Probing the viscosity of Venus's mantle using dynamic topography at Baltis Vallis

Summary

The interior properties of Venus are still poorly constrained. We tested a new method to constrain its mantle viscosity. To do so we have used a unique feature of Venus’ surface: Baltis Vallis, a lava channel about as long as the Nile River on Earth. Since its formation, the terrain along Baltis Vallis has been deformed by the planet’s tectonics. We used mantle dynamics simulations from the StagYY code to model topography (elevation) and the rate at which it possibly changed (decorrelation time) during Venus’ recent history. Comparison with the properties of Baltis Vallis lead us to favor simulations using lower mantle viscosities (10²⁰ Pa s).

Figure 1: Location and topography of Baltis Vallis on Venus. Left panel: a global mosaic overlain with colorized topography showing Baltis Vallis's location. Right panel: a topographic map of Baltis Vallis in Atla Regio.

 

Background and motivation

Baltis Vallis (BV) is a 6,800-km long lava channel on Venus. Its apparent uphill flow direction must be a consequence of deformation changing topography after flow emplacement. The topography of BV thus retains a record of Venus’ convection history, as mantle convection causes time-dependent surface deformation. Venus’ mean surface age is likely in the range 300-500 Ma. The observed deformation of BV indicates that mantle convection was active over the past ∼400 Myr and provides constraints on the length scales and vertical amplitudes involved. We place constraints on Venus’ present-day internal structure and dynamics by comparing dynamical topography produced by numerical convection codes with the topography of BV.

 

Methods

Our approach contrasts with previous studies by using an established feature of the surface of Venus, Baltis Vallis, and its time-dependent topography instead of global spectral analysis at a single prescribed time (present-day, and its assumed corresponding simulated time in models). We simulate time-dependent stagnant-lid mantle convection on Venus with a suite of coupled interior-surface evolution models for a range of assumed mantle properties. Models are designed to reproduce as closely as possible a present-day quasi steady-state behavior and run for 1.5 Gyr, representing the state of Venus since the time of the formation of the bulk of its surface. StagYY simulates dynamic topography by calculating it from the vertical component, at the free slip surface, of the stress tensor due to the convection. StagYY includes both the effects of thermal and density variations on mantle dynamics, as well as partial melting (crust formation) and phase transitions. The viscoplastic rheology is temperature- and depth-dependent with Newtonian diffusion creep. In the current test of the methodology, only extrusive melt is considered, and the convection is forced into a stagnant-lid-like regime during the studied era by making plastic yielding impossible, as a proxy for recent evolution. Reference viscosity is varied between 10¹⁹ and 10²¹ Pa.s.

We compare the simulated topography of model BV profiles to the actual topography of BV using two metrics: the root-mean-square (RMS) height and the “decorrelation time”. The correlation between model BV topography at time τ₂ and an earlier time τ₁ is calculated. When this correlation first falls to zero, the decorrelation time is then τ₂ – τ₁. The decorrelation time is inspired by the observation of BV’s present-day uphill flow and the inference that the present-day topography must be uncorrelated. A model is considered successful if the decorrelation time is less than the surface age of Venus.

Figure2: Decorrelation time and RMS height for all models. The range for Baltis Vallis's RMS height is shown as a red shaded area.

 

Results

The relatively short decorrelation time required (likely 250 Myr) and the relatively low RMS topography of Baltis Vallis (217 m) both imply vigorous convection. From 14 three-dimensional mantle convection models, each initialized with different parameters, we identified two convection models that best fit our metrics. These models have a viscosity contrast ∆η of 10⁸ and 10⁷, respectively, and both have a Rayleigh number Ra of 10⁸. Although Venus’ heat flux is highly uncertain, our model fluxes are consistent with some inferred heat fluxes. Models with higher total surface heat fluxes tend to yield lower decorrelation times; our favored models have some of the highest heat fluxes. We also find that models with a higher Ra tend to have a lower RMS height.

Our favored models have vigorous convection beneath a stagnant lid, and high surface heat fluxes. The viscosity of the lower mantle in these models is 10²⁰ Pa s, roughly two orders of magnitude lower than that of Earth’s. This difference could be either the result of a warmer mantle on Venus, here due to the stagnant-lid-like insulation of the mantle leading to the increase of the interior temperature, or the presence of volatile species, for example water, if outgassing is prevented by high surface pressures. The majority of the surface heat flux is due to melt advection, indicating high rates of volcanic resurfacing. To be consistent with surface ages of volcanic activity inferred from surface observation, most of the melt should be intruded, which will likely change the thermal structure of the crust and lithosphere. Our calculated core-mantle boundary heat fluxes indicate that a dynamo should be operating, unless the core is stably stratified due to compositional layering. While current data are insufficient to test these predictions, once paired with forthcoming observations from several new Venus missions, our work will be able to bring Venus’ interior into sharper focus.

Figure 3: Radial mantle viscosity profiles (laterally averaged) for our preferred models (solid lines), shown alongside estimated viscosity-depth profiles for Earth (dashed lines) and Venus (dash-dotted lines) from other studies.