A new free-surface stabilization algorithm for geodynamical modelling:Theory and numerical tests

The surface of the solid Earth is effectively stress free in its subaerial portions, and hydrostatic beneath the oceans. Unfortunately, this type of boundary condition is difficult to treat computationally, and for computational convenience, numerical models have often used simpler approximations that do not involve a normal stress-loaded, shear-stress free top surface that is free to move. Viscous flow models with a computational free surface typically confront stability problems when the time step is bigger than the viscous relaxation time. The small time step required for stability (<2. Kyr) makes this type of model computationally intensive, so there remains a need to develop strategies that mitigate the stability problem by making larger (at least ~10 Kyr) time steps stable and accurate. Here we present a new free-surface stabilization algorithm for finite element codes which solves the stability problem by adding to the Stokes formulation an intrinsic penalization term equivalent to a portion of the future load at the surface nodes. Our algorithm is straightforward to implement and can be used with both Eulerian or Lagrangian grids. It includes α and β parameters to respectively control both the vertical and the horizontal slope-dependent penalization terms, and uses Uzawa-like iterations to solve the resulting system at a cost comparable to a non-stress free surface formulation. Four tests were carried out in order to study the accuracy and the stability of the algorithm: (1) a decaying first-order sinusoidal topography test, (2) a decaying high-order sinusoidal topography test, (3) a Rayleigh-Taylor instability test, and (4) a steep-slope test. For these tests, we investigate which α and β parameters give the best results in terms of both accuracy and stability. We also compare the accuracy and the stability of our algorithm with a similar implicit approach recently developed by Kaus et al. (2010). We find that our algorithm is slightly more accurate and stable for steep slopes, and also conclude that, for longer time steps, the optimal α controlling factor for both approaches is ~2/3, instead of the 1/2 Crank-Nicolson parameter inferred from a linearized accuracy analysis. This more-implicit value coincides with the velocity factor for a Galerkin time discretization applied to our penalization term using linear shape functions in time

The temporal evolution of plate driving forces: Importance of “slab suction” versus “slab pull” during the Cenozoic

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/95131/1/jgrb14092.pd

Three dimensional lithospheric structure of the western continental margin of India constrained from gravity modelling: implication for tectonic evolution

This paper describes a 3-D lithospheric density model of the Western Continental Margin of India (WCMI) based on forward modelling of gravity data derived from satellite altimetry over the ocean and surface measurements on the Indian peninsula. The model covers the north-eastern Arabian Sea and the western part of the Indian Peninsula and incorporates constraints from a wide variety of geophysical and geological information. Salient features of the density model include: (1) the Moho depth varying from 13 km below the oceanic crust to 46 km below the continental interior; (2) the lithosphere–asthenosphere boundary (LAB) located at depths between 70 km in the southwestern corner (under oceanic crust) and about 165 km below the continental region; (3) thickening of the crust under the Chagos–Laccadive and Laxmi Ridges and (4) a revised definition of the continent–ocean boundary. The 3-D density structure of the region enables us to propose an evolutionary model of the WCMI that revisits earlier views of passive rifting. The first stage of continental-scale rifting of Madagascar from India at about 90 Ma is marked by relatively small amounts of magmatism. A second episode of rifting and large-scale magmatism was possibly initiated around 70 Ma with the opening of the Gop Rift. Subsequently at around 68 Ma, the drifting away of the Seychelles and formation of the Laxmi Ridge was a consequence of the down-faulting of the northern margin. During this second episode of rifting, the northern part of the WCMI witnessed massive volcanism attributed to interaction with the Reunion hotspot at around 65 Ma. Subsequent stretching of the transitional crust between about 65 and 62 Ma formed the Laxmi Basin, the southward extension of the failed Gop Rift. As the interaction between plume and lithosphere continued, the Chagos–Laccadive Ridge was emplaced on the edge of the nascent oceanic crust/rifted continental margin in the south as the Indian Plate was moving northwards

Liseuse de micro-films à pistes multiples

Note présentée par M. L. Pauwen.info:eu-repo/semantics/publishe

Convection in an internally heated mantle

Un estudio numérico de la convección en un manto de viscosidad variable, sometido a calentamiento interno, indica que la capa fronteriza de alta viscosidad (litósfera) incrementa la relación de aspecto de las celdas de convección por lo menos a 4:1. Este estudio permite además poner límites precisos al perfil posible de la viscosidad con la profundidad. Se confirma que la temperatura debajo de la litósfera es cercana a la adiabática