On models of Mars' interior and amplitudes of forced nutations 1. The effects of deviation of Mars from its equilibrium state on the flattening of the core-mantle boundary

摘要

In a static approach the effects of deviation of Mars from its equilibrium state on the flattening of the core-mantle boundary (CMB) are Studied. The calculations are performed for a set of interior structure models with 50- and 100-km thick crust and averaged crustal density varying in the range of 2700-3200 kg m(-3), which are based on new values for the moment of inertia and the elastic tidal Love number k(2)(s) defined by Konopliv et al. [Konopliv, A.S., Yoder, C.F., Standish, E.M., Yuan, D.-N., Sjorgen, W.L., 2006. A global solution for the Mars static and seasonal gravity, Mars orientation, Phobos and Deimos masses, and Mars ephemeris. Icarus, 182, 23-50]. The models differ in density contrast at the crust-mantle boundary and the core radius. The observational data constrain the radius of a liquid core to be within 1700-1800 km. For joint interpretation of gravity and topography data an outer Surface of a hydrostatical model is chosen as a reference surface. The Green's functions (or loading factors) technique for the case of a single anomalous density wave located at two depth level is used to compute the second-degree CMB deformation, and then the CMB flattening. Two types of models have been Calculated: an elastic model and a model with an elastic lithosphere and weakened layers below it (relaxed values of shear Modulus): the effective shear modulus of the mantle is reduced in comparison with an elastic one and in extreme case it is approaching zero everywhere except the elastic lithosphere. Non-equilibrium state of Mars results ill three-axiality of the core-mantle boundary. For an elastic case the deformation of CMB leads to the large decrease of the semiaxis b, going through the central region of Tharsis rise, by 660-780 m, and the increase of the equatorial semiaxis a by 240-300 m, and the polar axis c by 400-490 m. Tharsis rise plays a constitutive role for the CMB deformation. The second-degree harmonics in the expansion of non-equilibrium part of gravity field and topography are sensitive, first of all, to the properties of the crust in the Tharsis region. Non-hydrostatic contributions decrease the flattening of the CMB by about 5-6%. The effect of loading increases when the Value of shear modulus decreases by a factor of 10, but as the shear modulus is decreasing up to zero the flattening is approaching its hydrostatic Value.