Quantifying mixing and age variations of heterogeneities in models of mantle convection: Role of depth‐dependent viscosity

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Abstract
Using a two‐dimensional finite element model of mantle convection containing over a million tracer particles, we examine the effects of depth‐dependent viscosity on the rates and patterns of mixing. We simulate the processes of recycling crust at subduction zones and the homogenization of recycled material (by dispersion and by melting at mid‐ocean ridges). Particles are continually introduced at downwellings and destroyed when they either are so thoroughly dispersed that it would be impossible to measure their presence in the geochemical signature of mid‐ocean ridges or oceanic islands, or when they are close to spreading centers, at which point melting would “reset” the geochemical clock. A large number of factors influence the flow pattern and thus the rate at which heterogeneities are dispersed by convection. We examine the effect of increasing the viscosity with depth, and determine how both the residence time of heterogeneities and the extent of lateral mixing and exchange between the upper and lower mantle vary with the viscosity profile of the mantle. We determine the particle distribution resulting from convection models with three viscosity profiles: uniform viscosity, a smooth increase of viscosity with depth, and an abrupt jump in viscosity between the upper and lower mantle. We characterize the resulting distribution of heterogeneities in space and time by examining the age distribution of particles and their locations relative to others introduced into the flow at separate downwellings. Mixing rates in the three models are calculated as a function of the number of particles removed from the flow through time. We found that an increase of viscosity at depth does not induce age stratification in which older particles stagnate in the lover mantle, and it does not produce an upper layer (the source of mid‐ocean ridge basalt) that is well‐mixed compared to the deeper regions. However, pronounced lateral heterogeneity is evident in the distribution of particles of different ages and starting locations that is not apparent from the particle positions alone.

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