where g is the acceleration due to gravity. Convection will occur if Ra is greater than some critical value, which is approximately 1000.
None of the landed spacecraft has measured surface heat flow on Mars, so all heat flux estimates are based on modeling. While conduction is expected to be the dominant mechanism of heat transport through the lithosphere, convection should occur in the deep martian interior. Mantle convection can be driven by bottom heating, where heat from the core drives the convection, or from internal heating caused by the decay of radioactive elements within the mantle itself. Kiefer (2003) argues that the broad topographic rises associated with Tharsis and Elysium result from internal heating, which produces broad convective upwellings. Mantle plumes, responsible for the individual volcanic constructs, can be embedded within these broad upwelling zones.
McGovern et al. (2002, 2004a) used MGS gravity and topography data to estimate the thickness of the elastic lithosphere at the time of surface loading and from that determine the surface heat flux. They estimate that the oldest surface
units were emplaced when heat flux was >40 milliwatts per square meter (mW m )
and that Q has declined to values typically <20 mW m in recent times (McGovern
et al., 2004a). These values are consistent with an estimated Q of ~37 mW m near 3.0-3.7 Ga ago based on the spacing of tectonic wrinkle ridges (Montesi and Zuber, 2003). However, Grott et al. (2005) suggest Q between 54 and 66 mW m-2 between 3.5 and 3.9 Ga ago based on elastic thickness estimates in the Coracis Fossae region. Heat flux likely varies with location on Mars, as it does on Earth, so the variations in time and geographic position suggested by these different studies may not be inconsistent. Improved constraints on heat flux will have to await emplacement of a network of seismic and geothermal measurement stations across the martian surface.
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