The effect of a shallow low viscosity zone on mantle convection and its expression at the surface of the earth
Citable URI
https://hdl.handle.net/1912/3969Location
Central Pacific OceanIndian Ocean
DOI
10.1575/1912/3969Keyword
MantleAbstract
Many features of the oceanic plates cannot be explained
by conductive cooling with age. A number of these anomalies
require additional convective thermal sources at depths
below the plate: midplate swells, the evolution of fracture
zones, the mean depth and heat flow relationships with age
and the observation of small scale (150250 km) geoid and
topography anomalies in the Central Pacific and Indian
oceans. Convective models are presented of the formation
and evolution of these features. In particular, the effect
of a shallow low viscosity layer in the uppermost mantle on
mantle flow and its geoid, topography, gravity and heat flow
expression is explored. A simple numerical model is
employed of convection in a fluid which has a low viscosity
layer lying between a rigid bed and a constant viscosity
region. Finite element calculations have been used to
determine the effects of (1) the viscosity contrast between
the two fluid layers, (2) the thickness of the low viscosity
zone, (3) the thickness of the conducting lid, and (4) the
Rayleigh number of the fluid based on the viscosity of the
lower layer.
A model simple for midplate swells is that they are
the surface expression of a convection cell driven by a heat
flux from below. The low viscosity zone causes the top
boundary layer of the convection cell to thin and, at high
viscosity contrasts and Rayleigh numbers, it can cause the
boundary layer to go unstable. The low viscosity zone also
mitigates the transmission of normal stress to the
conducting lid so that the topography and geoid anomalies
decrease. The geoid anomaly decreases faster than the
topography anomaly, however, so that the depth of
compensation can appear to be well within the conducting
lid. Because the boundary layer is thinned, the elastic
plate thickness also decreases and, since the low viscosity
allows the fluid to flow faster in the top layer, the uplift
time decreases. as well. We have compared the results of
this modeling to data at the Hawaii, Bermuda, Cape Verde and
Marquesas swells, and have found that it can reproduce their
observed anomalies. The viscosity contrasts that are
required range from 0.20.01, which are in agreement with
other estimates of shallow viscosity variation in the upper
mantle. Also, the estimated viscosity contrast decreases as
the age of the swell increases. This trend is consistent
with theoretical estimates of the variation of such a low
viscosity zone with age.
Fracture zones juxtapose segments of the oceanic plates
of different ages and thermal structures. The flow induced
by the horizontal temperature gradient at the fracture zone
initially downwells immediately adjacent to the fracture
zone on the older side, generating cells on either side of
the plume. The time scale and characteristic wavelength of
this flow depends initially on the viscosity near the
largest temperature gradient in the fluid which, in our
model, is the viscosity of the low viscosity layer. They
therefore depend on .both the Rayleigh number and the
viscosity contrast between the layers. Eventually the flow
extends throughout the box, and the time scales and the
characteristic wavelengths of the flow depend on the
thickness and viscosity of both layers. When the Rayleigh
number based on the viscosity of the top later, and the
depth of both fluid layers, is less than 106 , the geoid
anomalies of these flows are dominated by the convective
signal. When this Rayleigh number exceeds 106, the geoid
anomalies retain a step across the fracture zone out to
large ages. We have compared our results to geoid anomalies
over the Udintsev fracture zone, and have found that the
predicted geoid anomalies, with high effective Rayleigh
numbers, agree at longer wavelengths with the observed
anomalies and can produce the observed geoid slopeage
behaviour. We have also compared the calculated topographic
steps to those predicted by the average depthage
relationships observed in the oceans. We have found that
only with a low viscosity zone will the flow due to fracture
zones not disturb the average depth versus age
relationships.
We have also applied the model to a numerical study of
the effect of a low viscosity zone in the uppermost mantle
on the onset and surface expression of convective
instabilities in the cooling oceanic plates. We find that
the onset and magnitude of the geoid, topography and heat
flow anomalies produced by these instabilities are very
sensitive to the viscosity contrast and the Rayleigh number,
and that the thickness of the low viscosity zone is
constrained by the wavelength of the observables. If the
Rayleigh number of the low viscosity zone exceeds a critical
value then the convection will be confined to the low
viscosity zone for a period which depends on the viscosity
contrast and the Rayleigh number. The small scale
convection will eventually decay into longer wavelength
convection which extends throughout the upper mantle, so
that the small scale convective signal will eventually be
succeeded by a longer wavelength signal. We compare our
model to the small scale geoid and topography anomalies
observed in the Southeast Pacific. The magnitude (0.500.80
m in geoid and 250 m in topography), early onset time (510
m.y.) and lifetime (over 40 m.y.) of these anomalies suggest
a large viscosity contrast of greater than two orders of
magnitude. The trend to longer wavelengths also suggests a
high Rayleigh number of near or over 10 and their original
150250 km wavelength indicates a low viscosity zone of 75125
km thickness. We have found that the presence of such
small scale convection does not disturb the slope of the
depthage curve but elevates it by up to 250 m, and it is
not until the onset of long wavelength convection that the
depthage curves radically depart from a cooling halfspace
model. In the Pacific, the depthage curve is slightly
elevated in the region where small scale convection is
observed and it does not depart from a halfspace cooling
model until an age of 70 m.y.. Models that produce the
small scale anomalies predict a departure time between 55
and 65 m.y.. These calculations also predict an asymptotic
heat flow on old ocean floor which is higher than the plate
model and between 50 and 55 mW/m2. This value agrees with
measurements of heat flow on old seafloor in the Atlantic.
In conclusion, we prefer an approximate model for the
viscosity structure of the upper mantle which initially has
a 125 km thick low viscosity zone that represents a
viscosity contrast of two orders of magnitude. The
viscosity contrast decreases as the plate ages to one order
of magnitude or less by 130 m.y., and the. low viscosity zone
may also thicken with age. Finally, the Rayleigh number of
the upper mantle is at least 105 and may be as large as 107.
With this model, the evolution of the surface plates would
initially involve small scale convection which is driven by
shear coupling to instabilities downstream and to small
scale convection associated with fracture zones. This
convective flow would begin at close to 5 m.y. and remain
confined to the low viscosity zone until nearly 40 m.y.. As
this convective flow cools the upper mantle beneath the low
viscosity zone, longer wavelength convection begins
throughout the upper (or whole) mantle, and the heat
transport from the longer wavelength convection flattens the
depthage curve and may form swells.
Description
Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution August 1987
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