show that thermal evolution models with a large core and a dry mantle viscosity can match the latest tidal deformation estimates determined from radio tracking measurements from Mars Odyssey, Mars Reconnaissance Orbiter, and Mars Global Surveyor (Konopliv et al., 2020). Similar to the study of Plesa et al. (2021), we compute the seismic velocities in the entire 3D thermal evolution model. We use the mantle compositions of Taylor (2013), Yoshizaki & McDonough (2020), and include the most recent composition of Khan et al. (2022). Independent of the assumed compositional model, seismic velocity variations show a pattern similar to that of the crustal thickness and these variations can extend to depths of 400 km or deeper for models with a thick lithosphere. Our models can be used to estimate the seismogenic layer thickness and the present-day seismicity of Mars and to compare the results with the recent estimates from InSight (Banerdt et al. 2020). Using isotherms of 573 K and 1073 K that have been suggested to mark the base of the seismogenic layer (Knapmeyer et al., 2006 and references therein), we calculate the thickness of the seismogenic zone at each location on Mars (Fig. 1f) and estimate the present-day seismicity. The seismogenic layer thickness follows crustal thickness variations and could be used to discriminate between geodynamic models, if the source depth and location of seismic events is known. The present-day seismicity calculated from the geodynamic models that use the crustal thickness and core size estimates from InSight is compatible with the values derived from InSight's seismic data. Future models need to analyze in greater detail the consequences of the large present-day elastic lithosphere thickness at the north pole of Mars from recent estimates on the present-day thermal state. Geodynamic models combined with seismic waves propagation calculations need to investigate the effects of spatial variations of seismic velocities in the mantle and lithosphere, and future studies are necessary to test the spatial distribution of seismicity by comparing model predictions to observations.

SUMMARY Constraining initial conditions and parameters of mantle convection for a planet often requires running several hundred computationally expensive simulations in order to find those matching certain ‘observables’, such as crustal thickness, duration of volcanism, or radial contraction. A lower fidelity alternative is to use 1-D evolution models based on scaling laws that parametrize convective heat transfer. However, this approach is often limited in the amount of physics that scaling laws can accurately represent (e.g. temperature and pressure-dependent rheologies or mineralogical phase transitions can only be marginally simulated). We leverage neural networks to build a surrogate model that can predict the entire evolution (0–4.5 Gyr) of the 1-D temperature profile of a Mars-like planet for a wide range of values of five different parameters: reference viscosity, activation energy and activation volume of diffusion creep, enrichment factor of heat-producing elements in the crust and initial temperature of the mantle. The neural network we evaluate and present here has been trained from a subset of ∼10 000 evolution simulations of Mars ran on a 2-D quarter-cylindrical grid, from which we extracted laterally averaged 1-D temperature profiles. The temperature profiles predicted by this trained network match those of an unseen batch of 2-D simulations with an average accuracy of $99.7\, {\rm per~cent}$.

The Earth-like planets and moons in our solar system have iron-rich cores, silicate mantles, and a basaltic crust. Differentiated icy moons can have a core and a mantle and an outer water–ice layer. Indirect evidence for several icy moons suggests that this ice is underlain by or includes a water-rich ocean. Similar processes are at work in the interiors of these planets and moons, including heat transport by conduction and convection, melting and volcanism, and magnetic field generation. There are significant differences in detail, though, in both bulk chemical compositions and relative volume of metal, rock and ice reservoirs. For example, the Moon has a small core [~ 0.2 planetary radii (RP)], whereas Mercury’s is large (~ 0.8 RP). Planetary heat engines can operate in somewhat different ways affecting the evolution of the planetary bodies. Mercury and Ganymede have a present-day magnetic field while the core dynamo ceased to operate billions of years ago in the Moon and Mars. Planets and moons differ in tectonic style, from plate-tectonics on Earth to bodies having a stagnant outer lid and possibly solid-state convection underneath, with implications for their magmatic and atmosphere evolution. Knowledge about their deep interiors has improved considerably thanks to a multitude of planetary space missions but, in comparison with Earth, the data base is still limited. We describe methods (including experimental approaches and numerical modeling) and data (e.g., gravity field, rotational state, seismic signals, magnetic field, heat flux, and chemical compositions) used from missions and ground-based observations to explore the deep interiors, their dynamics and evolution and describe as examples Mercury, Venus, Moon, Mars, Ganymede and Enceladus.

Here, we show the first results of coupling a grey atmosphere model (i.e., we assume that the absorption coefficients are constant and hence independent of frequency) considering only CO2 and H2O as greenhouse gases to the geodynamic code Gaia (Hüttig et al., 2013). The evolution of the atmospheric composition of a planet is largely determined by the partial melting and volcanic outgassing of the interior. In turn, the composition of the atmosphere dictates the surface temperature of the planet (due to processes like the greenhouse effect), which is an important boundary condition for crustal and mantle processes in the interior of a planet. Venus in particular has a thick atmosphere at present with an abundance of the greenhouse gas CO2 and a small amount of water vapour. However, the surface conditions may have been much milder up to recent times (e.g., Way et al., 2016). Volcanic outgassing during the thermal history of Venus is thought to have significantly affected the planet's surface temperature and hence its global mantle evolution. Here, we calculate the outgassing of CO2 and H2O from the melt and then use the resulting partial pressures to calculate the surface temperature, which we then use as our boundary condition for the mantle convection. We compare our results to previous studies who employed similar coupled models to address the interaction between the interior and atmosphere of Venus (e.g., Noack et al., 2012; Gillmann & Tackley, 2014; Höning et al., 2021). Ultimately, we aim to consider more chemical species than CO2 and H2O to shed light on the Venus’ interior and atmosphere evolution. Therefore, we also show preliminary results of outgassing models that consider chemical speciation of the entire C-O-H system, i.e., CO2, H2O, H2, O2, CO, and CH4.

The presence of delta deposits on Mars has been thoroughly demonstrated for decades and large scale mapping [1,2] highlighted the presence of several delta fans mainly located on the dichotomy boundary. While a previous delta inventory was compiled by Morgan et al. [3], we aim to update and finalize a complete mapping of delta deposits in order to allow the examination of the evolution and distribution of standing bodies of water on Mars. The objective of our project focuses on the production of a global catalogue of water-related features at the Martian surface, which are commonly studied separately or at smaller scales.Globally, we located around 150 deltas among which many were not previously included in published literature [e.g. 1,2,4]. We then examined the deltas based on two main traits. Firstly, we measured the length of the feeding channels since it may be (i) a proxy for the duration of the aqueous activity in the channel-delta system, and (ii) proportional to the age of the delta [2]. The latter relationship links older deltas near Chryse Planitia (>3 Ga) to longer valleys, while younger deltas are usually fed by shorter valleys [2]. Secondly, we measured the elevation of the delta population and compared the obtained dataset with the hypothesized sea level elevation of -2540 ± 177 m firstly suggested by Di Achille and Hynek [1] for a northern ocean through the analysis of deltas.We observed that, if the relationship between feeding channel length and delta age found for a sub-group of the population [2] is applicable as a rule of thumb to all deltas, many of the deposits have the potential to be Hesperian or Amazonian in age. They would thus be younger than the ocean that might have occupied the northern lowlands during the Noachian-Hesperian boundary period [1] and thus be unrelated to a global sea level range. In fact, less than half of the delta population is related to medium/long feeding channels (>30 km). Abundant pristine morphologies, both related to channels and deltas, also supports the hypothesis that part of the population is younger than Noachian. Additionally, the large variety of elevations where the deltaic deposits can be found and the very small amount of deltas included in the sea level elevation range proposed by Di Achille and Hynek [1] raise questions about the generation and environmental implications of these features, especially when seen at global scale. [1] Di Achille, G. & Hynek, B. M., Nat. Geosci. 3, 459–463 (2010).[2] Hauber, E. et al., J. Geophys. Res. E Planets 118, 1529–1544 (2013).[3] Morgan, A. M., et al., Lunar Planet. Sci. Conf. (2018).[4] Ori, G.G. et al., J. Geophys. Res. E Planets 105, 17629–17641 (2000).

