# Probing the viscosity of Venus mantle from dynamic topography at Baltis Vallis

## Cite this dataset

McGregor, Nathan et al. (2024). Probing the viscosity of Venus mantle from dynamic topography at Baltis Vallis [Dataset]. Dryad. https://doi.org/10.5061/dryad.brv15dvg6

## Abstract

The Baltis Vallis channel on Venus preserves a record of long-wavelength deformation generated by a convecting mantle, providing a unique window into the planet's geodynamics. Notably, the observed topography along the channel is not downhill, suggesting complex interactions between surface processes and mantle dynamics. We statistically compare the observed dynamic topography of Baltis Vallis with dynamic topographies generated by a suite of stagnant-lid mantle convection models to constrain Venus' interior dynamics. Baltis Vallis's relatively young age (likely less than 250 Myr) and low root-mean-square relief of 217 m indicate vigorous convection in Venus's mantle, with a Rayleigh number greater than 4x10^{8}, implying a mantle viscosity 1-2 orders of magnitude lower than Earth's. This difference may result from either a water-rich, less-degassed interior or a higher-temperature mantle beneath an insulating lid. Additionally, our simulations suggest that melt advection may dominate heat transport on Venus, potentially leading to non-linear temperature profiles in the crust. Upcoming missions such as *VERITAS *and *EnVision *will deliver higher-resolution gravity and topographic data, providing further constraints on Venus's present-day internal dynamics and the origin of Baltis Vallis.

## README: Probing the viscosity of Venus' mantle from dynamic topography at Baltis Vallis

### Description of the data and file structure

In this repository, there are three zipped directories housing the generated data from our models and subsequent analysis. Column headings are explicitly defined for clarity. Units are noted in the column headings unless the variable is unitless (e.g., Rayleigh number, viscosity contrast). Further details about each directory are provided below.

### Files for Baltis Vallis observations and modeled results

*data_and_analysis.zip*

*data_and_analysis.zip*

**BaltisVallis_gravity_at_L_150.txt**: Magellan gravity measurements along the Baltis Vallis profile truncated at spherical harmonic degree*l*= 150**BaltisVallis_topography_at_L_150.txt**: Magellan topography measurements along the Baltis Vallis profile truncated at spherical harmonic degree*l*= 150**decorrelation_time_20_rotations.txt**: Median decorrelation time for preferred model VL3 along with 25th and 75th percentiles for 20 rotations of the Baltis Vallis profile across the sphere**decorrelation_time_50_rotations.txt**: Median decorrelation time for preferred model VL3 along with 25th and 75th percentiles for 50 rotations of the Baltis Vallis profile across the sphere**decorrelation_time_100_rotations.txt**: Median decorrelation time for preferred model VL3 along with 25th and 75th percentiles for 100 rotations of the Baltis Vallis profile across the sphere**L3_viscosity_profile.txt**: Radial mantle viscosity profile for preferred model L3**models_decorrelation_times.txt**: Median decorrelation time for each model along with 25th and 75th percentiles**models_heat_fluxes.txt**: Median heat fluxes for each model along with 25th and 75th percentiles**models_rayleigh_number_and_viscosity.txt**: Median Rayleigh number and viscosity contrast for each model along with 25th and 75th percentiles**models_root_mean_square_height.txt**: Median root mean square height for each model along with 25th and 75th percentiles**root_mean_square_height_20_rotations.txt**: Median root mean square height for preferred model VL3 along with 25th and 75th percentiles for 20 rotations of the Baltis Vallis profile across the sphere**root_mean_square_height_50_rotations.txt**: Median root mean square height for preferred model VL3 along with 25th and 75th percentiles for 50 rotations of the Baltis Vallis profile across the sphere**root_mean_square_height_100_rotations.txt**: Median root mean square height for preferred model VL3 along with 25th and 75th percentiles for 100 rotations of the Baltis Vallis profile across the sphere**VL3_viscosity_profile.txt**: Radial mantle viscosity profile for preferred model VL3

### Output data generated by our mantle convection simulations

*Baltis_Vallis_topo_StagYY.zip*

*Baltis_Vallis_topo_StagYY.zip*

- The simulated topographies for Baltis Vallis.
- A brief experimental description is as follows. Using the Generic Mapping Tools (GMT) 6 software package (Wessel et al., 2019), we first load the global Venus topography dataset for a model (see
*Venus_topo_StagYY.zip*) which generates a global topographic map from the modeled topography form our convection simulations. We then load the Baltis Vallis topography (see BaltisVallis_topography_at_L_150.txt)**,**project it on to the global topography, extract the corresponding elevation for Baltis Vallis along its profile, and output it to a .txt file. These .txt files are stored in this .zip file. Each .txt file corresponds to a model timestep as identified in their filename (i.e., Myr: million years). They are stored in subdirectories that correspond to a different model (e.g. F, F3, etc.), each initiated with unique starting parameters (see McGregor et al., 2024 for these values). - Column headings are explicitly defined for clarity. Units are noted in the column headings unless the variable is unitless (e.g., Rayleigh number, viscosity contrast).

