Attilio Rivoldini

Constraints on thermal state and composition of the Earth's lower mantle from electromagnetic impedances and seismic data

Despite the tight constraints put by seismology on the elastic properties of the Earths lower mantle, its mineralogical composition and thermal state remain poorly known because the interpretation of seismic measurements suffers from the trade-off between temperature, iron content, and mineralogical composition. In order to overcome this difficulty, we complement seismic data with electromagnetic induction data. The latter data are mostly sensitive to temperature and iron content, while densities and acoustic speeds mostly constrain the mineralogy. A 0.5 log unit increase in electrical conductivity can be caused either by a 400 K increase of the temperature or by an increase of iron content from 10% to 12.5%. Acoustic velocity is only marginally sensitive to temperature but it increases by 0.8 km s−1 on average as the perovskite fraction increases from 50% to 100%. Olsens (1999) apparent resistivities in the period range [15 days, 11 years], and Preliminary reference Earth model (PREM) densities and acoustic speeds are jointly inverted in the depth range [800 km, 2600 km] by using a Monte Carlo Markov Chain method. Given the uncertainties on these data, estimates of perovskite fraction are well constrained over the whole depth range, but information on temperature and iron content is only obtained for depths less than 2000 km, corresponding to the penetration depth of the long-period electromagnetic field. All parameter values are determined with an uncertainty better than 15–20% at the 1σ confidence level. The temperature in the uppermost lower mantle (i.e., down to 1300 km depth) is close to a value of 2200 K and increases along a superadiabatic gradient of 0.4 K km−1 between 1300 and 2000 km depth. Extrapolation of this gradient at greater depth leads to a temperature close to 2800 K at 2600 km depth. The iron content of the lower mantle is found to be almost constant and equal to 10–11% whatever the depth, while a significant linear decrease of the perovskite content is observed throughout the whole depth range, from 80% at 800 km depth down to ∼65% at 2600 km depth.

Influence of an inner core on the long-period forced librations of Mercury

Abstract The planetary perturbations on Mercury’s orbit lead to long-period forced librations of Mercury’s mantle. These librations have previously been studied for a planet with two layers: a mantle and a liquid core. Here, we calculate how the presence of a solid inner core in the liquid outer core influences the long-period forced librations. Mantle–inner core coupling affects the long-period libration dynamics mainly by changing the free libration: first, it lengthens the period of the free libration of the mantle, and second, it adds a second free libration, closely related to the free gravitational oscillation between the mantle and inner core. The two free librations have periods between 2.5 and 18y depending on the internal structure. We show that large amplitude long-period librations of a few tens of arcsec are generated when the period of a planetary forcing approaches one of the two free libration periods. These amplitudes are sufficiently large to be detectable by spacecraft measurements of the libration of Mercury. The amplitudes of the angular velocity of Mercury’s mantle at planetary forcing periods are also amplified by the resonances, but remain much smaller than the current precision of Earth-based radar observations unless the period is very close to a free libration period. The inclusion of mantle–inner core coupling in the rotation model does not significantly improve the fit to the radar observations. This implies that it is not yet possible to determine the size of the inner core of Mercury on the basis of available observations of Mercury’s rotation rate. Future observations of the long-period librations may be used to constrain the interior structure of Mercury, including the size of its inner core.

A generalized bayesian inference method for constraining the interiors of super Earths and sub-Neptunes