Introduction During the early stages of lunar evolution, the large amount of heat available from the lunar forming impact led to extensive melting of the Moon’s silicate mantle giving rise to a magma ocean. The fractional crystallization of the latter resulted in an inhomogeneous mantle with cumulate layers of increasing density towards the surface, due to iron enrichment in the residual magma ocean [1]. Such an unstable density distribution is prone to overturn and sets the stage for the subsequent thermo-chemical history of the mantle. In particular, this initial stage can significantly affect mixing of mantle material and the partial melt production, as well as the melt composition during the later stages of lunar evolution. The melt composition is directly linked to the composition of lunar basalts, whose variability at the lunar surface indicates complex melting processes and the presence of various mantle reservoirs. In this study we model the solid-state convection, mixing and partial melt production in the lunar mantle. We investigate the effects of an initially layered mantle as a consequence of the fractional crystallization of the lunar magma ocean. To this end, we combine geodynamical models using the mantle convection code GAIA with petrological calculations that provide information about the composition and structure at the end of lunar magma ocean (LMO) solidification. While previous mantle convection studies investigated lunar mantle melting in a purely homogeneous mantle [2] or with a localized KREEP layer [3,4], here we combine petrological and geodynamical models to investigate the degree of heterogeneity that can be produced by melting and mixing an initially heterogeneous lunar mantle. Petrological modeling The petrological model computes the crystallization sequence of the LMO. For the calculations in the deeper part of the mantle we use FOXMTR, for the shallower part alphaMELTS, as this approach is in good agreement with experimental data for the whole solidification process. We assume fractional crystallization of a spherical shell with an initial thickness of 1350 km, and a bulk lunar mantle composition from [5]. During crystallization the temperature is lowered stepwise and all minerals (except plagioclase) are assumed to accumulate at the bottom of the LMO and equilibrate with the melt at the respective pressure conditions. Plagioclase is assumed to float to the surface and form anothoritic crust. The resulting mantle structure is characterized by 5 compositional layers, where the predominant minerals are olivine, orthopyroxene, clinopyroxene, clinopyroxene and ilmenite (ilmenite bearing cumulates = IBC) and plagioclase (crust), respectively. For each of those layers an average density is calculated from the density profile after crystallization, as well as the change in density as a function of depletion. The solidus and liquidus temperature profiles are calculated for the average layer compositions using alphaMELTS. The depths and densities of the compositional layers, the initial temperature profile, the solidus and liquidus profiles for each layer and the density-depletion functions of each layer composition are provided in the form of read-out tables. The results from the petrological model are shown in figure 1. The densities of the mantle layers increase with radius due to the enrichment of iron in the melt during crystallization. The crust has a comparative low density (figure 1a). The temperature profile follows the crystallization temperatures of the cumulates. In figure 1b the temperature profile is shown together with the individual layers and their corresponding solidi and liquidi. From olivine to IBC the solidus and liquidus temperatures decrease because of the crystallization sequence (figure 1b). Geodynamical modelling We use the mantle convection code GAIA [6] in a 2D quarter cylinder geometry to model the thermochemical evolution of the compositionally heterogeneous lunar mantle. The nondimensional conservation equations of mass, momentum, thermal energy, and composition are solved under the extended Boussinesq approximation. We use an Arrhenius law to calculate the temperature- and depth-dependent viscosity. To track the composition of the mantle we use a particle-in-cell (PIC) method [7], where tracer particles carry information about material properties such as density, melting temperature, degree of depletion, amount of heat producing elements etc. Our models use between 35 to 50 particles per cell that are advected at each time step according to the velocity field. In our simulations we account for core cooling and radioactive decay, as well as mechanical mixing. In addition, we consider the effects of melting by accounting for the latent heat during mantle melting, as well as solidus and density increase/decrease due to mantle depletion [8]. During melting, low melting point components are extracted from the mantle as the melt rises to the surface to form the basaltic crust. This leads to an increase of the solidus temperature requiring a higher temperature to further melt the residual mantle material. Gradual changes in density and solidus temperatures are extracted from the precomputed read-out tables of the petrological modelling. Summary and Outlook Our coupled petrological-geodynamical model of mantle convection and melt production will be used to investigate the thermochemical evolution of an initially heterogeneous lunar mantle structure (figure 2). Preliminary results show a smaller amount of melt produced in a heterogeneous mantle in comparison to a homogeneous one. We will present the distribution of the compositional layers as a function of time and compare the amount of melting produced from each individual component. With this approach we aim to provide a link between melting processes in the interior of the Moon and the compositional diversity of basalts observed at the lunar surface. This in turn will help us to put constraints on the LMO crystallization and the subsequent thermochemical history of the Moon. Acknowledgements We thank Brian Doherty for his contribution to the numerical implementation. I.B. and S.S. were supported by the German Research Foundation (Deutsche Forschungsgemeinschaft) SFB-TRR170, (subprojects C4 and A5). References [1] Elkins-Tanton et al., Annu. Rev. Earth Planet Sci. 2012; [2] Ziethe et al., PSS, 2009; [3] Laneuville et al., JGR, 2013 [4] Laneuville et al., JGR, 2018; [5] O’Neill et al., 1991; [6] Hüttig et al., PEPI, 2013; [7] Plesa et al., IGI Global, 2013; [8] Doherty et al., AGU, 2018.

