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The proposal for convection driven by 'dripping' lower lithosphere also encoun-
ters the topographic constraint, but in this case the model implies only that there
should be depressions where lower lithosphere is detaching [131]. The amplitude
of such depressions has not been accurately estimated. Since a substantial amount
of heat transport is required in order to 'flatten' the sea floor (about 40 mW/m 2
through old sea floor [99]), a significant and detectable amount of topography
would be expected. Indeed, the higher viscosity of the cooler drips would enhance
such topography by coupling their negative buoyancy more strongly to the surface.
On the other hand, the elastic strength of the lithosphere would reduce the short-
wavelength components of this signal. On balance, it is likely that there should be a
network of depressions across the older sea floor, probably with amplitudes at least
of the order of a few hundred metres. Such a signal should be readily observable,
but it is not evident in Figures 2.4 or 8.4. Corresponding signals in the gravity field
should also be present.
Some such signals have been demonstrated in restricted regions, but they appear
to be due to something other than small-scale convection. The best-developed
signals are in the southeast Pacific, where there are undulations of the sea floor
with a wavelength of about 200 km and amplitudes of less than 200 m. Associated
gravity and geoid anomalies have also been detected. The gravity anomalies are
of low amplitude (5-20 mgal) and linear, with wavelengths of 100-200 km and
lengths of the order of 1000 km [132]. Narrow volcanic ridges have also been
found, coinciding with the gravity lows, and Sandwell and others [133] have
argued that these are not compatible with small-scale convection. They propose
instead that the lithosphere has been stretched over a broad region and that it has
developed boudins, which are thinner, necked bands oriented perpendicular to the
direction of stretching.
A further problem with the dripping lower lithosphere hypothesis is that its long-
term effect would actually be to increase the rate of subsidence, not to decrease it as
claimed. This is because it would enhance the rate of heat loss from the mantle, and
thus would enhance the thermal contraction that is the primary reason for seafloor
subsidence [134]. Previous conclusions had only taken account of the replacement
of cool lower lithosphere by warm mantle, and had overlooked the influence of the
cool lithospheric material as it sinks into the mantle.
The evidence for small-scale convection is thus absent or equivocal. As well,
the claim that the old sea floor asymptotically approaches a constant depth, which
motivated the idea of small-scale convection, is a misreading of the observations.
We can conclude that, if any such mode of convection exists, other than the plate
and plume modes, it must be a minor phenomenon that transports only a small
amount of heat and generates only small geophysical signatures that are hard to
resolve.
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