Bernard Lago

Geosat‐derived geoid anomalies at medium wavelength

Geosat profiles of the Exact Repeat Mission have been averaged over a 1-year period and high-pass-filtered using inverse method techniques. The geoid surface constructed with both ascending and descending profiles shows at medium wavelengths band-shaped anomalies preferentially elongated in the east-west direction. These anomalies have an average amplitude of ∼30 cm and dominant wavelengths to 750km and 1100 km. We have performed numerous tests to show that the lineations are not artefacts created by the filtering process. Moreover, two-dimensional (2-D) filtering with the inverse method applied on a regional basis over the Pacific gives essentially similar results, indicating that the filtered geoid is not affected by directional bias. Seafloor topography in the Pacific filtered by 2-D inverse method also shows east-west trending depth anomalies positively correlated to medium-wavelength geoid lineations. Along the East Pacific Rise, there is a clear correlation between geoid lineations and regional variations in axial depth. Cross-spectral analysis carried out on geoid and topography data over the Pacific area gives coherence maxima at 750-km and 1100-km wavelengths and admittance values of 2–3 m/km. Observed admittance matches the magnitude and shape of admittance predicted by lithospheric cooling models, suggesting that the lineations are related to regional variations in the plate cooling process. Convection models produce much higher admittances than observed unless a low-viscosity layer is assumed so that dynamical support cannot be completely discarded. In most instances, however, the position and direction of the lineations seem to be controlled by major fractures zones which is in favor of a lithospheric origin. In the south central Pacific where the lineations appear parallel to absolute plate motion, there may be a combination of both lithospheric and sublithospheric processes.

Long wavelength topography, seafloor subsidence and flattening

Seafloor subsidence effects due to cooling of the oceanic lithosphere have been removed from bathymetry data. The corrected ocean floor topography presents long wavelength highs, in particular over western Pacific. We show in this study that this long wavelength residual topography can be interpreted as either a term of seafloor flattening at old ages or a dynamic response to large-scale convection. Whatever its origin, this long wavelength residual topography is dominated by a degree 2 pattern highly correlated with geoid, lower mantle heterogeneities and plate age.

Possible dynamical evolution of the rotation of Venus since formation

The past evolution of the rotation of Venus has been studied by a numerical integration method using the hypothesis that only solar tidal torques and core-mantle coupling have been active since formation. It is found quite conceivable that Venus had originally a rotation similar to the other planets and has evolved in 4.5×109 years from a rapid and direct rotation (12-hour spin period and nearly zero obliquity) to the present slow retrograde one.While the solid tidal torque may be quite efficient in despinning the planet, a thermally driven atmospheric tidal torque has the capability to drive the obliquity from ∼0° towards 180° and to stabilize the spin axis in the latter position. The effect of a liquid core is discussed and it is shown that core-mantle friction hastens the latter part of the evolution and makes even stronger the state of equilibrium at 180°. The model assumes a nearly stable balance between solid and atmospheric tides at the current rotation rate interpreting the present 243 day spin period as being very close to the limiting value.A large family of solutions allowing for the evolution, in a few billions years, of a rapid prograde rotation to the present state have been found. Noticeably different histories of evolution are observed when the initial conditions and the values of the physical parameters are slightly modified, but generally the principal trend is maintained.The proposed evolutionary explanation of the current rotation of Venus has led us to place constraints on the solid bodyQ and on the magnitude of the atmospheric tidal torque. While the constraints seem rather severe in the absence of core-mantle friction (aQ≃15 at the annual frequency is required, and a dominant diurnal thermal response in the atmosphere is needed), for a large range of values of the cores viscosity, the liquid core effect allows us to relax somewhat these constraints: a solid bodyQ of the order ∼40 can then be allowed. ThisQ value implies that a semi-diurnal ground pressure oscillation of ≃2 mb is needed in the atmosphere in order for a stable balance to occur between the solid and atmospheric tides at the current rotation rate. No model of atmospheric tides on Venus has been attempted in this study, however the value of 2 mb agrees well with that predicted by the model given in Dobrovolskis (1978).

Regional variations in subsidence rate of lithospheric plates : implication for thermal cooling models

Abstract Although simple thermal models of lithospheric cooling predict to first order the general behaviour of observed seafloor depth with increasing age, important regional variations in seafloor subsidence, in the range 250–400 m Ma 1 2 , are reported for several lithospheric plates. Such variations cannot be accounted for by classical cooling models unless implausible variations in asthenospheric temperature of ∼550°C are assumed. Here we present an alternative cooling model, which assumes that at the ridge axis the temperature may deviate from the mean asthenospheric temperature. Such a model satisfactorily explains the data provided that the temperature deviation is ±100°C only.

