3D spherical models of Martian mantle convection constrained by melting history
Introduction
The Tharsis region, consisting of the shield volcanoes Olympus Mons, Arsia Mons, Pavonis Mons, Ascraeus Mons and Alba Patera, is one of the most prominent features of Mars. High resolution Mars Orbiting Laser Altimeter (MOLA) topography provides a view of the Tharsis region and its shield volcanoes, showing that this region consists of two rises: the southern rise from 40°S to 20°N which includes Arsia, Pavonis and Ascraeus Mons, and the northern rise which consists of Alba Patera. Unlike the other shield volcanoes, Olympus Mons sits off the western edge of the Tharsis rise (Smith et al., 1999). Previous studies have suggested that one or more plumes could be responsible for the formation of Tharsis (Harder and Christensen, 1996, Kiefer, 2003, Wenzel et al., 2004, Solomon et al., 2005, Zhong, 2009, Sramek and Zhong, 2010).
The relative and absolute ages of surface features can be studied by impact cratering studies (Tanaka, 1986, Tanaka et al., 1992, Hartmann et al., 1999, Hartmann et al., 2008, Werner, 2009). The southern hemisphere is heavily cratered with older geological features in contrast to the lightly cratered northern hemisphere, possibility due to volcanic resurfacing (Mutch et al., 1976, Carr, 1981, Zuber et al., 2000, Zhong and Zuber, 2001, Frey et al., 2002, Carr and Head, 2010). The northern hemisphere is lower in elevation and has a thinner crust than the southern highlands (Zuber et al., 2000, Neumann et al., 2004, Solomon et al., 2005). However, a number of buried impact basins, known as Quasi-Circular Depressions (QCD), were discovered underneath the surface in the northern hemisphere indicating a basement surface equal in age, if not older than, the southern highlands (Frey et al., 2002).
The southern highlands have abundant valley networks (Phillips et al., 2001) and nearly all of these appear to flow into or away from the Tharsis trough, a topographic depression that surrounds Tharsis. These valleys formed after most of Tharsis was emplaced because the Tharsis slope determines the direction of flow. The majority of the valley networks are late Noachian in age, suggesting that Tharsis had formed by Noachian (Phillips et al., 2001), while a few regions have a younger Hesperian age (Smith et al., 1999). The Noachian age suggests that the lithospheric structure underneath Tharsis has remained stable through Marsʼs evolution (Anderson et al., 2001), with majority of the crust having formed during the early and mid-Noachian (Scott and Tanaka, 1986, Greeley and Guest, 1987, Tanaka and Scott, 1987, McEwen et al., 1999, Anderson et al., 2001, Phillips et al., 2001, Head et al., 2001, Zuber, 2001, Frey et al., 2002, Solomon et al., 2005, Werner, 2008, Carr and Head, 2010).
While most of Tharsis was emplaced during the Noachian period, images from Mars Express shows that a few volcanic regions lack visible craters and these have been interpreted to be areas resurfaced by young lava flows (Plescia, 1990, Hartmann et al., 1999, Hartmann et al., 2008, Hartmann and Berman, 2000, Berman and Hartmann, 2002, Neukum et al., 2004, Hartmann, 2005, Hauber et al., 2011). It was once believed that volcanism at Elysium province ended prior to 2.2 Gyr, leading to a conceptual model of a one-plume planet (e.g., Harder and Christensen, 1996). However, recent data shows volcanism remained active in the Elysium region into the Amazonian (e.g., Werner, 2009, Carr and Head, 2010). Two mechanisms have been proposed to explain the recent volcanism: decompression melting due to an upwelling mantle plume (Harder and Christensen, 1996, Kiefer, 2003, Redmond and King, 2004, Roberts and Zhong, 2004, Li and Kiefer, 2007, OʼNeill et al., 2007, Kiefer and Li, 2009, Grott and Breuer, 2010), or melting due to heat trapped beneath an isolated thick region of crust (Montesi and Zuber, 2003, Schumacher and Breuer, 2007).
Previous work suggested that the pattern of mantle convection on Mars may be dominated by a single, strong upwelling under Tharsis (Harder and Christensen, 1996, Zuber, 2001, Roberts and Zhong, 2004, Zhong, 2009) or multiple plumes (Kiefer, 2003, Li and Kiefer, 2007, Grott and Breuer, 2010). Harder and Christensen (1996) studied Martian mantle convection in a 3D spherical shell. In their calculation, initially several plumes develop and as the model evolves, the weaker plumes die out until finally, only the strongest plume survives. The long duration of the single surviving plume is consistent with the stability of the Tharsis volcanic region. This is quite different from the convection process on Earth where the mobile lithosphere plays an important role with downwelling slabs and multiple upwelling plumes (cf. Schubert et al., 2001).