*Venus_topo_StagYY.zip*

*Venus_topo_StagYY.zip*

- The simulated topographies generated by our mantle convection models for the surface of Venus. Each subdirectory corresponds to a model. Within each subdirectory are .txt files corresponding to model time steps, identified in their filename (i.e., Myr: million years).
- A brief experimental description is as follows. Our mantle dynamics simulations utilize the StagYY code within a 3D spherical shell framework, employing the yin-yang grid scheme. StagYY employs finite-volume discretization and solves the velocity-pressure equation using a multigrid solver. The temperature field is advected using the MPDATA advection technique, while tracer particles track the advection of composition and melt. The grid resolution is set at 2x32x96x32 cells, accommodating 30-120 million tracers, with refined grid points in the boundary layers at the top and bottom. Near the surface, the resolution ranges from 20-30 km between grid points, and close to the core-mantle boundary (CMB), it is approximately 50 km. The simulations consider the infinite Prandtl number approximation and compressibility through the truncated anelastic approximation, using dimensional conservation equations for mass, momentum, energy, and bulk chemistry. Radiogenic heating, shear heating, and heat release or consumption from mantle phase transitions are included.

Mantle composition is tracked between basalt and harzburgite, considered linear mixtures of the olivine and pyroxene-garnet mineral systems. The mantle starts homogeneously composed of 80% harzburgite and 20% basalt, with phase transitions occurring at specific depths. The simulations assume a fixed surface temperature of 740 K and a CMB temperature of 4125 K, with an initial adiabatic temperature field having a potential temperature of 1900 K. The models incorporate strongly temperature- and pressure-dependent rheology, phase transitions, and partial melting, with free-slip and isothermal boundaries at the surface and core-mantle boundaries. Viscosity parameters are chosen based on experimental data for dry olivine in the upper mantle and perovskite in the lower mantle. The simulations span 1.5 Gyr, approximating the current conditions on Venus, with internal radiogenic heating and boundary temperatures kept constant. Melting and its effects on mantle composition are considered, with melt extracted and emplaced at the surface when partial melting occurs at less than 400 km depth. Mantle convection is characterized by the effective Rayleigh number, calculated using representative mantle properties in the convective layer, and the average viscosity is determined using a weighted arithmetic mean.

* Column headings are explicitly defined for clarity. Units are noted in the column headings unless the variable is unitless (e.g., Rayleigh number, viscosity contrast).

Further descriptions of parameters and their uses are described in the paper for which this dataset was produced (McGregor et al., 2024). Contact the corresponding author for all inquiries: Nathan J. McGregor (nmcgregor@ucsc.edu).

### Access information

Baltis Vallis data was derived from the following sources:

- https://astrogeology.usgs.gov/search/map/Venus/Magellan/RadarProperties/Venus_Magellan_Topography_Global_4641m_v02
- https://astrogeology.usgs.gov/search/map/Venus/Magellan/Venus_Magellan_LeftLook_mosaic_global_75m

The convection code StagYY is fully documented in Tackley, 2008. It is the property of Paul J. Tackley and Eidgenössische Technische Hochschule (ETH) Zürich and is available for collaborative studies from Paul J. Tackley.

This dataset was produced for the following paper: McGregor, N. J., Nimmo, F., Gillmann, C., Golabek, G. J., Plattner, A. M., & Conrad, J. W. (2024). *Probing the viscosity of Venus’ mantle from dynamic topography at Baltis Vallis.*

## Methods

Our mantle dynamics simulations use the StagYY code in a 3D spherical shell, using the yin-yang grid scheme (Tackley, 2008). StagYY uses a finite-volume, primitive variable discretization, solves the velocity-pressure equation using a multigrid solver, advects the temperature field using the MPDATA advection technique (Smolarkiewicz, 1984) and uses tracer particles to track composition and melt (Tackley & King, 2003). We use the Generic Mapping Tools (GMT) 6 software package (Wessel et al., 2019) to generate a topographic map from the modeled topography, project the topography onto the BV profile, and extract the model topography for further analysis. The data is then analyzed using Python scripts. We compare the simulated topographies of model BV profiles to the observed topography of BV using two metrics. The first metric is the root-mean-square (RMS) height (Shepard et al., 2001). The second metric is the decorrelation time, inspired by the observation of BV’s present-day uphill flow and the inference that the present-day topography must be uncorrelated with the original topography since BV formed flowing downhill. We assume a cutoff value of zero based on correlations between synthetic profiles randomly generated from a power-law distribution function and BV’s topography. The BV profile along with all model profiles are detrended prior to calculating their decorrelation times and RMS heights. See our paper (McGregor et al., 2024) for further details about the StagYY code (Tackley, 2008) as well as our models and statistical analysis.