Introduction An invaluable source of information about the present interior structure of Venus is the measurement of surface deflections and disturbances to the planet's gravity field caused by tidal deformation. The planet is mainly loaded by the semidiurnal solar tide that probes the interior at the angular frequency ω ≈ 1.25×10-6 rad s-1 [e.g., 1]. The tidal response is then determined by the rheological properties of the body. In this work, we combine interior structure and tidal modeling of Venus to compute and compare measurable quantities, namely the tidal Love numbers k2, the moment of inertia factor MoIF, and the tidal quality factor Q. Our predictions can be tested with future measurements, should current Venus mission proposals (e.g., Veritas and EnVision) be selected. Interior structure and thermal state models In order to calculate the tidal parameters (k2 and Q), we first generate 1-D interior structure models of Venus. Our method is similar to that of [2] in which the interior is subdivided into chemically separated layers: an iron core, a rocky mantle, and a basaltic crust. In addition, steady-state temperature profiles are calculated by applying a mixing-length approach [3], and we vary poorly constrained parameters (crustal density and thickness, iron content in the mantle, reference viscosity of mantle and core, surface and core-mantle heat fluxes). Tidal deformation models Tidal deformation modeling is based on the normal mode theory for a radially-stratified nonrotating incompressible viscoelastic sphere [e.g., 4]. In this approach, the deformations, tractions, and additional potential in the planet are expanded into spherical harmonics and the governing equations for the viscoelastic continuum are solved analytically. The resulting deformation state is then described by parametric functions, the parameters of which can be obtained from the boundary conditions. We compute the potential Love numbers by using two different techniques. In the first approach, the radial profiles of the deformations, tractions, and additional potential are computed by using a matrix propagation method [e.g., 5, 6]. In the second approach, we seek directly the parameters of the aforementioned parametric functions [7]. We use the well-known Maxwell model for the core and adopt an Andrade model to compute the response of the Venusian mantle and crust [8, 9]. In contrast to the Maxwell model, the Andrade rheology accounts not only for the instantaneous elastic deformation and the viscous (steady-state) creep but also for the transient effects governed by the Andrade hereditary terms. Results (a) Comparison of Love numbers We select representative interior structure models and compute the tidal parameters according to the two methods described above. Both methods provide the same results for various sets of input parameters. Furthermore, we compare our results with published data from [1]. To this end, we used the same interior temperature profiles, core size, and viscosity as in [1], and employed two end-member compositions (i.e., BVSP(81)-Ve1 with a low and BVSP(81)-Ve4 with a high iron content in the Venusian mantle) similar to their models V1 and V4. Our results in Fig. 1, calculated with the tidal model of [7], are in close agreement with the data presented in Fig. 4 of [1]. (b) Effect of mantle composition We observe two distinct ranges of MoIF according to the bulk composition used in our interior structure models (Fig. 2). All models corresponding to the mantle mineralogy with a negligible low iron content [BVSP(81)-Ve1] are found at significantly lower MoIF than their iron-rich [BVSP(81)-Ve4] counterparts. Furthermore, it can be seen that an iron-rich mantle leads to smaller core sizes when comparing the two compositional models. Combining the MoIF and the potential Love number k2 delivers additional information about the state and size of the core. In Figure 2, the models with a completely solid core (stars) have the smallest core size and thus the lowest k2, whereas the models with a completely liquid core (circles) have in general large core sizes and thus high k2. In between these two end-members, we find the models with solid inner and liquid outer cores (squares). These models usually have medium-sized cores and intermediate potential Love numbers k2. However, the highest k2 value is obtained for models with partially liquid iron cores. Their much hotter counterparts with completely liquid cores, which would lead to even higher k2, contain a fully molten mantle layer, and have been excluded here. Thus, the determination of the state and size of the core could be challenging for high potential Love numbers k2 due to a model degeneracy from input parameters. Conclusions In this study, we have presented a comparison between two tidal deformation models [6,7] to compute Venusian tides. The results show a close agreement between the two tidal deformation models and the study of [1]. We have applied our interior models to investigate the effects of composition on the tidal parameters and moment of inertia factor. The results indicate two families of models with distinct MoIF that could be constrained by future measurements. In the next step, we plan to combine the tidal deformation model with thermal evolution calculations to study the secular tidal evolution. To this end, we will couple the tidal model to 1-D parametrized [e.g., 12] and 2-D geodynamical [e.g., 13] models that treat the cooling history and melt production in the interior of Venus. Furthermore, our coupled tidal-thermal evolution model can be applied to study the interior of Venus-like extrasolar planets. References [1] Dumoulin, C. et al. (2017): JGR:Planets, 122. [2] Sohl, F. & Spohn, T. (1997): JGR:Planets, 102(E1). [3] Wagner, F. W. et al. (2019): GJI, 217(1). [4] Sabadini, R. & Vermeersen, B. (2004): Springer. [5] Segatz, M. et al. (1988): ICARUS, 75(2). [6] Steinbrügge, G. et al. (2018): JGR:Planets, 123(10). [7] Walterová, M. & Běhounková, M. (2020): ApJ, 900(1). [8] Jackson, I. & Faul, U. H. (2010): PEPI, 183. [9] Castillo‐Rogez, J. C. et al. (2011): JGR:Planets, 116(E9). [10] Basaltic Volcanism Study Project (1981): Pergamon Press. [11] Konopliv, A. S. & Yoder, C. F. (1996): GJI, 23(14). [12] Tosi, N. et al. (2017): A&A, 605. [13] Plesa, A.-C. & Breuer, D. (2021): LPSC, No. 2548.

We use a large data set of 3D thermal evolution models to predict the distribution of present-day seismic velocities in the Martian interior. Our models show a difference between maximum and minimum S-wave velocity of up to 10% either below the crust, where thermal variations are largest, or at the depth of the olivine to wadsleyite phase transition, located at around 1000 – 1200 km depth. Models with thick lithospheres on average have weak low-velocity zones that extend deeper than 400 km, and seismic velocity variations in the uppermost 400 – 600 km that closely follow the crustal thickness pattern. For these cases the crust contains more than half of the total amount of heat producing elements. Models with limited crustal heat production have thinner lithospheres and shallower but prominent low-velocity zones that are incompatible with InSight observations. Seismic events suggested to originate in Cerberus Fossae indicate the absence of S-wave shadow zones in 25° - 30° epicentral distance. This result is compatible with previous best-fit models that require a large average lithospheric thickness and a crust containing more than half of the bulk amount of heat producing elements to be compatible with geological and geophysical constraints. Ongoing and future InSight measurements that will determine the existence of a weak low-velocity zone will directly bear on the crustal heat production. ISSN:0148-0227 ISSN:2169-9097 ISSN:2169-9100

The accretion of the debris resulting from the giant collision that formed the Earth‐Moon system caused the formation of a deep lunar magma ocean. The initial composition profile of the Moon results from the solidification of this magma ocean. One of the late solidification products is a thin layer containing ilmenite, which is highly enriched in titanium and forms over a depth of about 40–80 km. This layer is much denser than the underlying mantle, it tends thus to overturn and sink toward the core. The overturn hypothesis explains several features of the evolution of the Moon. However, the strong temperature dependence of the viscosity makes the part of the mantle where this titanium‐rich layer solidifies very stiff and its overturn very difficult. In this work, we used numerical simulations to infer which deformation properties the mantle needs to have for the overturn to be possible. We found that the overturn requires a significantly weaker and less temperature dependent viscosity than usually thought. The required low viscosity and its weak temperature dependence can be explained by the presence of water and residual melt in the Moon and/or by the effects of nonlinear deformation dependent both on temperature and stress.

The surface of Mars has been well mapped and characterized, yet the subsurface — the most likely place to find signs of extant or extinct life and a repository of useful resources for human exploration — remains unexplored. In the near future this is set to change.

Scaling laws used in 1-D parametrized thermal models to describe the cooling of planets have mainly been derived from steady-state convection models. Here, fully dynamic 2-D and 3-D models are employed to compute the interior thermal evolution using strong temperature-dependent viscosity, mixed heating with radioelement decay, spherical geometry. The results of these models are compared to those of parametrized models, where we distinguish between the upper thermal boundary layer (TBL) and the stagnant lid, in a Monte Carlo framework to derive scaling laws valid for the entire planet evolution. The upper TBL thickness depends on the Rayleigh number to the power β u , while the lid base is determined by the mantle temperature and the rate of viscosity change with temperature multiplied by a prefactor a rh . By varying β u and a rh we find that, although the heating conditions change as a function of time, the thermal evolution of a cooling planet in a stagnant lid regime can be represented by a wide range of combinations of a rh and β u . Suitable fits are found for different values of a rh and β u that vary depending on the model set-up. The observed relationship between suitable values of a rh and β u is explained by a trade-off between the lid and the TBL thicknesses. Only when considering a specific definition of the stagnant lid thickness in 3-D simulations, suitable combinations for all models converge to specific values of a rh and β u . Using a stagnant lid defined by the intersection between the depth axis and the tangent to the velocity profile at the depth corresponding to the maximum velocity gradient, we find best-fit values of 2.54 and 0.335 for a rh and β u , respectively.

