Читать книгу Mantle Convection and Surface Expressions - Группа авторов - Страница 22

We carried out a suite of 3D geodynamic models in spherical geometry using CitcomS version 3.1.1 (Zhong et al., 2000, 2008) with modifications to impose time‐dependent plate motions as a surface boundary condition (Zhang et al., 2010). CitcomS solves the equations of mass, momentum, and energy conservation for incompressible creeping (zero Reynolds number) flow under the Boussinesq approximation in 3D spherical shell geometry. All of the models include a compositionally distinct layer (advected using tracers), meant to be analogous to the LLSVP material, which is assigned an excess density of 3.75%, equivalent to a buoyancy ratio of B = 0.5. The intrinsic density difference adopted here is chosen such that the compositionally distinct material remains stable against entrainment and is consistent with other geodynamic modeling studies (Mc‐Namara and Zhong, 2004, 2005), leading to a net buoyancy compatible with the available constraints from normal modes and solid earth tides Moulik and Ekström (2016); Lau et al. (2017). The compositionally distinct material is initially present as a uniform layer of 250 km thickness. All of the models include time‐dependent prescribed surface plate motions, which shape the large‐scale structure of mantle flow. We adopt plate motions from a recent paleogeographic reconstruction by Matthews et al. (2016), which spans 410 Ma‐present, although some of the calculations do not include the entire plate motion history. All of the models except Case 40 (Table 1.1) impose the initial plate motions for a period of 150 Myr to spin‐up the model and initialize large‐scale structure following Zhang et al. (2010). The mechanical boundary conditions at the core‐mantle boundary are free‐slip, and the temperature boundary conditions are isothermal with a nondimensional temperature of 0 at the surface and 1 at the core–mantle boundary. We use a temperature‐ and depth‐dependent viscosity with the form η(z) = η_z(z) exp [E(0.5 − T)], where η_z(z) is a depth‐dependent viscosity prefactor and E = 9.21 is a dimensionless activation energy, which gives rise to relative viscosity variations of 10⁴ due to temperature variations. The models are heated by a combination of basal and internal heating, with a dimensionless internal heating rate Q = 100.

We include the effects of a phase transition at 660 km depth in some of the models. Phase transitions are implemented in CitcomS using a phase function approach (Christensen and Yuen, 1985). We adopt a density increase across 660 km of 8%, a reference depth of 660 km, a reference temperature of 1573 K, and a phase change width of 40 km. We assume a Clapeyron slope of –2 MPa/K. Recent experimental work favors a range of –2 to –0.4 MPa/K (Fei et al., 2004; Katsura et al., 2003), considerably less negative than values employed in earlier geodynamical modeling studies that produced layered convection (Christensen and Yuen, 1985). The models shown in the present work are a subset of a more exhaustive suite of models from Lourenço and Rudolph (in review), which consider a broader range of convective vigor and additional viscosity structures. We list the parameters that are varied between the five models in Table 1.1 and the radial viscosity profiles used in all of the models are shown in Figure 1.4.