Geoscience Reference
In-Depth Information
Earth. The conditions in the hotter Archean and
early Proterozoic mantle likely caused slabs to
fully dehydrate at shallow depth. The transi-
tion from the form of ''dry'' to ''wet'' subduction
(where ''wet'' indicates water is transported past
the arc and into the deep Earth) likely only oc-
curred when the mantle temperature was close
to that of the present-day mantle. The present-
day flux of water (estimated by van Keken
et al
.,
2011, to be in the order of one ocean mass over
the age of the Earth) would increase the average
mantle concentration by 370 ppm. This contrast
to an average of 100 ppm in the upper mantle
(Dixon
et al
., 2002). Since the present day rate is
high compared to the average we can make the
simple estimate (as in van Keken
et al
., 2011)
that the time averaged subduction rate subduc-
tion efficiency is about 9% (compared to the
present-day rate of 30%) to match the overall
increase of water by 100 ppm. This matches quite
well with the independent estimate from the
heavy noble gas recycling observed by Holland
and Ballentine (2006).
This likely change from pre-plate tectonics to
dry to wet plate tectonics has important conse-
quences for the long term chemical and thermal
evolution. The increased water content of the
Earth will strongly control the viscosity and melt
behavior but in a nonlinear fashion. Water reduces
viscosity (e.g., Karato
et al
., 1986; Mei & Kohlst-
edt, 2000; Karato & Jung, 2003) and would en-
hance convective vigor, but higher water content
also increases the depth of melting (Hirschmann,
2006). Melting over a deeper region will increase
the thickness of the basaltic layer (and that of
the underlying harzburgite) creating a thicker
than normal compositional layering that has
positive buoyancy and will therefore counteract
the effects of thermal cooling and densification
of the lithosphere. This will reduce the efficiency
of plate tectonics (Vlaar
et al
., 1994). Similarly,
the deeper extraction of volatiles from the litho-
sphere will render the plates stiffer and make
plate tectonics again less efficient (e.g., Korenaga,
2003). A similar set of arguments can be made for
the formation of plates in a hotter Earth (deeper
melting causes stronger compositional buoyancy
and stiffer plates) so there is an intriguing balance
between the effects of the cooling of the Earth
and the introduction of fluids. The combined
effect may cause a balance in the depth of melting
(as the Earth cools the thermal effect will render
the crustal layer thinner, but the addition of
water will make it thicker) and this may, at least
qualitatively, offer an explanation of the relative
stability of plate tectonics since the late Archean.
Finally, it remains possible that the secular
evolution of the Earth causes thermal and chemi-
cal shifts that may partly reverse the mantle-core
differentiation and therefore cause a material ex-
change across the core-mantle boundary (e.g.,
Buffett, 2010; Helffrich & Kaneshima, 2010).
12.4
Mixing Processes and Modeling
The mixing efficiency of the Earth's mantle can
be quantitatively investigated using theoretical
(''box'') models, laboratory (''tank'') experiments
or
numerical
models
of
mantle
convection.
A
summary
of
these
approaches
is
provided
for
example
by
van
Keken
et al
.
(2002).
I'll
provide
a
short
update
to
the
discussion
in
that paper.
Box models are attractive given their easy im-
plementation, low computational cost, and flexi-
bility in adjusting parameters, assumptions about
mixing rates, etc. The approach allows for a rapid
investigation of a broad parameter space and al-
lows for statistical tests. The model set up is
simple: the geochemical reservoirs are modeled
as boxes in which the chemical composition
is changed by influx, extraction and internal
changes (such as those due to radioactive de-
cay). This allows for the formulation of a set of
coupled ordinary differential equations that can
be readily solved. The fluxes need to be assumed
in a parameterized fashion and can be adjusted to
create a final model of reservoirs that represent
the observations. The fluxes may also be based
on independent observations or comparisons with
numerical models of mantle convection. Internal
mixing can be parameterized (see e.g., Kellogg
et al
., 2002).
