DOI: 10.5061/dryad.brv15dvg6
title: Probing the viscosity of Venus mantle from dynamic topography at Baltis Vallis

description: 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 4x108, 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.
description: 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.
description: # 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***
 * **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*** * 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*** * 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](mailto: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.*