Dynamics of ULVZ-mantle interaction using fast multipole boundary element method

Seismic observations over the past two decades show evidence of areas immediately above the core-mantle boundary characterized by sharp, differential drops in seismic velocities. These aptly named UltraLow Velocity Zones (ULVZs) are typically localized (50-100km wide) and thin (10-40 km thick). High concentration of the observed ULVZ patches near the edges of Large Low Shear Velocity Provinces (LLSVPs) indicate that the shape and distribution of the dynamic ULVZ patches are strongly coupled with the flow in the adjacent mantle. Two important properties modulating the extent of this coupling are the contrasts in density and viscosity between the ULVZ patches and the surrounding mantle. This work explores the interaction, coalescence, and break-up of ULVZ patches excited by an imposed mantle flow using the Fast Multipole Boundary Element Method (FMBEM). We model the ambient mantle as a high viscosity medium containing viscous, deformable ULVZ patches. The ambient mantle and ULVZ patches are both homogeneous but may differ from each other in viscosity and density. Mass and momentum conservation within each patch and the mantle are governed by the Stokes flow equation. The governing partial differential equations, aided with stress jump and no-slip boundary conditions at the ULVZ-mantle interfaces, are converted into a set of Fredholm integral equations of the second kind. Unlike traditional Boundary Element Methods (BEM), discretization of this integral equation using FMBEM produces a system of linear equations solvable by iterative sparse solver methods. This work reports a set of numerical experiments over a range of viscosity and density contrasts.