A number of recent Martian mantle convection investigations have used quasi-steady-state calculations (Kiefer, 2003, Roberts and Zhong, 2006, Li and Kiefer, 2007). Kieferʼs work (2003) is based on the Wanke and Dreibus (1994) heating rates and is consistent with present day radioactive element concentrations while Roberts and Zhong (2006) used a much higher internal heating value (Fig. 1). In both cases the value of the internal heating rate was constant with time. Roberts and Zhong (2006) suggested that the single upwelling (i.e., a degree-one structure) could explain the formation of Tharsis; this convective platform requires a strongly temperature/depth-dependent viscosity (Lenardic et al., 2004, Roberts and Zhong, 2004, Roberts and Zhong, 2006).
Based on in situ measurements and SNC meteorite isotope data; the planet differentiated around 4.5 Ga, forming a crust, mantle and core (Breuer and Spohn, 2006). Shortly after the formation of the planet, the mantle temperatures were high and melting was prevalent throughout shallow part of the upper mantle, leading to the formation of the crust. As mantle temperatures cooled, most volcanic activity was restricted to two areas: Tharsis and Elysium rises (e.g., Harder and Christensen, 1996). Partitioning of radioactive elements between crust and mantle must have happened when the crust formed, because there appears to be little large-scale modification of the crust after formation. The initial melt would be enriched in radiogenic elements and continued melting will cause depletion of these elements in the mantle (Breuer and Spohn, 2006, Schumacher and Breuer, 2007). If majority of the heat producing elements were not concentrated in the crust, there would be widespread melting of the lower mantle, providing a further constraint on the melt production during the early stages of Marsʼ formation.
In this study, numerical models are constrained by the conceptual model for the development of Tharsis by a mantle plume with the timing above. The partitioning of radioactive elements between the crust and the mantle has a significant impact on mantle temperature, which in turn affects melt production (e.g., Kiefer, 2003). The concentration of radioactive elements in the crust and mantle is still unclear; however 50% of the total radiogenic material is probably in the crust (McLennan, 2001). We seek to identify a region of parameter space that allows sufficient melt to produce most of Tharsis region by the end of Noachian, with small amounts of melt continuing to present. We do not consider the problem of how melt is extracted from the mantle, as this is a challenging unresolved problem and beyond the resolution of global models.
Section snippets
Numerical method
Mantle convection on Mars is currently in the stagnant-lid convection regime (Solomatov, 1995, Solomatov and Moresi, 1996, Solomatov and Moresi, 2000, Reese et al., 1998, Reese et al., 1999, Grasset and Parmentier, 1998). We consider a Newtonian rheology with a strong temperature-dependent viscosity and a layered viscosity structure that includes a viscosity increase by a factor of 8 and 25 at a depth of 996 km (Roberts and Zhong, 2006). We consider both a constant heating rate and heating rate
Results
We present two sets of calculations: one set with an internal heating rate that is constant with time and one set with internal heating rates based on the decay of radioactive elements using the concentrations in Lodders and Fegley (1997). For the constant heat source calculations, we compare our 3D spherical convection calculations with the 2D axisymmetric hemispherical convection calculations from Kiefer (2003). We also test the effects of varying fraction of radiogenic elements between the
Discussion
The constant heating rate models illustrate the strong effect of internal heating rate on melt. The low internal heating rate model, PS1 produces a pulse of melt early but no melt at present day while the high internal heating rate model, PS2 produces a significant amount of melt around 4.2 Ga and continues to produce melt to present day. While the low internal heating rate model produces a global layer of melt early, the high internal heating rate model produces isolated blobs of melt on plume
Conclusion
We modeled 3D spherical convection with both constant and varying heat sources with a hot isothermal interior and with the inclusion of latent heat and ran for 4.3 Gyr. A constant and low value of internal heating, PS1, consistent with our best estimate of present day radioactive isotope abundances produces abundant melt distributed in a global layer due to the presence of many smaller plumes. A constant and high value of internal heating, PS2, consistent with our best estimate of radioactive
Acknowledgments
We acknowledge support from NASA, Mars Data Analysis Program, grant NNX08AD07G. We thank James Roberts and three anonymous reviewers for their constructive reviews. The sponsor had no role in the design study, collection or analysis of the work.
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