The thermal and convective evolution of terrestrial planets like Mars is governed by a number of initial conditions and parameters, which are poorly constrained. We use Mixture Density Networks (MDN) to invert various sets of synthetic present‐day observables and infer five parameters: reference viscosity, activation energy and activation volume of the diffusion creep rheology, an enrichment factor for radiogenic elements in the crust, and initial mantle temperature. The data set comes from 6,130 two‐dimensional simulations of the thermal evolution of Mars' interior. We quantify the possibility of constraining a parameter using the log‐likelihood value from the MDN. Reference viscosity can be constrained to within 32% of its entire range (1019 − 1022 Pa s), when all the observables are available: core‐mantle‐boundary heat flux, surface heat flux, radial contraction, melt produced, and duration of volcanism. Furthermore, crustal enrichment factor (1–50) can be constrained, at best, to within 15%, and the activation energy (105 − 5 × 105 J mol−1) to within 80%. Initial mantle temperature can be constrained to within 39% of its range (1,600–1,800 K). Using the full present‐day temperature profile or parts of it as an observable tightens the constraints further. The activation volume (4 × 10−6 − 10 × 10−6 m3 mol−1) cannot be constrained. We also tested different levels of uncertainty in the observables and found that constraints on different parameters loosen differently, with initial temperature being the most sensitive. Finally, we present how a joint probability model for all parameters can be obtained from the MDN., Plain Language Summary: The mantle of rocky planets like Mars behaves like a highly viscous fluid over geological time scales. Key parameters and initial conditions for the non‐linear partial differential equations governing mantle flow are poorly known. Machine Learning (ML) can help us avoid running several thousand computationally expensive fluid dynamic simulations each time to determine if an observable can constrain a parameter. Using an ML approach, we invert a set of synthetic observables such as present‐day surface heat flux, duration of volcanism and radial contraction to constrain important parameters controlling the long‐term evolution of the planet's interior, such as the reference mantle viscosity or the partitioning of radiogenic heat sources between mantle and crust. We demonstrate that by training a probabilistic ML algorithm on the data and applying it, we can quantify the constraints on parameters. This provides a high‐dimensional framework for analyzing inverse problems in geodynamics., Key Points: Mixture Density Networks provide a probabilistic framework for inverting observables to infer parameters of Mars' interior evolution Reference viscosity, crustal enrichment in heat‐producing elements and initial mantle temperature can be well constrained Activation energy of diffusion creep can be weakly constrained; constraining activation volume requires new observational signatures, Helmholtz Einstein International Berlin Research School in Data Science (HEIBRiDS), Berlin Institute for the Foundations of Learning and Data (BIFOLD), Deutsche Forschungsgemeinschaft (DFG) Research Unit FOR 2440

Bulletin of the AAS, 53 (4)

We derive synthetic electrical conductivity, seismic velocity, and density distributions from the results of martian mantle convection models affected by basin-forming meteorite impacts. The electrical conductivity features an intermediate minimum in the strongly depleted topmost mantle, sandwiched between higher conductivities in the lower crust and a smooth increase toward almost constant high values at depths greater than 400 km. The bulk sound speed increases mostly smoothly throughout the mantle, with only one marked change at the appearance of $\beta$-olivine near 1100 km depth. An assessment of the detectability of the subsurface traces of an impact suggests that its signature would be visible in both observables at least if efficient melt extraction from the shock-molten target occurs, but it will not always be particularly conspicuous even for large basins; observations with extensive spatial and temporal coverage would improve their detectability. Electromagnetic sounding may offer another possibility to investigate the properties of the mantle, especially in regions of impact structures. In comparison with seismology and gravimetry, its application to the martian interior has received little consideration so far. Of particular interest is its potential for constraining the water content of the mantle. By comparing electromagnetic sounding data of an impact structure with model predictions, it might also be possible to answer the open question of the efficiency of extraction of impact-generated melt., Comment: 5 figures

Charles D. Edwards (Jet Propulsion Laboratory, California Institute of Technology). Co-Authors: 1. Vlada Stamenkovic Jet Propulsion Laboratory, California Institute of Technology; 2. Penelope Boston NASA Ames; 3. Kennda Lynch LPI/USRA … et al.

Primary author: Suzanne Smrekar Jet Propulsion Laboratory/California Institute of Technology, Pasadena CA ; Co-authors: Jeff Andrews-Hanna (U.AZ), Doris Breuer (DLR Berlin), Paul Byrne (NCSU), Debra Buczkowski (JHU/APL), Bruce Campbell (Nat. Air Space Museum), A. Davaille (CNRS/U. Paris-Saclay), Darby Dyar (Mt. Holyoke/PSI), G. Di Achille (INAF/Astro Obs. Teramo), Caleb Fassett (Marshall), Martha Gilmore (Wesleyan), Robert Grimm (SWRI), Jorn Helbert (DLR Berlin), Scott Hensley (JPL), Robert Herrick (U. Alaska), Luciano Iess (U.Roma), Lauren Jozwiak (JHU/APL), Tiffany Katiaria (JPL), Marco Mastrogiuseppe (U. Roma), Erwan Mazarico (Goddard), Nils Mueller (DLR Berlin), Daniel Nunes (JPL), Joseph O'Rourke (ASU); Patrick McGovern (LPI), Maria Raguso (Caltech), Joann Stock (Caltech), Constantine Tsang (SwRI), Thomas Widemann (Obs. Paris), Jennifer Whitten (Tulane), Thomas Widemann (LESIA), Howard Zebker (Stanford)

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...

