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NASA’s InSight (Interior exploration using Seismic Investigations, Geodesy and Heat Transport) mission landed in Elysium Planitia on Mars on 26 November 2018. It aims to determine the interior structure, composition and thermal state of Mars, as well as constrain present-day seismicity and impact cratering rates. Such information is key to understanding the differentiation and subsequent thermal evolution of Mars, and thus the forces that shape the planet’s surface geology and volatile processes. Here we report an overview of the first ten months of geophysical observations by InSight. As of 30 September 2019, 174 seismic events have been recorded by the lander’s seismometer, including over 20 events of moment magnitude Mw= 3–4. The detections thus far are consistent with tectonic origins, with no impact-induced seismicity yet observed, and indicate a seismically active planet. An assessment of these detections suggests that the frequency of global seismic events below approximately Mw= 3 is similar to that of terrestrial intraplate seismic activity, but there are fewer larger quakes; no quakes exceeding Mw= 4 have been observed. The lander’s other instruments—two cameras, atmospheric pressure, temperature and wind sensors, a magnetometer and a radiometer—have yielded much more than the intended supporting data for seismometer noise characterization: magnetic field measurements indicate a local magnetic field that is ten-times stronger than orbital estimates and meteorological measurements reveal a more dynamic atmosphere than expected, hosting baroclinic and gravity waves and convective vortices. With the mission due to last for an entire Martian year or longer, these results will be built on by further measurements by the InSight lander.

Recent estimates of the crustal thickness of Mars show a bimodal result of either ∼20 or ∼40 km beneath the InSight lander. We propose an approach based on random matrix theory applied to receiver functions (RFs) to further constrain the subsurface structure. Assuming a spiked covariance model for our data, we first use the phase transition properties of the singular value spectrum of random matrices to detect coherent arrivals in the waveforms. Examples from terrestrial data show how the method works in different scenarios. We identify three previously undetected converted arrivals in the InSight data, including the first multiple from a deeper third interface. We then use this information to jointly invert RFs with the absolute S‐wave velocity information in the polarization of body waves. Results show a crustal thickness of 43 ± 5 km beneath the lander with two mid‐crustal interfaces at depths of 8 ± 1 and 21 ± 3 km. Recent analysis of seismic data from InSight shows that the crustal thickness beneath the InSight lander can be either 20  or 40 km. To resolve this ambiguity, we apply results from random matrix theory to receiver function (RF) analysis. The distribution of singular values of a random matrix shows well‐behaved deterministic properties that can be used to separate them from those of an underlying coherent signal if present. We use examples from terrestrial data to show how the method works. When applied to RFs computed from InSight seismic data, we identify three new energy arrivals, including one that supports the existence of a deeper third layer. Using this information, we simultaneously inverted the RF data along with the measured incidence angle of body waves. Results show a crustal thickness of 43 ± 5 km beneath the lander with two mid‐crustal interfaces at depths of 8 ± 1 and 21 ± 3 km. We apply recent results from random matrix theory to identify crustal phases in noisy receiver functions for Mars from InSight dataOnce identified, we jointly invert these phases with frequency‐dependent apparent S‐wave velocity curvesResults show a crustal thickness of 43 km with two inter‐crustal discontinuities at 8 and 21 km beneath the lander We apply recent results from random matrix theory to identify crustal phases in noisy receiver functions for Mars from InSight data Once identified, we jointly invert these phases with frequency‐dependent apparent S‐wave velocity curves Results show a crustal thickness of 43 km with two inter‐crustal discontinuities at 8 and 21 km beneath the lander

We present seismic images of the upper mantle below the Quaternary Eifel volcanic fields, Germany, determined by teleseismic travel time tomography. The data were measured at a dedicated network of more than 200 stations. Our results show a columnar low P-velocity anomaly in the upper mantle with a lateral contrast of up to 2%. The 100 km wide structure extends to at least 400 km depth and is equivalent to about 150–200 K excess temperature. This clear evidence for a plume below a region of comparatively minor volcanism suggests that deep mantle plumes could be more numerous than commonly assumed. They may often be associated with small volcanic fields or may have no volcanic surface expression at all.

