Geology Reference
In-Depth Information
One key feature of this solution is that the slope
at the mid-point of the scarp, which is often
the steepest slope on the feature, decays as the
square root of time, making the measurement of
this slope in the field a useful target for con-
straining the scarp age (Hanks
et al
., 1984). The
simplicity of this approach is indeed appealing,
although one must be very aware of the geomor-
phic and seismic setting (Was the scarp formed
in one event or is it a composite feature built
through multiple events?) to apply this technique
properly for the dating of scarp-like features.
modification of scarp profiles. Using examples
from New Zealand and Idaho, they attempted to
model measured profiles on slopes facing either
the equator or the poles. They deduced a non-
linear hillslope transport function and found
that the hillslopes in Idaho displayed an effec-
tive diffusivity that was roughly twice that of
their New Zealand counterparts, and that slopes
facing the poles were consistently steeper than
those facing the equator (Fig. 11.7). Given that
the climate, scarp ages, and sediment character
are quite similar between these two sites, the
differences in diffusivity seem likely to reflect
vegetation and moisture differences, as well as
perhaps the roles of freeze-thaw cycles and
burrowing mammals: the latter drive diffusive
transport in some Northern Hemisphere sites
(Gabet, 2000), but were largely absent in New
Zealand until very recently.
Applications
Early application of diffusive analysis to tectoni-
cally active landscapes included the treatment of
wave-cut scarps in the Lake Bonneville basin,
Utah, whose age had been determined indepen-
dently (by
14
C), and which were cut by recent fault-
ing or warped by isostatic deformation. Knowledge
of the present profiles, an estimate of the initial
profile shape by appeal to modern wave-cut fea-
tures, and knowledge of the age led to constraints
on the diffusivity,
k
, of 5-100m
2
/kyr (or 0.005-
0.1 m
2
/yr). Based on these estimates of diffusivity,
ages of scarps of unknown age in arid landscapes
nearby were subsequently estimated (Bucknam
and Anderson, 1979; Colman and Watson, 1983;
Mayer, 1986; Nash, 1984, 1986; Wallace, 1978).
Using another feature of the solutions to the
diffusion equation, Avouac
et al
. (1993) have
surveyed numerous profiles across scarps
separating terrace risers in arid Tibet (Fig. 2.15)
to deduce the ages of the terraces. They then plot
the pattern of the derivative of the topography
(in other words, the slope) versus distance. This
pattern should be a broadening Gaussian through
time if diffusion controlled the evolution of the
terrace riser (Avouac, 1993; Avouac
et al
., 1993).
Avouac
et al
. use the best fits to the breadth of
this distribution to constrain what they call the
scarp degradation (m
2
), which is the product of
the diffusivity and time since the scarp step was
generated. If the diffusivity is uniform from scarp
to scarp, then the scarp degradation should be a
good surrogate for scarp age.
More recently, Clarke and Burbank (2010b)
have addressed the potential role of climate in
Complexities
Geomorphologists have recognized several
pitfalls that face the modeling of scarp evolution
with the simple diffusion equation. In the devel-
opment outlined in the previous section, and in
the applications cited, several assumptions were
made, the following among them: (i) The proper
initial condition is that left by whatever erosional
or tectonic process caused the topographic step
in the first place. (ii) The diffusion coefficient is
spatially uniform along the profile, which allowed
pulling the
k
out of the derivative when the two
equations were combined. (iii) The diffusion
coefficient is not dependent upon the aspect
(facing direction) of the slope, i.e., it would be
the same from profile to profile within the same
landscape. (iv) The simple linear relation of flux
to local slope is valid, i.e., it is not nonlinear and
is not related to other factors, such as distance
from the top of the slope. (v) Weathering of the
material to be transported may be ignored. We
summarize subsequent work addressing some of
these complexities in the following paragraphs.
Initial conditions
It was early recognized, in dealing with fault (and
other) scarps in arid regions, that another process