Predicting surface dynamic topographies of stagnant lid planetary bodies
 Research areas:
 Year:
 2013
 Authors:

 Caroline Dumoulin
 O. Cadek
 Gaël Choblet
 Journal:
 GEOPHYSICAL JOURNAL INTERNATIONAL
 Volume:
 195
 Number:
 3
 Pages:
 14941508
 Month:
 December
 ISSN:
 0956540X
 BibTex:
 Abstract:
 Although planetary mantles are viscoelastic media, numerical models of thermal convection in a viscoelastic spherical shell are still very challenging. Here, we examine the validity of simplified mechanical and rheological frameworks classically used to approximate viscoelastic dynamic topography. We compare three simplified approaches to a linear Maxwell viscoelastic shell with a pseudo upper freesurface, considered as the reference model. A viscous model with a freeslip boundary condition at the surface correctly reproduces the final relaxed shape of the viscoelastic body but it cannot reproduce the time evolution of the viscoelastic topography. Nevertheless, characterizing the topography development is important since it can represent a significant fraction of the history for planets having a thick and rigid lithosphere (e.g. Mars). A viscous model with a pseudo freesurface, despite its timedependency, also systematically fails to describe correctly these transient stages. An elastic filtering of the instantaneous viscous topography is required to capture the essence of the time evolution of the topography. We show that a single effective elastic thickness is needed to correctly reproduce the constant transient viscoelastic topography obtained when the lithosphere corresponds to a steplike viscosity variation, while a timedependence of the effective elastic thickness must be considered to take account of realistic temperaturedependent viscosity variations in the lithosphere. In this case, the appropriate thickness of the elastic shell can be evaluated, at a given instant, with a simple procedure based on the local Maxwell time. Furthermore, if the elastic filtering is performed using the thin elastic shell formulation, an unrealistic degreedependence of the thickness of the elastic shell is needed to correctly approximate the viscoelastic topography. We show that a model that fully couples a viscous body to an elastic shell of finite thickness estimated using the local Maxwell time gives the best approximation of the viscoelastic deformation, whatever the degree of the load and the time of loading.