The Nusselt number for two-dimensional Bénard convection with free boundaries at infinite Prandtl number is determined numerically with high precision for Rayleigh numbers in the range 104-1011. The coefficients for the asymptotic dependence of the Nusselt number on the cubic root of the Rayleigh number according to boundary layer theory are also re-evaluated. The numerical data indicate a slow approach to the cubic root law with a deviation of 1% at Ra=1011.

A two-dimensional numerical convection model in cartesian geometry is used to study the influence of trench migration on the ability of subducted slabs to penetrate an endothermic phase boundary at 660 km depth. The transient subduction history of an oceanic plate is modelled by imposing plate and trench motion at the surface. The viscosity depends on temperature and depth. A variety of styles of slab behaviour is found, depending predominantly on the trench velocity. When trench retreat is faster than 2–4 cm/a, the descending slab flattens above the phase boundary. At slower rates it penetrates straight into the lower mantle, although flattening in the transition zone may occur later, leading to a complex slab morphology. The slab can buckle, independent of whether it penetrates or not, especially when there is a localised increase in viscosity at the phase boundary. Flattened slabs are only temporarily arrested in the transition zone and sink ultimately into the lower mantle. The results offer a framework for understanding the variety in slab geometry revealed by seismic tomography.

At least two different types of convection should exist in the earth's mantle: a large scale flow which is revealed by the creation and subduction of oceanic crust, and a circulation of unknown scale under the continents, which does not approach the surface. The effects of these coexisting and interacting modes on mantle dynamics and thermal regime are investigated by means of a finite element model system of two adjacent cells which are coupled thermally and mechanically at their interface. An a-priori viscosity distribution is applied in such a way that the surface layer of the longer cell can move with almost uniform velocity, while it is immobile on the shorter cell. The results suggest that the pattern of sub-oceanic convection is stabilized to some extent by the frame of the highly viscous but moving lithosphere, whereas convection under continents is more complex and less stable. Most of the sub-continental heat is transferred into the oceanic cell. This causes an imbalance of surface heat flow which is well in accordance with recent determinations of global heat loss distribution. Furthermore the model reflects at least semiquantitatively the continent-ocean differences in lithospheric thickness, mean topographic level and upper mantle temperatures. While the average geotherms below ocean and continent diverge by up to 400 K at moderate depth, they nearly coincide below 250 km depth, thus giving no support for deep reaching continent-ocean differences. These results refer to convection penetrating the lower mantle, if the circulation is confined to moderate depth the continental upper mantle is too hot compared with the oceanic. However, this may be due to the strict separation of the flow on either side. The model results stimulate some speculations on the possible form of whole mantle convection.

We present 3-D solutions for buoyancy-driven flow with variable viscosity in a spherical shell. A hybrid finite difference and spectral method is used to assess the influence of lateral-viscosity variations (LVV) on the long-wavelength (ℓ = 1–6) observable features of mantle convection: geoid anomalies, topography anomalies and surface velocities. The non-linear coupling of the various spherical harmonic modes is calculated by an interative technique. The density anomalies δp that drive the flow are taken to be proportional to the anomalies of seismic velocity from several tomographic models. Two viscosity models are used: a Newtonian ‘temperature dependent’ model in which the viscosity varies exponentially with δp, and a non-Newtonian model in which the viscosity varies with strain rate. Our calculations show that the effects of LVV on the geoid are of second order relative to those due to changes in radial-viscosity structure. The geoid is hardly affected by LVV if the mantle viscosity is radially uniform, but the effect on the higher order (δ > 3) modes of the geoid can be significant if the viscosity is radially stratified. However, for the models tested neither temperature-dependent viscosity nor non-linear rheology is found to reduce the misfit between the observed and the modelled geoid. Toroidal motion is generated by lateral viscosity differences inferred from the tomography results, but the toroidal-to-poloidal ratio is small (<20 per cent).

Phase boundaries are included in dynamical finite element models of mantle convection. They are represented by point chains which act as additional sources of buoyancy forces when distorted, and as additional source or sink of heat. The influence of the exothermic olivine-spinel transition is studied in both shallow and deep convection models. The flow is only slightly enhanced by the transition. The increase of temperature due to latent heat release is step-like in the deep model, in the case of shallow convection it is more diffuse. Other quantities like ocean-floor topography, gravity anomalies, and stress distribution are no more than moderately affected. In a further investigation the effect of spinel post-spinel transition, whether endothermic or exothermic, on deep convection is examined. The effect on the flow is negligibly small in both cases.