Introduction: Estimates of the bulk silicate Moon (BSM) composition have been proposed based on a number of different geochemical, petrological and geophysical arguments but have yet to arrive at a general consensus.In order to obtain further constraints on the BSM composition, we investigated the effect of the BSM FeO content on the physical properties of lunar mantle reservoirs and tested the consistency of different lunar interior models with the bulk Moon density and moment of inertia. Methods: To cover all lunar interior models that are consistent with a given BSM composition, we modeled the properties of the chemical reservoirs forming from lunar magma ocean (LMO) solidification, considered the re-distribution of these reservoirs in the lunar mantle by solid state convection, and calculated the bulk Moon density and moment of inertia of the resulting interior models, assuming varying core properties and selenotherms.Lunar Magma Ocean Crystallization:We modeled LMO cumulate mineralogies using a combination [1] of crystallization algorithms from the software packages alphaMELTS [2] and SPICES [3], that has been validated against recent experiments on LMO fractional crystallization [4, 5]. Thereby we assumed pure fractional crystallization of a deep LMO, that extends to the core-mantle boundary so that the LMO comprises the whole BSM. The bulk LMO composition was chosen based on the estimate of [6]. FeO/MgO ratios of the bulk LMO composition were varied (8.0-13 wt% FeO) to investigate the effect of the FeO content on the densities and mineralogies of individual cumulate layers. All crystals forming in the LMO were assumed to sink and equilibrate with the liquid at the bottom of the magma ocean prior to fractionation, except for plagioclase which was assumed to float to the surface to form anorthositic crust. The average lunar crust thickness was assumed to be 40 km in accordance with recent GRAIL data [7]. Any excess plagioclase that formed after that final crust thickness was reached was assumed to remain in the mantle due to imperfect plagioclase floatation.Mantle Mixing and Overturn: As a consequence of the higher compatibility of lighter Mg compared to denser Fe in the LMO cumulate minerals, the density of the cumulate increases with progressing LMO solidification. Since the LMO solidifies from bottom to top, this results in a gravitationally unstable cumulate stratification that facilitates convective overturn, during which dense material sinks towards the core mantle boundary while lighter material migrates toward the surface. The respective changes in pressure and temperature experienced by individual cumulate layers, as well as mixing and chemical equilibration of different layers during overturn, can affect the mineralogy and physical properties of the lunar mantle. To investigate these effects, we calculated equilibrium mineral parageneses of different cumulate layers using Perple_X [8]. For simplicity we considered five homogeneous cumulate reservoirs (olivine-dominated, pyroxene-dominated, IBC, KREEP and crust), whose compositions were derived from the results of the LMO crystallization models by averaging the compositions of adjacent cumulate layers with similar mineralogies.The mineralogies and densities of each reservoir were calculated as a function of depth along different selenotherms (e.g. [9]). To evaluate the effect of mixing and chemical equilibration, we also made the same calculations for different compositional mixtures of the layers.The results of these calculations were used as input in a simple density structure model in order to investigate the effect of mantle overturn on the bulk lunar density and moment of inertia. Lunar core sizes and densities were thereby varied within the range of proposed values (e.g. [10]). Results: Changing the FeO/MgO ratio of the BSM composition leads to an earlier appearance and higher abundance of Fe-rich minerals in the LMO cumulate. This results in an increased thickness of the late formed, dense ilmenite bearing cumulate (IBC) reservoir, that we defined based on its high density compared to underlying cumulate layers. As a consequence, IBC thickness correlates linearly with the assumed LMO FeO content, varying by a factor of about 4 over the assumed range of FeO contents.Due to its high density the radial distribution of IBC material in the lunar interior has a significant effect on the BSM moment of inertia, even though its volume is comparatively small. The effect of the distribution of IBC on the BSM moment of inertia increases systematically with increasing IBC volume, which is in turn linked to the FeO content.Depending on the chosen core models and selenotherms, realistic bulk Moon densities and BSM moments of inertia could be reached assuming FeO contents of 8-13.5 wt%. Discussion: The range of possible FeO contents determined here is valid for a large variation of lunar interior properties and can be narrowed considerably by imposing constraints on the selenotherm, core properties or mantle structure. Seismic and selenodetic data indicate a mantle stratigraphy with a pyroxenitic upper mantle and a dunitic lower mantle [11] and suggest the presence of a dense, partially molten zone at the core mantle boundary [12], that might consist of sunken IBC material. These constraints on the interior structure of the lunar mantle indicate that BSM FeO contents of 9 – 11 wt% are most probable. This estimate could be further limited by tighter constraints on the size and density of the lunar core, e.g. by future seismic investigations. References:[1] Schwinger and Breuer (2018), AGU Fall Meeting, Washington, USA.[2] Smith and Asimow (2005), G³, 6.2.[3] Davenport (2013), Planet. Sci Res. Disc. Report 1, 173.[4] Rapp and Draper (2018), Meteoritics & Planet. Sci. 53.7, 1432-1455.[5] Charlier et al. (2018), Geochim. Cosmochim. Acta, 234, 50–69.[6] O’Neill (1991), Geochim. Cosmochim. Acta, 55 (4), 1135-1157.[7] Wieczorek et al. (2013) Science, 339, 671.[8] Connolly (2005), EPSL, 236 (1-2), 524-541.[9] Laneuville et al. (2013), JGR: Planets, 118 (7), 1435-1452.[10] Weber et al. (2011), science, 331 (6015), 309-312.[11] Gagnepain-Beyneix et al. (2006), Physics of the Earth and Planetary Interiors, 159 (3-4), 140-166.[12] Matsumoto et al. (2015), GRL, 42 (18), 7351-7358.

If Venus were a newly discovered exoplanet, it would be one of the most Earth-like yet identified. Its similarity in size, bulk density and cloud top temperatures give no clue to the hellish temperatures at its surface. Venus hosts an array of geological features as complex as Earth, but without its organisation, and sustains a chemically reactive atmosphere, but without life. Proposed in response to ESA’s M5 call, with enabling support from NASA, EnVision is currently in Phase A study for the next medium-class mission opportunity proceeding towards a final mission selection in summer 2021 for a launch in 2032. Here we discuss the science questions motivating the mission in more detail. Building on discoveries from Magellan, Venus Express and Akatsuki, EnVision will focus on three overarching questions: Is Venus geodynamically active? How did Venus arrive at its current state? How does the Venus climate work and how do the interior, surface and atmosphere interact? 1 – Is Venus geodynamically active? Venus should be geologically active today and its globally young surface implies extensive volcanic resurfacing, but whether this happened in episodic global events or in a continuous process of small-scale resurfacing is uncertain. Constraining the rate of volcanic and tectonic activity can reveal whether Venus occupies one of these end members, or lies somewhere on the spectrum between. Magellan radar image mosaic of a 550 km wide region of Lada Terra (47°S, 25°E) showing a system of radar-bright and dark lava flows breaching a ridge belt and ponding in a large radar-bright deposit covering 100,000 km². Ammavaru, the source caldera, lies 300 km to the west (JPL/Caltech). Understanding the tectonic regime driving resurfacing and heat loss is as important as knowing the rate of activity. The surface appears partitioned into areas of low strain bounded by narrow high strain margins. The abundance of steep slopes and landslides implies active uplift in these high strain areas, but existing data provide no constraint on the frequency of landslides or rates of tectonic movement. Are the low strain regions actively created and destroyed, like Earth’s oceanic plates, or simply mobilised locally? What is the significance of the global network of elevated rift systems and linear lowland wrinkle-ridged plains? Unique to Venus are coronae, quasi-circular volcano-tectonic features, typically 100–500 km across. Are they the surface expression of plumes, or magmatic intrusions, or subduction zones? The processes of weathering, mass wasting and aeolian transport are critical for understanding both the geological history and climatic evolution of Venus. Venus Express found anomalously high IR emissivities near suspected active volcanoes, interpreted as fresh, unweathered lava flows, but both their mineralogy and the weathering processes involved are unknown. Magellan detected several, probably impact-related, dune fields at the limit of its resolution, and found indirect evidence for globally distributed smale-scale ripples. 2 – How Did Venus Arrive at its Current State? The cratering record reveals that the Venus surface is, on average, under 1 Ga old. While some areas are likely active today, other regions, e.g. the tessera highlands, may be considerably older. Magellan data imply a variety of age relationships and long-term activity, with a non-random association between geological features and elevation, e.g. the uplands are consistently more deformed than the lowlands. Impact craters themselves show alteration to dark floors, perhaps from airfall deposits or magmatic resurfacing. Densely fractured plains (right) abutting tessera (bottom); both are embayed by younger plains (dark areas). A steep-sided volcanic dome (upper left) may be the source of the plains or unrelated to them, and older or younger than the tesserae. Magellan image at 46°N, 360°E, after Basilevsky and McGill (2007). Constraining the history is critical to understanding not only when and how resurfaced, but whether that activity has changed systematically through time. Were the plains formed in a short period by massive outpourings or by many thousands of small flows over their entire history? Or did many different mechanisms – including sedimentary processes – operate at different times and places? Globally, Venus exhibits perhaps even more tectonic deformation than Earth: what is its role in resurfacing the planet and have the regimes of tectonic deformation changed over time? How did tesserae, especially, accumulate their extraordinary degree of deformation? The interior of Venus is probably Earth-like, but not the same; its core size is poorly constrained by Magellan gravity data. These data are consistent with an organised pattern of mantle convection but lack the resolution necessary to connect it with geological-scale features. 3 - How does the Venus climate work and how do the Interior, Surface and Atmosphere Interact? How and why the atmospheres of two Earth-like planets evolved so differently is one of the many compelling reasons to study Venus, directly addressing the question of how our own world became habitable. Understanding its evolution depends on knowing the exchanges between its interior, surface and space. The lower/middle clouds of Venus as imaged by Akatsuki IR2 camera. Dark areas represent thicker clouds, which may represent volcanic plumes of ash or sulphate particulates. (JAXA/ISAS/DART/Damia Bouic) Models suggest that the clouds are maintained by a constant input of H2O and SO2, both of which vary considerably, perhaps because of volcanic emissions. Elevated D/H ratios indicate the loss of early oceans, but the ‘starting’ mantle D/H ratio is unknown. Identification of granites in the ancient highlands would support this inference, but the direct detection and characterisation of volcanic volatiles is key to inferring past climate evolution. Beyond the specific investigations outlined above, however, the most important unknown factor in determining the present day state of Venus and its atmosphere, and how it arrived at that state, is the interaction between the interior, surface and atmosphere: the whole being more than the sum of the parts. References Basilevsky and McGill (2007), Surface evolution of Venus, in Exploring Venus as a Terrestrial Planet, Geophysical Monograph Series 176, edited by L. W. Esposito, E. R. Stofan and T. E. Cravens, pp. 23-43, American Geophysical Union, Washington, DC

