Geology Reference
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discontinuities in the crustal material. The strat-
egy here is instead to capture the large-scale
forcing within the lithospheric mass as it
responds to lithospheric-scale tectonic forcing,
e.g., continental collision rates. One strategy is
kinematic: a vertical and/or horizontal deforma-
tion pattern is simply assumed. Other models
that more properly capture the dynamics,
although still in their infancy, will ultimately be
more useful in the exploration of the nature of
the feedbacks in  these systems. The dynamic
models differ in the assumptions made about
the rheology of the lithosphere at long time and
length scales. For example, in some models, the
rheology is assumed to be captured by a non-
linear flow law in which the flow parameter
corresponding to  the effective viscosity of the
material is temperature dependent, such that
the shear strain rate changes as a power of the
local shear stress. This sort of model, therefore,
requires proper modeling of the thermal evolu-
tion of the lithosphere as well. Whereas such
models are quite complex, they can embody
important feedbacks between the tectonic forc-
ing and the geomorphic response.
1200
A
load (m)
1000
flexure (m)
new topo (m)
800
Flexural
Support
of Loads
load
600
400
new topography
200
0
-200
flexure
B
load (m)
flexure (m)
new topo (m)
1000
800
600
400
200
0
-200
-400
-200
-150
-100
-50
0
50
100
150
200
Horizontal Distance (km)
Fig. 11.3 Flexural response to a distributed set
of line loads.
Load shape in A is a single linear mountain range with
a Gaussian cross-section 1 km tall. Load in B has in
addition a second crest centered at 50 km to the right of
the first, with 500-m amplitude. Final topography is the
sum of the load and the flexure from each individual load.
Effective elastic thickness of 10 km is used in both cases.
Flexure
Over long time scales, deep Earth materials
behave as a fluid. All fluids flow in response
to pressure gradients, moving from sites of high
pressure to sites of low pressure. Because the
pressure at depth depends on the density and
height of the column of rock above it, the
tectonic and geomorphic modification of the
topography represents a rearrangement of
surface loads, which can force deep Earth mate-
rials to flow. This flow in turn modifies the
surface topography at long wavelengths and on
time scales of many thousands of years, and
it  operates in such a fashion as to reduce the
lateral pressure gradients at depth. This process
is one of isostatic adjustment , the static case
being one of isostatic equilibrium ( isostatic
meaning “equal pressure”). That the near-surface
rock is too strong to deform in a ductile way
over these same time scales requires that it
respond instead as a broad, flexing elastic plate.
The wavelength of the response of the surface
to this motion at depth, called the flexural wave-
length , is dictated by the average rigidity of the
near-surface materials. The flexural response
(Fig. 11.3) is calculated as if it were the bending
of a beam of uniform thickness. This thickness is
fictitious in that one could not drill to this depth
and find either a material or a chemical discon-
tinuity; rather, this represents the thickness of a
beam that reflects the average or integrated
strength of the near-surface rock - see the full
discussion in Watts' (2001) wonderful topic on
isostasy and flexure.
The complexity of the flexural component of
the models depends in part on the symmetry
of  the problem. For simple one-dimensional
cases, one may easily turn to analytic solutions
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