Numerical experiment applicable to the latest stage of planet growth

Abstract A three-dimensional numerical model was developed with the goal of studying limited dynamical problems relevant to the latest stage of planet growth in the accretion theory. A small number of large protoplanets (∼ Moon size) of different masses, moving around the Sun, are considered. The dynamical evolution and growth of the population is studied under mutual gravitational perturbations, accretion, and collisional fragmentation processes. Gravitational encounters are treated exactly by numerical integration of the N-body problem. Outcomes of collisional fragmentation are modeled according to the results of R. Greenberg et al. (1978, Icarus , 35 , 1–26). In the present work, we consider 25 protoplanets with uniform mass distribution in the range 2 × 10 25 −4 × 10 26 g on heliocentric orbits in the Earth zone. These bodies are initially confined to a small volume of space to permit gravitational perturbations by close approaches and collisions within a finite length of integration time. The dynamical evolution of the swarm is followed for four different sets of initial ranges in semimajor axis, eccentricity, and inclination: Δa =0.01, 0.02, 0.04, 0.08 AU; Δe = 0.005, 0.01, 0.02, 0.04; Δi =0°3, 0°6, 1°2, 2°4. Among other results, it is found that average eccentricities and inclinations evolve toward a steady state such that i ⋍ 1 2 , e ; it is also found that, whatever the initial conditions, the population evolves toward a quasi-equilibrium relative velocity distribution corresponding to a Safronov parameter value θ⋍10 . Moreover, the growth process of the growing planet presents very similar behavior in the four cases considered, except for the time scale of evolution, which increases with the initial range of orbital elements. Earlier works of this kind have been presented by L.P. Cox and J.S. Lewis (1980, Icarus , 44 , 706–721) and by G.N. Wetherill (1980b, In Geol. Soc. Canad. Spec. Publ. , p. 20), although a number of differences exist between the three approaches.

Gaseous drag and planetary formation by accretion

Abstract We have made numerical experiments of the collisional and gravitational interaction of a planetesimal swarm in the early Solar System. In particular we study the dynamical evolution of an initial population of kilometer-size planetesimals subject to collisions (accretion, rebound, cratering, and catastrophic fragmentation). This study is based on a Monte-Carlo statistical method and provides the mass and velocity distributions of the planetesimal swarm as a function of time as well as their distribution in heliocentric distance. Several experiments have been performed and three of them are presented here. They simulate the accretional growth of numerous planetesimals in the absence (or presence) of gaseous drag, with (or without) one larger embryo among them, and with (or without) a size gradient. The results show that (i) for a population of planetesimals submitted to a negative gradient in size as the heliocentric distance increases, the outer planetesimals spiral toward the Sun faster than inner ones, leading after some time to an accumulation of bodies inside the cloud which allows the formation of an embryo; (ii) the growth of one embryo among a population of planetesimals is accelerated by the presence of gas and is warranted as long as its feeding zone is fed by the inward flow of planetesimals due to gas drag. These results offer some complementary new insights in the understanding of the accretional formation of 4–5 terrestrial planets instead of the numerous Moon-size planets generally found in numerical experiments.

Evolution of cometary perihelion distances in oort cloud: Another statistical approach

Abstract The evolution of the perihelion distance distribution in the Oort cloud was studied over the age of the solar system, under the gravitational perturbations of random passing stars, using a statistical approach. These perturbations are accounted for through an empirical relation relating the change in cometary perihelion distance to the closest-approach comet-star distance; this relation is deduced from a previous study [H. Scholl, A. Cazenave, and A. Brahic, Astron. Astrophys. 112 , 157–166 (1982)]. Two kinds of initial perihelion distances are considered: (a) perihelion distances 4 AU), possibly representative of comet formation as satellite fragments in the accretion disk of the primitive solar nebula. Distant star-comet encounters, as well as rare close encounters, are considered. Several quantities are estimated: (i) number of “new” comets entering into the planetary region, (ii) number of comets escaping the Sun sphere of influence or lost by hyperbolic ejection and (iii) percentage of total comet loss over the age of the solar system. From these quantities, the current and original cloud populations are deduced, as well as the corresponding cloud mass, for the two types of formation scenarios.

Thermal and mechanical behaviour of the oceanic lithosphere constrained by geoid and gravity anomalies over the Mid-Atlantic Ridge axial valley

Abstract Geoid profiles derived from Seasat altimetry data, crossing the North Atlantic mid-oceanic ridge are analysed; an obliquity of about 60° does not perturb the analysis much. Conjointly, with bathymetric and gravimetric profiles of the Famous campaign, these geoid profiles are compared with theoretical ones. Assumptions made in this study concern the neglect of the variations along the ridge axis; the choice of the half-space model for the cooling of the plate, which is improved by the introduction of a lead term and the use of a flat Earth approximation in the computation of geoid and gravity anomalies. The choice of a full two-dimensional numerical technique allows a good evaluation of these anomalies for the detailed structure close to the axis. The models take into account the thermal cooling of the plate, the shifting of the isotherms due to the axial valley, the contribution of the crust; different assumptions are made relative to crustal thinning beneath the valley, to a lithospheric necking or to a viscous drag effect of the rising magma, eventually connected with the formation of the axial valley. Isostatic compensation of the axial valley by crustal thinning is clearly confirmed by the gravimetric data alone, but not by the altimetric data; differences in Δg and Δh (gravimetry and geoid low, respectively) are not large enough to really discriminate between the proposed models; the theoretical amplitudes appear overestimated for gravity anomalies and underestimated for geoid anomalies; if confirmed, this fact would give indications to improve the model.