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 aspect...

The parameters and initial conditions governing mantle convection in terrestrial planets like Mars are poorly known meaning that one often needs to randomly vary several parameters to test which ones satisfy observational constraints. However, running forward models in 2D or 3D is computationally intensive to the point that it might prohibit a thorough scan of the entire parameter space. We propose using Machine Learning to find a low-dimensional mapping from input parameters to outputs. We use about 10,000 thermal evolution simulations with Mars-like parameters run on a 2D quarter cylindrical grid to train a fully-connected Neural Network (NN). We use the code GAIA (Hüttig et al., 2013) to solve the conservation equations of mantle convection for a fluid with Newtonian rheology and infinite Prandtl number under the Extended Boussinesq Approximation. The viscosity is calculated according to the Arrhenius law of diffusion creep (Hirth & Kohlstedt, 2003). The model also considers the effects of partial melting on the energy balance, including mantle depletion of heat producing-elements (Padovan et., 2017), as well as major phase transitions in the olivine system. To generate the dataset, we randomly vary 5 different parameters with respect to each other: thermal Rayleigh number, internal heating Rayleigh number, activation energy, activation volume and a depletion factor for heat-producing elements in the mantle. In order to train in time, we take the simplest possible approach, i.e., we treat time as another variable in our input vector. 80% of the dataset is used to train our NN, 10% is used to test different architectures and to avoid over-fitting, and the remaining 10% is used as test set to evaluate the error of the predictions. For given values of the five parameters, our NN can predict the resulting horizontally-averaged temperature profile at any time in the evolution, spanning 4.5 Ga with an average error under 0.3% on the test set. Tests indicate that with as few as 5% of the training samples (= simulations x time steps), one can achieve a test-error below 0.5%, suggesting that for this setup, one can potentially learn the mapping from fewer simulations. Finally, we ran a fourth batch of GAIA simulations and compared them to the output of our NN. In almost all cases, the instantaneous predictions of the 1D temperature profiles from the NN match those of the computationally expensive simulations extremely well, with an error below 0.5%.

SUMMARY Heat transfer in one-plate planets is governed by mantle convection beneath the stagnant lid. Newtonian diffusion creep and non-Newtonian dislocation creep are the main mechanisms controlling large-scale mantle deformation. Diffusion creep strongly depends on the grain size (d), which in turn controls the relative importance of the two mechanisms. However, dislocation creep is usually neglected in numerical models of convection in planetary mantles. These mostly assume linear diffusion creep rheologies, often based on reduced activation parameters (compared to experimental values) that are thought to mimic the effects of dislocation creep and, as a side benefit, also ease the convergence of linear solvers. Assuming Mars-like parameters, we investigated the influence of a non-evolving grain size on Rayleigh–Bénard convection in the stagnant lid regime. In contrast to previous studies based on the Frank–Kamentskii approximation, we used Arrhenius laws for diffusion and dislocation creep—including temperature as well as pressure dependence—based on experimental measurements of olivine deformation. For d ≲ 2.5 mm, convection is dominated by diffusion creep. We observed an approximately equal partitioning between the two mechanisms for d ≈ 5 mm, while dislocation creep dominates for d ≳ 8 mm. Independent estimates of an average grain size of few mm up to 1 cm or more for present-day Mars suggest thus that dislocation creep plays an important role and possibly dominates the deformation. Mimicking dislocation creep convection using an effective linear rheology with reduced activation parameters, as often done in simulations of convection and thermal evolution of Mars, has significant limitations. Although it is possible to mimic mean temperature, mean lid thickness and Nusselt number, there are important differences in the flow pattern, root mean square velocity, and lid shape. The latter in particular affects the amount and distribution of partial melt, suggesting that care should be taken upon predicting the evolution of crust production when using simplified rheologies. The heat transport efficiency expressed in terms of the Nusselt number as a function of the Rayleigh number is thought to depend on the deformation mechanisms at play. We show that the relative volume in which dislocation creep dominates has nearly no influence on the Nusselt–Rayleigh scaling relation when a mixed rheology is used. In contrast, the flow pattern influences the Nusselt number more strongly. We derived a scaling law for the Nusselt number based on the mean lid thickness (〈L〉) and on the effective Rayleigh number (Raeff) obtained by suitably averaging the viscosity beneath the stagnant lid. We found that the Nusselt number follows the scaling $\mathrm{Nu} = 0.37 \langle L \rangle ^{-0.666} \mathrm{Ra}_{\mathrm{eff}}^{0.071}$ regardless of the deformation mechanism.

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 ...

