Mantle Mixing: Processes and Modeling - Physics and Chemistry of the Deep Earth - page 356

equations to that of an annulus (Hernlund &
Tackley, 2008).
While a significant number of models take into
account viscosity variations by simulating stiff
plates and a higher viscosity lower mantle (e.g.,
van Keken & Ballentine, 1998, 1999; Davies,
2002; Naliboff & Kellogg, 2007; Brandenburg
et al ., 2008), the rheology functions used are
generally quite simple. They often ignore stress-
dependent rheology, which is certainly important
in the upper mantle (Karato & Wu, 1993). A num-
ber of recent studies have suggested that realistic
rheology variations may have a strong influence
on mantle mixing and sampling of heterogeneity.
For example, the use of realistic grain-size de-
pendent rheology that takes into account crystal
growth (Solomatov & Reese, 2008) suggests
mantle domains may become more isolated than
without such rheology (Hall & Parmentier, 2003).
Manga (2010) suggested that low viscosity regions
will be preferentially sampled, which may imply
an important selective sampling mechanism that
acts as a filter to the bulk Earth heterogeneity.
This suggests that variations due to water content
(e.g., Jung & Karato, 2003), grain-size (Karato
et al ., 2001) and composition (e.g., Yamazaki &
Karato, 2001) may play an important role in the
mixing of the Earth's mantle.
An important area of research is to understand
how well the 2D models represent 3D mixing.
A number of 3D spherical models with mixing
are available in the literature (e.g., van Keken &
Zhong, 1999; Huang & Davies, 2007) but due to
either the relatively low convective or lack of
temporal variation in the velocity field it is not
clear how these apply to mixing in the Earth.
It has been clear from earlier studies that the
additional toroidal component of the flow may
enhance mixing (e.g., Ferrachat & Ricard, 1998;
van Keken & Zhong, 1999), but it also has been
suggested that 3D flow is less efficient without
toroidal flow (Schmalzl et al ., 1995) or about as
efficient as 2D mixing when toroidal flow is taken
into account (Coltice & Schmalzl, 2006). A recent
study also compared how kinematic stretching
is

12.5 Sampling Heterogeneity

Our understanding about the geochemical het-
erogeneity of the Earth relies principally on the
basalts sampled from ocean islands and mid-
oceanic ridges. The melting that occurs due to
decompression melting or higher mantle temper-
atures clearly provides a filter by causing isotopic
fractionation and magma mixing (Ito & Mahoney,
2005; Bryce & DePaolo, 2006; Elkins et al ., 2008;
Stracke & Bourdon, 2009; Bianco et al ., 2011).
There is noble gas evidence that mixing between
plume and ridge material happens in the melt
(Stroncik et al ., 2008) which complicates the in-
terpretation of the differences between MORB
and OIB. Of particular interest is the behavior
of helium during melting. There are suggestions
that He is more compatibility than U and Th
(Parman et al ., 2005) which may help explain
why He concentrations in high 3 He / 4 He OIBs are
smaller than that in average MORB (Hopp and
Trieloff, 2008). The melt filter is also important
in understanding how the scale of heterogeneity
in the ''marble cake'' mantle can be preserved
upon melting (Kogiso et al ., 2004). Intriguingly,
melting of a mixed pyroxenite-peridotite source
can in itself generate enhanced chemical isolation
(Katz & Rudge, 2011).
In general MORBs are seen as fairly homo-
geneous and thereby characterize a well-mixed
MORB source that is distinct from a poorly mixed
OIB source. This heterogeneity is particularly ev-
ident in He isotopes (Barfod et al ., 1999), but as
Hofmann (2003) cautioned, the isotopic spread
in mid-oceanic ridges away from hotspot is ac-
tually quite significant and may indicate strong
regional variations and a MORB source that is
not as uniform as sometimes suggested. Yet it
is clear that the OIBs have a larger spread in
isotopic ratios than MORB. It is important to
understand how plumes sample the mantle het-
erogeneity and how plumes themselves impact
mixing. Recent dynamical models suggest mix-
ing in plumes is strong, but that some regions
of poorly mixed material are generally retained
(Lin & van Keken, 2006; Huang et al ., 2010). Geo-
chemical observations of the Hawaiian and other

affected by 3D geometries (Subramanian

et al ., 2009).