Convective Mixing in Porosity Waves during Melt Migration
Abstract:Models of trace element partitioning during non-reactive, one-dimensional melt migration predict the decoupling of tracers with different partition coefficients (e.g. La and Sm)(Navon & Stolper 1987, DePaolo 1996 Liang 2008). Such decoupling is often not observed in igneous products at the surface. We propose a numeric melt migration model derived from first principles to aid our understanding of mixing during melt migration in the mantle. We assert that circulation within a porosity wave could provide an explanation for this disparity.
Buoyancy drives regions of elevated melt fraction through the overlying mantle as porosity waves (Richter & McKenzie 1984, Spiegelman 1993). Within those waves we expect porous flow to lead to the transport and mixing of distinct peridotite-derived lithologies (Kelemen 1997). A consequence of this mixing includes partitioning of trace elements in the partially molten, mixing lithologies.
We begin our numeric experiment by imposing a partially molten region in a nearly impermeable background. As the partially molten region rises, the buoyant melt races to the front of the porosity wave. Once the melt reaches the edge of the porosity wave, it encounters an extreme drop in permeability. Though the melt within the porosity wave may move faster than the wave itself, the permeable region confines the melt. Since the melt cannot outrun the porosity wave, it would pool at the edge of the impermeable region. However, the porosity wave continues to rise around the melt. This causes the melt to appear to double back into the more permeable region within the porosity wave. After “turning back”, the buoyant melt hugs the low permeability wall of the porosity wave as it continues to migrate. Near the bottom of the porosity wave the melt changes direction and begins to move upward again. The porosity wave and melt create a convective mixing cell.
Modeled circulation of melt within the porosity wave could explain why the linear decoupling of trace elements is not observed in natural basalts. The relative position of trace elements moving at different velocities changes as the melt migrates upward. The model shows that increasing distance traveled (i.e. source depth) increases the mixing of tracers. The circulation we model reduces the decoupling of compatible and incompatible elements.