While liquid water is not thermodynamically stable at the surface due to the low temperature and pressure conditions, liquid groundwater may still exist in the Martian subsurface [1, 2]. In this study, we use fully dynamical 3D thermal evolution models [3] and 3D parametrized models [4] to calculate the depth at which favorable conditions for liquid water are present, assuming that a global subsurface cryosphere exists on Mars today. While fully dynamical 3D models take into account the effect of mantle plumes self-consistently, they are computationally expensive compared to 3D parametrized models that can cover a large range of mantle conditions, although requiring additional parametrizations for thermal anomalies in the interior. In all calculations, we use a 3D crustal model that is compatible with today’s gravity and topography data [5, 6]. Some of the most important parameters that affect the depth of liquid water are the spatial variations of crustal thickness and crustal thermal conductivity, since the crust has a lower thermal conductivity compared to that of the mantle and thickness variations can shift the groundwater table locally closer to the surface (Fig. 1). The amount and distribution of heat sources, and the presence of mantle plumes, can introduce additional perturbations to the depth of groundwater. The surface temperature distribution and the presence of salts and clathrate hydrates considerably affect the depth and locations where subsurface liquid water may be stable. Hydrated magnesium (Mg) and calcium (Ca) perchlorate salts, whose presence has been suggested at various locations on Mars [7], may significantly reduce the melting point of water ice. In addition to thick regolith layers, clathrate hydrates, if present in the subsurface, would provide an insulating effect reducing the crustal thermal conductivity at least locally [e.g., 8]. The effects of the crustal thermal conductivity and salt abundance on the depth of subsurface liquid water are shown in Fig. 1, where we use the same crustal thickness variations and crustal enrichment in radioactive heat sources in all simulations. The model in Fig. 1a assumes an average crustal conductivity of 3 W/mK, while the model in Fig. 1b has a lower conductivity of only 2 W/mK (see panel 1e for the spatially averaged conductivity profiles that, due to crustal thickness variations, show average values between mantle and crust in the topmost 110 km). Fig. 1d shows the effect of the crustal thermal conductivity on the subsurface temperature profile. For the lower conductivity case the subsurface temperature is warmer, and the groundwater table shifts, on average, 2.5 km closer to the surface. The model shown in Fig. 1c is similar to the one in Fig. 1a but assumes the presence of salts. Instead of using the melting temperature of pure water ice, as was done for the models in Fig. 1a and b, we lower the melting temperature to 199 K [9] over the entire depth, by assuming that Ca(ClO4)2 is present in eutectic concentration (Fig. 1f). This extreme, and unrealistic, assumption places constraints on the minimum depth at which liquid water may be present in the Martian subsurface today, since kinetic factors such as the flow of groundwater due to gravity may increase the depth of the water table, depending on the total amount of liquid water, porosity and permeability. In Fig. 1a and b, the depth of the groundwater shows the combined effect of crustal thickness distribution and surface temperature variations. Mantle plumes have only a small effect and may introduce perturbations only if the groundwater is located, on average, at about 5 km depth or deeper. The effect of the crustal thickness is evident in basins, along the dichotomy, and in volcanic provinces, whereas surface temperatures give general water table depth trends with latitude. In Fig. 1c, the depth variations of the groundwater table are mainly caused by the surface temperature distribution, as the groundwater table is located very close to the surface (between 0 – 1 km for latitudes between -57° and 57°). Nevertheless, in all cases (Fig. 1a – c), the water table is significantly shallower in equatorial regions compared to polar regions, mainly governed by lower surface temperatures at the poles. Our results suggest that the Martian subsurface has had, and still has, the potential to enable deep environments with stable liquid groundwater. Combined with the analysis of geomorphological features at the Martian surface that testify the involvement of water/ice activity and maps of subsurface water ice [10], such models could provide valuable estimates of the depth of liquid groundwater on past and present-day Mars providing key knowledge on the planet dynamics, evolution and astrobiological potential. The technology to probe the Martian subsurface at depths of many kilometers is maturing [2]: TH2OR (Transmissive H2O Reconnaissance), a low-mass and average low-power transient electromagnetic sounder capable of detecting the presence of liquid water to depths of many kilometers is currently being developed at JPL [11]. Moreover, mission concepts such as VALKYRIE (Volatiles And Life: KeY Reconnaissance & In-situ Exploration) [12], which would add to the liquid water sounder a drill capable of accessing depths of 10s-100s of meters or more and employ a (bio)geochemical analysis package on the surface, would provide the measurements necessary to characterize the modern-day subsurface habitability of Mars. References: [1] Clifford et al., 2010, JGR, 115(E7); [2] Stamenković V. et al., 2019, Nat. Astron., 3(2); [3] Plesa A.-C. et al., 2018, GRL, 45(22); [4] Breuer D. & Spohn T., 2006, PSS, 54(2); [5] Plesa A.-C. et al., 2016, JGR, 121(12); [6] Wieczorek M. & Zuber M., 2004, JGR, 109(E8); [7] Leshin L. et al., 2013, Science, 341; [8] Kargel J. et al. 2007, Geology, 35(11); [9] Marion G. et al., 2010, Icarus, 207(2); [10] Piqueux S. et al., 2019, GRL, 46.; [11] Burgin M. et al., 2019, AGU Fall Meeting, P44B-02; [12] Mischna M. et al., 2019, AGU Fall Meeting, P41C-3466. Acknowledgments: This work was performed in part at the Jet Propulsion Laboratory, California Institute of Technology, under contract to NASA. © 2020, California Institute of Technology.

The origin of the planets atmosphere is a profound question of comparative planetology. There are two competing models, i.e. outgassing from the interior or late delivery from comets or volatiles-rich asteroids after most of the planet has been formed, of which the former is currently preferred. Meteorite compositions as well as radial mixing during accretion derived from accretion models suggest that the building blocks of the terrestrial planets contained some volatiles. Processes like dehydration by hydrous melting, oxidation, impact devolatilization, and in particular degassing during magma ocean solidification will then lead to a significant volatile loss of the interior and to the formation of a dense atmosphere during the early stages of planetary evolution. These processes are also responsible for the oxidation state of this early atmosphere, i.e. whether it was more reduced or oxidized. Although this early volatile loss was very efficient, the interior probably retained some water. This was distributed in the subsequent evolution between interior and atmosphere, as well as on the surface as liquid water in case of favorable temperature and pressure conditions. The main processes responsible for the water distribution are volcanic outgassing driven by partial melting of the silicate mantle and formation of the crust and recycling of water-rich crustal material. Here, an important difference between the terrestrial planets is the tectonic style prevailing on the planet. For the Earth with its plate tectonics, recycling of water is very efficient and can even balance the outgassing. For terrestrial planets in the stagnant lid regime of mantle convection such as Mars, the exchange of water between the interior and the surface/atmosphere is mainly in one direction and results in a continuous depletion of the interior. In this talk, I will briefly review our current knowledge on these interactions between interior and atmosphere and on the problem we are facing to better understand the influence of the interior on the habitability of a planet.

Understanding the processes that led Venus to its current state and will drive its future evolution is a major objective of the next generation of orbiters. In this work we analyze the retrieval of the spin vector, the tidal response, and the moment of inertia of Venus with VERITAS, a NASA Discovery-class mission. By simulating a systematic joint analysis of Doppler tracking data and tie points provided by the onboard synthetic aperture radar, we show that VERITAS will provide accuracies (3σ) in the estimates of the tidal Love number k2 to 4.6 × 10−4, its tidal phase lag to 0°.05, and the moment of inertia factor to 9.8 × 10−4 (0.3% of the expected value). Applying these results to recent models of the Venus interior, we show that VERITAS will provide much-improved constraints on the interior structure of the planet.

We ran several series of two-dimensional numerical mantle convection simulations representing in idealized form the thermochemical evolution of a Mars-like planet. In order to study the importance of compositional buoyancy of melting mantle, the models were set up in pairs of one including all thermal and compositional contributions to buoyancy and one accounting only for the thermal contributions. In several of the model pairs, single large impacts were introduced as causes of additional strong local anomalies, and their evolution in the framework of the convecting mantle was tracked. The models confirm that the additional buoyancy provided by the depletion of the mantle by regular melting can establish a global stable stratification of the convecting mantle and throttle crust production. Furthermore, the compositional buoyancy is essential in the stabilization and preservation of local compositional anomalies directly beneath the lithosphere and offers a possible explanation for the existence of distinct, long-lived reservoirs in the martian mantle. The detection of such anomalies by geophysical means is probably difficult, however; they are expected to be detected by gravimetry rather than by seismic or heat flow measurements. The results further suggest that the crustal thickness can be locally overestimated by up to ∼20 km if impact-induced density anomalies in the mantle are neglected.

