As a prospective study for a future exploration of Venus, we compute the tidal response of Venus' interior assuming various mantle compositions and temperature profiles representative of different scenarios of Venus' formation and evolution. The mantle density and seismic velocities are modeled from thermodynamical equilibria of mantle minerals and used to predict the moment of inertia, Love numbers, and tide‐induced phase lag characterizing the signature of the internal structure in the gravity field. The viscoelasticity of the mantle is parameterized using an Andrade rheology. From the models considered here, the moment of inertia lies in the range of 0.327 to 0.342, corresponding to a core radius of 2900 to 3450 km. Viscoelasticity of the mantle strongly increases the potential Love number relative to previously published elastic models. Due to the anelasticity effects, we show that the possibility of a completely solid metal core inside Venus cannot be ruled out based on the available estimate of k2 from the Magellan mission (Konopliv and Yoder, 1996). A Love number k2 lower than 0.27 would indicate the presence of a fully solid iron core, while for larger values, solutions with an entirely or partially liquid core are possible. Precise determination of the Love numbers, k2 and h2, together with an estimate of the tidal phase lag, are required to determine the state and size of the core, as well as the composition and viscosity of the mantle.

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The habitability of Europa's subsurface ocean is conditioned by heat released from the deep interior and by intensity of magmatic activity. Here, we investigate the melting of the silicate mantle through time and its consequences for seafloor magmatism by modeling Europa's internal heat production and transfer using a three‐dimensional numerical model. We show that melt can be produced during most of Europa's history due to the limited efficiency of internal cooling by thermal convection and the presence of radiogenic heating. The melting rate is amplified by tidal friction, possibly leading to magmatic pulses during enhanced eccentricity periods and focusing melting to high latitudes. The volume of generated melts during magmatic episodes is comparable to those involved in Large Igneous Provinces, commonly observed on Earth, and may impact ocean chemistry. We predict that gravity measurements, detection of anomalous H2/CH4, and astrometric data by future missions could confirm ongoing large‐scale seafloor activity.

S U M M A R YNumerical simulations of 2-D Rayleigh-Bénard convection are designed to study the development of convection at the base of the cooling lithosphere. A zero temperature is suddenly imposed at the mantle surface, which has initially a homogeneous temperature. The strongly temperature-dependent viscosity fluid is heated from within, in order to balance the internal temperature drift resulting from global fluid cooling. For a while, the lithosphere cools approximatively as a conductive half-space and the lithospheric isotherms depth grows as the square root of age. As instabilities progressively develop at the base of the lithosphere, lithospheric cooling departs from the half-space model. We propose two different parametrizations of the age of the first dripping instability, using boundary layer marginal stability or quantifying the characteristic timescale of the instability exponential growth as a function of the Rayleigh number and of the viscous temperature scale. Both parametrizations account very well for our numerical estimates of onset times, but with a slightly better adjustment of the viscous temperature scale dependence in the second case. The absolute value of the onset time depends on the amplitude and location of initial temperature perturbations within the box and on the initial temperature structure of the thermal boundary layer (TBL). Furthermore, thermal perturbations of finite amplitude located within the lithosphere (such as the ones induced by transform faults, for example) strongly reduce the age of the first dripping instability. However, the onset time parametrization derived from transient cooling experiments well adjusts the lithospheric age of the first drip instability below a lithosphere cooling perpendicularly to the ridge axis. This study emphasizes the role of the initial topography of the lithospheric isotherms on the development of instabilities.

S U M M A R YWe present a new numerical method to describe the internal dynamics of planetary mantles through the coupling of a dynamic model with the prediction of geoid and surface topography. Our tool is based on the simulation of thermal convection with variable viscosity in a spherical shell with a finite-volume formulation. The grid mesh is based on the 'cubed sphere' technique that divides the shell into six identical blocks. An investigation of various numerical advection schemes is proposed: we opted for a high-resolution, flux-limiter method. Benchmarks of thermal convection are then presented on steady-state tetrahedral and cubic solutions and time-dependent cases with a good agreement with the few recent programs developed to solve this problem.A dimensionless framework is proposed for the calculation of geoid and topography introducing two dimensionless numbers: such a formulation provides a good basis for the systematic study of the geoid and surface dynamic topography associated to the convection calculations. The evaluation of geoid and surface dynamic topography from the gridded data is performed in the spectral domain. The flow solver is then tested extensively against a precise spectral program, producing response functions for geoid as well as bottom and surface topographies. For a grid mesh of a reasonable size (6 × 64 × 64 × 64) a very good agreement (to within ∼1 per cent) is found up to spherical harmonic degree 15.Several of today's questions in the study of planetary interiors imply the use of models simulating thermal convection in a spherical geometry. This is either implicitly required by the internal dynamics (effect of curvature on thermal instabilities and heat flux budget, correct scaling of mass flux when addressing compositional gradients, modelling plate motion on a sphere) or due to a better comparison of these with geophysical data often expressed as a decomposition into spherical harmonics (e.g. in the case of data from space exploration). In addition, in order to address many problems a numerical model of thermal convection should handle large viscosity gradients: (i) the effective viscosity of silicates or ices is very sensitive to thermodynamical parameters, inducing very specific dynamical regimes such as the asymptotic conductive lid regime (e.g. Davaille & Jaupart 1993); (ii) in order to mimic the plate behaviour, more complex rheologies have been proposed that imply even larger viscosity gradients (e.g. Tackley 2000a,b; see also Bercovici 2003 for a review).The first programs simulating thermal convection in a spherical shell were based on a spectral approach (Glatzmaier 1988; Zhang 1995) since this allows an elegant treatment in the case of a viscosity field that is constant or radius-dependent. However, these methods lose part of their interest in the case of large lateral viscosity variations. A first attempt to solve variable viscosity convection with a grid-based method is proposed by Hsui et al. (1995) after a finite element discretization developed in the isovi...

Many islands of the eastern Indonesian Archipelago exhibit Late Cenozoic sequences of coral reef terraces. In SE Sulawesi, on the Tukang Besi and Buton archipelagos, we identified 23 islands bearing such sequences. Remote sensing imagery and field mapping combined to U/Th and 14 C dating enable to establish a chronologic framework of the reef terrace sequences from Wangi-Wangi, Buton as well as on the neighbouring, smaller islands of Ular, Siumpu and Kadatua. We identified the terraces from the last interglacial maximum (MIS 5e) at elevations lower than 20 m except on W Kadatua where it is raised at 34 ± 5 m. Such elevations yield low to moderate Upper Pleistocene uplift rates (<0.3 mm yr À1). On SE Buton Island, a sequence culminates at 650 m and includes at least 40 undated strandlines. Next to this exceptional sequence, on the Sampolawa Peninsula, 18 strandlines culminate at 430 m. Dated samples at the base of this sequence (<40 m) yield mean Middle Pleistocene uplift rates of 0.14 ± 0.09 mm yr À1. Extrapolation of these uplift rates compared to the geological setting suggests that the sequences of the Sampolawa Peninsula provide a record of sea-level high-stands for the last 3.8 ± 0.6 Ma. The sequences on SE Buton Island therefore constitute the best preserved long-lasting geomorphic record of Plio-Quaternary sea-level stands worldwide.

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