The aim of this part of the course is to discuss the observational evidence and the constraints that the phenomena of flexure has provided on the mechanical properties of the lithosphere. Particular emphasis is given to a consideration of flexure

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Geodynamics Flexure of the Lithosphere Graduate
Class Scrippss Institution of
Oceanography February 2005
Tony Watts tony_at_earth.ox.ac.uk
The aim of this part of the course is to discuss
the observational evidence and the constraints
that the phenomena of flexure has provided on the
mechanical properties of the lithosphere.
Particular emphasis is given to a consideration
of flexures role in understanding the evolution
of the geological features in the oceans and
continents .
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Outline
Lecture 1
Plate flexure. Elastic plate model. Line loads.
Oceanic lithosphere. Seamounts and oceanic
islands. River deltas. Trenches. Elastic
thickness Vs. Load and Plate age. Viscosity
structure. Time scales of isostatic adjustment.
Moat stratigraphy and facies. Curvature and
Yielding. Elastic and seismogenic layer. The
lithosphere as a filter.
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Resources
Journal Articles
Web
http//topex.ucsd.edu/geodynamics http//www.earth
.ox.ac.uk/tony/watts/INDEX.HTM
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Plate flexure
Seamounts.River Deltas.Trenches.Late Glacial
Rebound
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Elastic plate (flexure) model
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Line loads
Continuous plate
1/l flexural parameter
Distributed loads can be modelled as one or more
line loads
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Hawaiian-Emperor seamount chain
Sandwell Smith 1997 (offshore) Woollard et al
1966 (onshore)
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Gravity anomalies and crustal structure at
Oahu/Molokai
Watts ten Brink (1989)
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Estimating Te
Te can be estimated by comparing the amplitude
and wavelength of the observed gravity anomaly
to the predicted anomaly based on an elastic
plate model.
The minimum in the RMS difference
between observed and calculated gravity anomaly
indicate a best fit Te 30 km.
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Crustal structure and flexure along the Hawaiian
Ridge
Watts and ten Brink (1989)
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Sediment loading at the Amazon Cone
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Amazon Cone Flexure
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Topography seaward of the Kuril Trench
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Gravity anomalies and flexure
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Relationship between oceanic Te and plate and
load age
Oceanic Te increases with age of the lithosphere
at the time of loading but, decreases with load
age. There is therefore a competition between
thermal cooling, which strengthens the
lithosphere, and a load-induced stress-relaxation
which weakens it.
Watts Zhong (2000)
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Te and the Yield Strength Envelope
The elastic model implies that all stresses are
supported elastically and that the maximum
stresses accumulate in the uppermost and
lowermost part of the plate.
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Te , curvature and yielding
We can show using the YSE model that the amount
of yielding in a flexed plate depends on the
curvature and, hence, size of an applied load.
These considerations show that because of
curvature, the elastic thickness, Te, will
usually be less than the mechanical thickness, Te.
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Yielding on the seaward walls of deep-sea trenches
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Yield Strength Envelope
The Yield Strength Envelope (YSE) combines the
brittle and ductile deformation laws of rock
mechanics into a single strength profile for the
lithosphere.
The ductile flow law is given by
.
where n is a positive integer, An is the power
law stress constant, (s1-s3) is the stress
difference, Qp is the power law activation
energy, Rg is the universal gas constant and T is
temperature. Olivine n3, An 7.0 x 10-14 and
Qp 520 kJ mol-1
The area under the YSE is a measure of the
integrated strength of the lithosphere. The YSE
shows that the thickness of the strong zone is
greater than the elastic core and increases
linearly with the square root of age.
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Viscosity structure of oceanic lithosphere
Karato Wu (1993)
Creep Law - Olivine
where ? shear stress, m shear modulus, b
and d are material properties, P ambient
pressure, V activation volume, Qp activation
energy, Rg Universal Gas Constant and T
temperature.
.
Weertman Weertman (1975)
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Comparison of predictions of simple plate
(flexure) models with the Zhong (1997)
multilayered viscoelastic model
Watts Zhong (2000)
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Flexure and the time-scales of isostatic
adjustment
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Stratigraphy of flexural moats that flank oceanic
volcanoes
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Te, the seismogenic layer thickness, and the
strength of the mantle
Watts Burov (2003)
Oceans earthquakes occur in the sub-oceanic
mantle, but the mantle is also involved in the
support of long-term loads. Continents
earthquakes are rare in the sub-continental
mantle, but it is still involved in the support
of long-term loads
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The Lithosphere as a filter
It is useful when considering the flexural
response to consider the lithosphere as a
time-invariant filter which responds to loads in
a way that takes into account both the amplitude
and wavelength of loading. First, consider the
solution of the general equation for deflection
of an elastic plate when subject to a periodic
load i.e.
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The figure shows that the lithosphere is behaving
as a filter in the way that it responds to loads
suppressing the short-wavelength deformation
associated with local models of isostasy (e.g.
Airy) and passing the long wavelengths associated
with flexure.
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The non-isostatic (flexural) contribution to the
long-wavelength gravity field

• Continents
• Te lt 90 km
• max 2000 km
• n 20

• Oceans
• Te lt 25 km
• max 1000 km
• n 40