The Effects of Far-Field Boundary Conditions on 2D Numerical Solutions for Continental Rifting: Tests and Recipes for Improved Treatment of Asthenosphere Flow and Melting

Abstract:

This work focuses on improving current 2D numerical approaches to modeling the boundary conditions associated with computing accurate deformation and melting associated with continental rifting. Recent models primarily use far-field boundary conditions that have been used for decades with little assessment of their effects on asthenospheric flow beneath the rifting region. All are clearly extremely oversimplified — Huismans and Buiter assume there is no vertical flow into the rifting region, with the asthenosphere flowing uniformly into the rifting region from the sides beneath lithosphere moving in the opposing direction, Armitage et al. and van Wijk use divergent velocities on the upper boundary to impose break-up within a Cartesian box, while other studies generally assume there is uniform horizontal flow away from the center of rifting, with uniform vertical flow replenishing the material pulled out of the sides of the computational region. All are likely to significantly shape the pattern of asthenospheric flow beneath the stretching lithosphere that is associated with pressure-release melting and rift volcanism. Thus while ALL may lead to similar predictions of the effects of crustal stretching and thinning, NONE may lead to accurate determination of the the asthenospheric flow and melting associated with lithospheric stretching and breakup.

Here we discuss a suite of numerical experiments that compare these choices to likely more realistic boundary condition choices like the analytical solution for flow associated with two diverging plates stretching over a finite-width region, and a high-resolution 2-D region embedded within a cylindrical annulus ‘whole mantle cross-section’ at 5% extra numerical problem size. Our initial results imply that the choice of far-field boundary conditions does indeed significantly influence predicted melting distributions and melt volumes associated with continental breakup. For calculations including asthenospheric melting, the ‘finite width plate spreading’ and embedded subregion boundary condition treatments lead to significantly smaller BC-influenced signals when using high-resolution calculation regions of order ~1000km x 400km. We recommend their use when models are attempting to resolve the effects of asthenosphere flow and melting.