Plume-induced geoid anomalies from 2D axi-symmetric temperature- and pressure-dependent mantle convection models

Geoid and topography of Earth-like planets: A comparison between compressible and incompressible models for different rheologies

“…(Please see also appendix A of the author's previous paper, Shahraki and Schmeling, 2012). Indeed, the definition of the nominal Ra number for a system with variable coefficients, in particular, viscosity, is somewhat arbitrary.…”

“…Therefore, we attempt to get close to a realistic temperature-pressure-dependent viscosity by taking the Arrhenius law according to the new formulation introduced by Shahraki and Schmeling (2012), in which they have tried to adjust the activation energy, E, the activation volume, V a , and pre-exponential constant, A, by taking them as unknowns in a system of equations and then use these values in the Newtonian viscosity as known constants.…”

“…The method for calculating topography and geoid anomalies is described in Shahraki and Schmeling (2012) which is different from the classical method introduced by Kiefer and Hager (1992) and King and Hager (1994). This means that the stress is calculated directly from the velocity field with an advantage of having temperature-pressure-dependent viscosity .Then the dynamic topography of an interface i between two compositionally different media with density contrast Dq is related to the normal stress r zzðiÞ by:…”

“…In this section, we examine the effects of pressure-dependent viscosity by considering an activation volume equal to 1:166 Â 10 À6 m 3 =mol and activation energy equal to zero in our simulations. However, it should be noted that, in an Arrhenius type law it is not possible to eliminate the temperature dependence (Shahraki and Schmeling, 2012), because, the pressure dependence of the viscosity is also affected by the thermal energy (R g T). Fig.…”

Mass distribution and mass transport in the Earth system

“…Sharaki and Schmeling (2012) study the impact of rheological variations, i.e. temperature and depthdependent viscosity, on the shape of the geoid and of the dynamic topography above a plume through a series of numerical convection simulations.…”