Convection, elasticity and flexure inside terrestrial planets

David N. Barnett


Abstract

In this dissertation, the large-scale geophysical behaviour of the Earth, Venus and Mars are compared, using data collected by the Magellan spaceprobe (for Venus) and the Viking and Mars Global Surveyor (MGS) probes (for Mars).

The elastic thickness, Te, for various regions of Venus is estimated by calculating the admittance between gravity and topography in the frequency domain and by modelling lithospheric flexure in the space domain. The former is achieved by comparing the observed line of sight (LOS) acceleration of the Magellan spacecraft with that predicted using a spherical harmonic representation of the topography, to degree and order 360. Flexure of the lithosphere is modelled from residual topography (i.e. that topography which remains after the removal of the component which is dynamically supported by convection) at rifts, coronae, chasmata and the moats visible around certain large volcanoes. In addition, the elastic thickness is estimated at seven volcano-like structures by modelling the gravity predicted from the observed topography. The Te estimates carried out in the frequency domain are found generally to be more tightly constrained than the spatial estimates, but are averages over the box which is analysed in each case (and which is typically at least 4000 km across). The more localised estimates carried out in the space domain are less well-constrained and can usually give only a lower limit for Te. There is no convincing evidence that the elastic thickness of Venus is anywhere outside the range 29 ± 6 km, which is consistent with the lithospheric age of Venus being almost constant everywhere, as suggested by crater counting. The fact that the elastic thickness of Venus is similar to that of the old ocean basins on the Earth, despite the high surface temperature of Venus, is probably due to an absence of water in the interior of Venus allowing the lithosphere to maintain elastic stresses to higher temperatures than on the Earth. The heat flux estimates corresponding to the observed values of Te (i.e. 18-24 mW/m2) agree well with estimates of the heat flux obtained by convective modelling. A crustal density of 2700 kg/m3 provides a best-fit to the short wavelength admittance estimates, with a range of between 2500 and 2900 kg/m3 fitting the data within uncertainty.

Viking and MGS LOS data are processed using a topography dataset derived from Mars Orbiter Laser Altimeter (MOLA) altimetry to yield elastic thickness estimates for Mars by admittance analysis. However, the orbits of these craft are, at present, poorly determined, so the Te estimates are not well constrained. The long wavelength admittance estimates at Tharsis constrain the mechanical boundary layer (MBL) thickness at this location to be no greater than around 250 km, if the underlying asthenosphere is convecting with a Rayleigh number less than ~ 106. Estimates of the amounts of melt generated by convective plumes also suggest that the MBL thickness is between 150 and 250 km. This range is consistent with an elastic thickness for Tharsis of between approximately 75 and 125 km.

The MGS75D Mars spherical harmonic gravity field is consistent with the topography only if the crustal density is of order 3500 kg/m3, which is higher than the estimate of 3320 ± 40 kg/m3, obtained from the modal mineralogy of the Shergotty, Nakhla and Chassigny (SNC) meteorites. The transfer function between the observed LOS accelerations of MGS and those calculated from MGS75D is essentially unity at all wavelengths, suggesting the error in MGS75D arises from the interpolation between the MGS tracks. Interpolation errors are likely to result from the fact that adjacent tracks are parallel and widely separated, especially if there are inaccuracies in the orbital determination of MGS.

The elastic thickness at several large Martian volcanoes is estimated by comparing the gravity anomalies predicted from the MOLA topography with those given by MGS75D. This analysis yields Te estimates mostly in the range 70-170 km for the Tharsis volcanoes, and 25 (± ~ 20) km for Elysium Mons. An elastic thickness of around 100 km implies a surface heat flux of approximately 20 mW/m2, which is in good agreement with the value predicted by a numerical model of Martian crustal formation and radiogenic heat production.

The Earth, Venus and Mars are all likely to be undergoing active mantle convection at the present day. Sites including Beta, Bell, Atla and Phoebe Regiones on Venus are thought to be underlain by active plumes on the basis of their positive topographic and gravity anomalies, showing admittances of between 20 and 50 mGal/km at wavelengths longer than around 500 km, and the presence of rift and volcanic features visible in the synthetic aperture radar (SAR) images. Numerical modelling suggests that most of the topography and gravity of the Tharsis region on Mars can be explained by dynamic support, a conclusion which is consistent with the long wavelength admittance estimates.

Neither Venus nor Mars show evidence of plate tectonics operating at the present day. On Venus, the lack of water means the frictional resistance at faults and the viscous drag on the base of the moving lithospheric plates are too high to be overcome by the driving forces for plate tectonics. The high elastic thickness of Mars results in a large frictional resistance to fault motion, although the faults themselves are probably no stronger than those on the Earth, and means large compressive stresses are required to initiate subduction. The likely high viscosity of the Martian mantle, a consequence of its probable dryness and low temperature, may also result in large drag forces on the base of the lithosphere. Plate tectonics may have operated in the past on both planets, providing a possible explanation for the rapid resurfacing of Venus required by the crater counts and the linear magnetic anomalies recently discovered on Mars.


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