Mathematical model of Venus tectonics Fran¸cois JAMES & Guillaume RICHARD November 28, 2014 As revealed by the data from the Magellan spacecraft [Solomon et al., 1992], the topography of Venus is very different from the Earth’s one. This suggests that the tectonics of Venus is not in the ’plate mode’ that we observe on Earth. We know that this difference is mainly due to the high temperature of Venus surface (460 ℃) that has important effects on the rheology of its crust and lithosphere (i.e. the top boundary layer of Venus’ convecting mantle). Nevertheless, the dynamical behavior of Venus crust is still debated. To explain the specific tectonics features observed on Venus, it is commonly proposed that are due to interactions between mantle upwelling and lithosphere (see Fig. 1) and 3D numerical simulations including complex rheology (visco-elasto-plastic) have been used to reproduce them [Stein et al., 2010; Gerya, 2014]. The purpose of the present master thesis is to tackle the question of Venus tectonics with a simpler mathematical model. Do do so we propose to divide Venus lithosphere in two layers of simple rheology : The crust deforming as an elasto-plastic medium and the lithospheric mantle deforming as a purely viscous medium. Considering each of these layers, we will then obtain a model similar to the shallow water equations by integrating the Navier-Stokes system along the vertical direction. Solving for this system will allow us to compute the temporal evolution of the lithosphere thickness as a function of the constrain imposed at its base by the convecting mantle. This approach will allow to restrain the need of 3D simulations to the mantle where the deformation is purely ductile and thus easier to compute. The topography output by the model will be compared to Venus’ topography. Gravity field could also be computed and compared to the data measured on Venus [Schubert et al., 1994]. The last step will be to couple this 1D model to a 3D model of mantle convection and to compare our model with existing models (cf. [Stein et al., 2010; Gerya, 2014]) in terms of results as well as computational efficiency.

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Figure 1: A 1D 2 layers model of Venus lithosphere

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References Gerya, T. (2014). Plume-induced crustal convection: 3d thermomechanical model and implications for the origin of novae and coronae on venus. Earth and Planetary Science Letters, 391(0):183 – 192. Schubert, G., Moore, W. B., and Sandwell, D. T. (1994). Gravity over coronae and chasmata on venus. Icarus, 112(1):130 – 146. Solomon, S. C., Smrekar, S. E., Bindschadler, D. L., Grimm, R. E., Kaula, W. M., McGill, G. E., Phillips, R. J., Saunders, R. S., Schubert, G., Squyres, S. W., and Stofan, E. R. (1992). Venus tectonics: An overview of magellan observations. Journal of Geophysical Research: Planets, 97(E8):13199–13255. Stein, C., Fahl, A., and Hansen, U. (2010). Resurfacing events on venus: Implications on plume dynamics and surface topography. Geophysical Research Letters, 37(1):n/a–n/a.

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