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

Abstract

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 sinrelate 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 dowmvellings 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 fbund that an increase of viscosity at depth does not induce age stratification in which older particles stagnate in the lower 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.

Mantle Geochemical Geodynamics

“…Consistent with random sampling and the He ratio results of van Keken and Ballentine (1998), Hunt and Kellogg (2001) found that the a 100-fold viscosity jump at 660 km depth did not cause any age stratification. Seemingly inconsistent with Coltice (2005), Hunt and Kellogg (2001) found that the mean particle age increased by a factor of $2, but this could be because they removed particles not only when they were sampled by melting, but also when they became widely dispersed from other particles that were introduced at the same time, which means that the mean age cannot be interpreted as a simple residence time. The viscosity jump does, however, make a substantial difference to the ability of tracers to migrate laterally from their starting positions, because the flow is more steady, and this is something that should be studied further.…”

“…• The upper mantle that is not much better mixed than the lower mantle, as demonstrated by recent numerical results (Hunt and Kellogg, 2001;Stegman et al, 2002). ('Upper mantle' mixing time estimates are meaningless in whole-mantle convection, as discussed earlier).…”

A method to estimate the composition of the bulk silicate Earth in the presence of a hidden geochemical reservoir

“…In recent layered models, therefore, the upper and lower layers do not necessarily coincide with the upper and lower mantle, and the boundary between these two layers is often hypothesized to locate somewhere in the lower mantle (e.g., Kellogg et al, 1999). Other potential layering mechanisms such as higher viscosity in the deep mantle and depth-dependent thermal properties have also been explored (e.g., van Keken and Ballentine, 1998;Hunt and Kellogg, 2001;Naliboff and Kellogg, 2007), but it is always found to be difficult to maintain mantle layering without invoking intrinsic density stratification, i.e., stratification in major element composition. In this case, the major element composition of the lower layer must be substantially different from that of the upper layer (e.g., have to be found along the composition trend exhibited by upper-mantle rocks (unless the chemical differentiation that produced EER and EDR happens to have the trend of upper-mantle rocks-this cannot be assumed a priori because there is no terrestrial sample representing EER).…”

Geochemical processing in a three‐dimensional regional spherical shell model of mantle convection

“…How geochemical heterogeneity developed and survived in a convecting mantle for such a long time has been attracting interest from geodynamical community for about three decades [ Allegre and Turcotte , 1985; Hoffman and McKenzie , 1985; Gurnis , 1986a, 1986b; Kellogg and Turcotte , 1987; Christensen , 1989, 1990; Davies , 1990a, 2002; Kellogg and Turcotte , 1990; Christensen and Hofmann , 1994; Ferrachat and Ricard , 1998; van Keken and Ballentine , 1998, 1999; Hunt and Kellogg , 2001; van Keken et al , 2001; Xie and Tackley , 2004a, 2004b; Brandenburg and van Keken , 2007; Huang and Davies , 2007b]. There have been two distinct approaches to this problem, implicitly based on different hypotheses, but the distinction has not often been clearly articulated.…”