Geodynamic Simulations using the Fast Multipole Boundary Element Method

Abstract

Interaction between viscous fluids models two important phenomena in geophysics: (i) the evolution of partially molten rocks, and (ii) the dynamics of Ultralow-Velocity Zones. Previous attempts to numerically model these behaviors have been plagued either by poor resolution at the fluid interfaces or high computational costs. We employ the Fast Multipole Boundary Element Method, which tracks the evolution of the fluid interfaces explicitly and is scalable to large problems, to model these systems.

The microstructure of partially molten rocks strongly influences the macroscopic physical properties. The fractional area of intergranular contact, contiguity, is a key parameter that controls the elastic strength of the grain network in the partially molten aggregate. We study the influence of matrix deformation on the contiguity of an aggregate by carrying out pure shear and simple shear deformations of an aggregate. We observe that the differential shortening, the normalized difference between the major and minor axes of grains is inversely related to the ratio between the principal components of the contiguity tensor.

From the numerical results, we calculate the seismic anisotropy resulting from melt redistribution during pure and simple shear deformation. During deformation, the melt is expelled from tubules along three grain corners to films along grain edges. The initially isotropic fractional area of intergranular contact, contiguity, becomes anisotropic due to deformation. Consequently, the component of contiguity evaluated on the plane parallel to the axis of maximum compressive stress decreases. We demonstrate that the observed global shear wave anisotropy and shear wave speed reduction of the Lithosphere-Asthenosphere Boundary are best explained by 0.1 vol\% partial melt distributed in horizontal films created by deformation.

We use our microsimulation in conjunction with a large scale mantle deep Earth simulation to gain insight into the formation of anisotropy within dense and transient regions known as Ultralow-Velocity Zones, where there is an observed slowdown of shear waves. The results demonstrate a geometric steady state of the dynamic reservoirs by mechanical processes. Within the steady state Ultralow-Velocity Zones, we find significant anisotropy that can explain the speed reduction in shear waves passing through the region.