Relative continent - mid-ocean ridge elevation: a reference case for isostasy in geodynamics

Abstract

The choice of crustal and mantle densities in numerical geodynamic models is usually based on convention. The isostatic component of the topography is not calibrated to fit observations resulting in not very well constrained elevations. The density distribution on Earth is not easy to constrain because it involves multiple variables (temperature, pressure, composition, and deformation). We aim in this study to provide a reference case for geodynamic modelling where crustal and mantle densities are calibrated to fit the relative continent/mid-ocean ridge elevation in agreement with observations. We first review observed Earth topography of stable continents and of active mid-ocean ridges and define the characteristic average elevation of these domains. We use self-consistent thermodynamic calculations of dry mantle rocks that include partial melting to calibrate densities of the continental lithospheric mantle and beneath the mid-ocean ridge. The thermodynamic solutions are coupled with a 2-D incompressible plane strain finite element method for viscous-plastic creeping flows to solve for the dynamic evolution during extension from continental rifting to mid-ocean spreading. The combined results from 2-D thermo-mechanical models and 1-D isostatic calculations show that the relative elevation difference between mid-ocean ridges and continents depends on crustal density, mantle composition, and the degree of depletion of the lithospheric mantle. Based on these results we calibrate the reference density that only depends on temperature, which can be used in classic thermo-mechanical models based on the Boussinesq approximation. Finally the model calibration provides a solution that fits (1) the elevation of active mid-ocean ridges far from hotspots (-2750 ± 250 m), (2) the elevation of stable continents far from hotspots (+400 ± 400 m), (3) the average depletion buoyancy of the continental lithospheric mantle (between -20 and -50 ± 15 kg/m3 depending on lithospheric thickness) and (4) the average continental crust density (2835 ± 35 kg/m3 for a 35 km thick crust).