Aims. We aim to present a generalized Bayesian inference method for constraining interiors of super Earths and sub-Neptunes. Our methodology succeeds in quantifying the degeneracy and correlation of structural parameters for high dimensional parameter spaces. Specifically, we identify what constraints can be placed on composition and thickness of core, mantle, ice, ocean, and atmospheric layers given observations of mass, radius, and bulk refractory abundance constraints (Fe, Mg, Si) from observations of the host star’s photospheric composition. Methods. We employed a full probabilistic Bayesian inference analysis that formally accounts for observational and model uncertainties. Using a Markov chain Monte Carlo technique, we computed joint and marginal posterior probability distributions for all structural parameters of interest. We included state-of-the-art structural models based on self-consistent thermodynamics of core, mantle, high-pressure ice, and liquid water. Furthermore, we tested and compared two different atmospheric models that are tailored for modeling thick and thin atmospheres, respectively. Results. First, we validate our method against Neptune. Second, we apply it to synthetic exoplanets of fixed mass and determine the effect on interior structure and composition when (1) radius; (2) atmospheric model; (3) data uncertainties; (4) semi-major axes; (5) atmospheric composition (i.e., a priori assumption of enriched envelopes versus pure H/He envelopes); and (6) prior distributions are varied. Conclusions. Our main conclusions are: (1) given available data, the range of possible interior structures is large; quantification of the degeneracy of possible interiors is therefore indispensable for meaningful planet characterization. (2) Our method predicts models that agree with independent estimates of Neptune’s interior. (3) Increasing the precision in mass and radius leads to much improved constraints on ice mass fraction, size of rocky interior, but little improvement in the composition of the gas layer, whereas an increase in the precision of stellar abundances enables to better constrain mantle composition and relative core size; (4) for thick atmospheres, the choice of atmospheric model can have significant influence on interior predictions, including the rocky and icy interior. The preferred atmospheric model is determined by envelope mass. This study provides a methodology for rigorously analyzing general interior structures of exoplanets which may help to understand how exoplanet interior types are distributed among star systems. This study is relevant in the interpretation of future data from missions such as TESS, CHEOPS, and PLATO.

A geophysical perspective on the bulk composition of Mars

We invert the Martian tidal response and mean mass and moment of inertia for chemical composition, thermal state, and interior structure. The inversion combines phase equilibrium computations with a laboratory-based viscoelastic dissipation model. The rheological model, which is based on measurements of anhydrous and melt-free olivine, is both temperature and grain size sensitive and imposes strong constraints on interior structure. The bottom of the lithosphere, defined as the location where the conductive geotherm meets the mantle adiabat, occurs deep within the upper mantle (∼250–500 km depth) resulting in apparent upper mantle low-velocity zones. Assuming an Fe-FeS core, our results indicate: 1) a Mantle with a Mg# (molar Mg/Mg+Fe) of ∼0.75 in agreement with earlier geochemical estimates based on analysis of Martian meteorites; 2) absence of bridgmanite- and ferropericlase-dominated basal layer; 3) core compositions (13.5–16 wt% S), core radii (1640–1740 km), and core-mantle-boundary temperatures (1560–1660 ∘ C) that, together with the eutectic-like core compositions, suggest the core is liquid; and 4) bulk Martian compositions that are overall chondritic with a Fe/Si (wt ratio) of 1.63–1.68. We show that the inversion results can be used in tandem with geodynamic simulations to identify plausible geodynamic scenarios and parameters. Specifically, we find that the inversion results are reproduced by stagnant lid convection models for a range of initial viscosities (∼1019–1020 Pa·s) and radioactive element partitioning between crust and mantle around 0.001. The geodynamic models predict a mean surface heat flow between 15–25 mW/m2.

Dyadic frames of directional wavelets as texture descriptors

We propose a wavelet-based texture classification system. Texture descriptors are local energy measures within the feature images obtained by projecting the samples on Dyadic Frames of Directional Wavelets. Rotation invariant features are obtained by taking the Fourier expansion of the subsets of components of the original feature vectors concerning each considered scale separately. Three different classification schemes have been compared: the Euclidean, the weighted Euclidean and the KNN classifiers. Performances have been evaluated on a set of 13 Brodatz textures, from which both a training set and a test set have been extracted. Results are present in the form of confusion matrices. The KNN classifier provides the globally best performance, with an average recognition rate around the 96 percent for the original non-rotated test set, and 88 percent when the rotated versions are considered. Its simplicity and accuracy renders the proposed method highly suited for multimedia applications, as content-based image retrieval.