Energy sources involved in the early stages of planetary formation can cause partial or even complete melting of the mantle of terrestrial bodies leading to the formation of magma oceans. Upon planetary cooling, solidification is expected to take place from the bottom upwards because of the steeper slope of the liquid adiabat with respect to the liquidus (Elkins-Tanton, 2012; Solomatov, 2015). Fractional solidification, in particular, can lead to the formation of a compositional layering that can play a fundamental role for the subsequent long-term dynamics and evolution of the interior (Tosi et al., 2013; Plesa et al., 2014). In order to assess to what extent primordial compositional heterogeneities generated upon magma ocean solidification can be preserved, we investigate the cooling and solidification of a whole-mantle magma ocean along with the conditions that allow solid-state convection to start mixing the mantle before solidification has completed. To this end, we run 2-D numerical simulations in cylindrical geometry using the finite-volume code GAIA (Huttig et al., 2013). We treat the liquid magma ocean in a parametrized fashion while we self-consistently solve the conservation equations of thermochemical convection in the growing solid mantle accounting for pressure-, temperature- and melt-dependent rheology. We consider two end-member cases: fractional crystallization, where melt is instantaneously extracted into the overlying liquid leaving beneath a differentiated mantle, and batch crystallization where melt remains in contact with the silicate matrix throughout solidification causing no differentiation. By testing the effects of different cooling rates and Rayleigh numbers, we show that for a lifetime of the liquid magma ocean between 1 and 10 Myr (Lebrun et al., 2013), the onset of solid state convection prior to complete mantle crystallization is possible and that part or even all of the compositional heterogeneities generated upon fractionation can be erased by efficient mantle stirring (Figure 1). We discuss the consequences of our findings in relation to the early and long-term evolution of compositional heterogeneities generated via fractional crystallization of magma oceans in terrestrial bodies with emphasis on Mars' thermochemical history.

The first in situ Martian heat flux measurement to be carried out by the InSight Discovery-class mission will provide an important baseline to constrain the present-day heat budget of the planet and, in turn, the thermochemical evolution of its interior. In this study, we estimate the magnitude of surface heat flux heterogeneities in order to assess how the heat flux at the InSight landing site relates to the average heat flux of Mars. To this end, we model the thermal evolution of Mars in a 3-D spherical geometry and investigate the resulting surface spatial variations of heat flux at the present day. Our models assume a fixed crust with a variable thickness as inferred from gravity and topography data and with radiogenic heat sources as obtained from gamma ray measurements of the surface. We test several mantle parameters and show that the present-day surface heat flux pattern is dominated by the imposed crustal structure. The largest surface heat flux peak-to peak variations lie between 17.2 and 49.9 mW m−2, with the highest values being associated with the occurrence of prominent mantle plumes. However, strong spatial variations introduced by such plumes remain narrowly confined to a few geographical regions and are unlikely to bias the InSight heat flux measurement. We estimated that the average surface heat flux varies between 23.2 and 27.3 mW m−2, while at the InSight location it lies between 18.8 and 24.2 mW m−2. In most models, elastic lithosphere thickness values exceed 250 km at the north pole, while the south pole values lie well above 110 km.

Als erdahnliche oder terrestrische Planeten werden diejenigen Planeten in unserem Sonnensystem bezeichnet, die einen ahnlichen Aufbau mit einem eisenreichen Kern, einem Gesteinsmantel und einer Kruste besitzen – dies sind der Merkur, die Venus, der Mars und unsere Erde. Durch Vorgange im Planeteninneren und Einwirkungen von ausen wurden sie seit ihrer Entstehung vor etwa 4,5 Milliarden Jahren bestandig verandert, was sich naturlich insbesondere auf ihren Oberflachen widerspiegelt. Verschiedenste Daten von Raumsonden zeigen, dass sich die Planeten unterschiedlich entwickelt haben. Eine Beobachtung, die aber nicht nur fur ihre Oberflachen gilt, sondern auch fur ihre Magnetfelder, Atmospharen und fur die Existenz von Leben. Die Planetenphysik ist eine der Wissenschaften, die man heranzieht, um die Unterschiede, aber auch Gemeinsamkeiten in der Entwicklung der terrestrischen Planeten zu verstehen.

Space missions have shown that most terrestrial bodies have an internally generated magnetic field in their metallic core and/or a crustal field due to remanent magnetism. The latter indicates the presence of an old dynamo at the time of crust formation. Information on the two together helps to uncover the body’s magnetic field history, and it is generally accepted that convection flows driven by thermal or compositional buoyancy in the cores are the most likely source for maintaining global planetary magnetic fields. The convection flow in the core, in turn, is closely related to the interior dynamics of the mantles above and the thermal evolution of the body. This chapter describes the mechanisms for dynamo generation either by thermal or compositional convection in the core. It discusses the magnetic field evolution of Mercury, Moon, Mars, Ganymede, and planetesimals and will also address the possibility of dynamo generation in rocky exoplanets

International audience; Abstract The Interior exploration using Seismic Investigations, Geodesy, and Heat Trans-port (InSight) Mission will focus on Mars’ interior structure and evolution. The basic structure of crust, mantle, and core form soon after accretion. Understanding the early differentiation process on Mars and how it relates to bulk composition is key to improving our understanding of this process on rocky bodies in our solar system, as well as in other solar systems. Current knowledge of differentiation derives largely from the layers observed via seismology on the Moon. However, the Moon’s much smaller diameter make it a poor analog with respect to interior pressure and phase changes. In this paper we review the current knowledge of the thickness of the crust, the diameter and state of the core, seismic attenuation, heat flow, and interior composition. InSight will conduct the first seismic and heat flow measurements of Mars, as well as more precise geodesy. These data reduce uncertainty in crustal thickness, core size and state, heat flow, seismic activity and meteorite impact rates by a factor of 3–10× relative to previous estimates. Based on modeling of seismic wave propagation, we can further constrain interior temperature, composition, and the location of phase changes. By combining heat flow and a well constrained value of crustal thickness, we can estimate the distribution of heat producing elements between the crust and mantle. All of these quantities are key inputs to models of interior convection and thermal evolution that predict the processes that control subsurface temperature, rates of volcanism, plume distribution and stability, and convective state. Collectively these factors offer strong controls on the overall evolution of the geology and habitability of Mars.

The earliest stage of the evolution of a fully assembled planet is profoundly affected by a number of basin-forming impacts large enough to change the dynamics of its deeper interior. These impacts are in some cases quite closely spaced and follow one another in short time intervals, so that their effects interact and result in behavior that may differ from a simple sum of the effects of two individual and isolated impacts. We use two-dimensional models of mantle convection in a Mars-like planet and a simple parameterized representation of the principal effects of impacts to study some of the dynamical effects and interactions of multiple large impacts. In models of only two impacts, we confirm that the dynamical effects of the impacts reinforce each other the closer they are in space and time but that the effects do not always correspond to straightforward superpositions of those of single, isolated impacts. In models with multiple (4-8) impacts with variable sizes, distances, and frequencies, the global response of the mantle is as variable as the impact sequences in the short term, but in the long term the different evolutionary paths converge for several indicator variables such as the mean flow velocity, temperature, or heat flow. Nonetheless, beyond a certain impact frequency and energy, lithospheric instabilities triggered by large impacts occur on a global scale, reinvigorate mantle dynamics for long time spans, and entail a late stage of melt production in addition to the initial melting stage that is not observed in one- or two-impact models. After one or several very large impacts, some lithospheric material may founder and sink to the core-mantle boundary, and if enough of it accumulates there, it enhances the heat flux out of the core for several hundred millions of years, with possible effects on dynamo activity., Comment: 24 pages, 10 figures