Rheological decoupling at the Moho and implication to Venusian tectonics

Plate tectonics is largely responsible for material and heat circulation in Earth, but for unknown reasons it does not exist on Venus. The strength of planetary materials is a key control on plate tectonics because physical properties, such as temperature, pressure, stress, and chemical composition, result in strong rheological layering and convection in planetary interiors. Our deformation experiments show that crustal plagioclase is much weaker than mantle olivine at conditions corresponding to the Moho in Venus. Consequently, this strength contrast may produce a mechanical decoupling between the Venusian crust and interior mantle convection. One-dimensional numerical modeling using our experimental data confirms that this large strength contrast at the Moho impedes the surface motion of the Venusian crust and, as such, is an important factor in explaining the absence of plate tectonics on Venus.

the thermal gradient. The thermal gradient between samples was evaluated by changing the positions of thermocouples. The temperature is proportional to the distance from the central position of heater in our experimental configuration (Tg = 0.03 × Tc, Tg ; Thermal gradient Tc ; central temperature of graphite heater) (Fig. 3). The strain contrast was measured from the rotation of the nickel strain marker in the recovered samples (Fig. 2). We determined the strength contrast from the central portion of the strain-marker without considering the deformation around the interface of the samples and alumina piston in order to exclude the wall effect of the piston. The strain rate was calculated from the obtained strain and the duration of the deformation. The experimental conditions and results are summarised in the Supplementary Table 1.

Numerical modeling
Our numerical modeling considers the viscosity and moving velocity depth profiles of the lithosphere under a thrust fault, which simulates an embryonic subduction zone.
One-dimensional simple shear deformation in the lithosphere was calculated under the boundary condition with thrust shear traction and the moving velocity of the base of the lithosphere. The Moho depth was assumed to be 20 or 7 km (Fig. 1b). We considered the thrust to occur between colliding lithospheres (Fig. S3). We assumed that friction at the thrust section generates shear traction that resists the lithospheric subduction. In the deeper part of the section, shear stress was estimated to be much smaller due to viscous deformation in the crust and mantle at high temperature. In our modeling, the shear traction value (τ) was set to be equal to the maximum friction in the deepest part of the thrust, which is expressed by a Byerlee's law as where f c is the frictional coefficient, σ n is the normal stress, ρ is the density, is the gravitational acceleration, and l d is the maximum depth of the thrust. The value of f c is assumed to be 0.85 and the value of l d depends on the crustal thickness of the model ( Fig. 1). In the model with a depth of 7 km to the Moho, the value of l d was set to 13 km, whereas l d was assumed to be 6 km in the case of a Moho depth of 20 km (Fig. 1b). The velocity in the mantle lithosphere at depths of 10 and 25 km for Moho depths of 7 and We calculated four cases with variable viscosity differences between the crust and mantle in the lithosphere. The first model has no viscosity contrast at the Moho ( Fig. 4a and S4a). The second and third models have differences in viscosity of 10 2 and 10 4 Pa s at the Moho (Fig. 4b, 4c, S4b, and S4c). Under these stress and velocity boundary conditions, the entire lithosphere has a constant stress value. Therefore, the viscosity (η) of the crust and mantle is given by an Arrhenius-type equation as follows: where A´ is a pre-exponential factor, E * is the activation energy, P is the hydrostatic pressure, V * is the activation volume, R is the gas constant, and T is temperature. The viscosity contrast between the crust and mantle is introduced by changing A´ of the crust. The activation energies of the crust and mantle are assumed to be 460 and 495 kJ/mol, respectively, which are smaller than those for power-law creep formula that mimics the Peierls mechanism at constant stress.
The temperature gradient of the lithosphere was set to be constant at 6 K/km. This value was calculated from the shallow temperature of a lithosphere with an age of 200 Ma, which was estimated for Artemis Chasma 25 using a half-space cooling model 36 . The thermal gradient used in our study is comparable to the thermal gradient of Artemis Chasma reported in previous studies 29, 37 . Our calculation results for the velocity in the lithosphere are largely insensitive to the temperature gradient.
The moving velocity at each depth was calculated from the one-dimensional Navier-Stokes equation as follows: where u is the moving velocity. The z-direction was chosen to be the direction towards the lithospheric interior (Fig. S3). The equation was solved by the finite volume method.
The parameters for the numerical models are summarised in Supplementary Table 2. Although the numerical calculations were conducted at various crustal thicknesses (20, 45, and 70 km), our conclusions are independent of the assumed crustal thickness (i.e., the strength contrast at the Moho efficiently decreases the plate velocity).   Figure S4. Viscosity (left) and moving velocity (right) profiles calculated using the one-dimensional deformation model for the Venusian lithosphere at a crustal thickness of 7 km. All parameters apart from the crustal thickness are the same as those for the models shown in Figure 4. The truncation of the negative velocity at zero in case c in this figure is the same as for case c in    Table S3. Parameters of flow law of olivien and plagioclase used in this study.