Geology Reference
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governed by differing suites of geomorphic rules,
are shown. The land-surface model employed
here is CASCADE (Braun and Sambridge, 1997),
whereas the thermal model is Pecube. At every
pixel, the time since passage of the rock now at
the surface through a particular temperature, here
the closure temperature for the apatite (U-Th)/He
system, is shown. The spatial patterns of the
calculated He ages can then be compared with
data. The models shown are two of many models
run in this investigation. Braun (2005) discusses
several strategies for how one might search more
efficiently through the many possible models,
rather than simply sweeping through the full
ranges of the many parameters in such models.
A major challenge in the application of such a
strategy to real landscapes, rather than generic
ones, is that one must choose both a proper
initial condition for the model (an initial land-
scape some millions of years ago) and a suite of
geomorphic processes and rates that will cause
the landscape to evolve to the present one. You
can imagine that many such scenarios exist. No
simple “inverse problem” treatment of the geo-
morphic system is feasible. Several strategies
have emerged to deal with this issue. One is to
run zillions of forward models in which initial
conditions are chosen and process rates are
prescribed, and then model results are assessed
by how well they reproduce simultaneously the
thermochronometric data and the topography.
A second strategy, which can work in certain
special circumstances, is to assert that the
ancient topography looked like a faint echo of
the present and subsequently “morphs” into the
present topography. This strategy assures that
every run of the model will result in the modern
topography, meaning that many fewer models
must be run. But, the special circumstances are
rather restrictive.
This strategy works in landscapes in which
much of the present topography is a relict,
frozen-in version of the past topography. In
Fig. 11.29 and Plate 13, we show results from
Schildgen
et al.
's (2009) attempt to model the
incised edge of the Andean Altiplano into which
river canyons have been deeply etched, while
much of the remaining landscape has been geo-
morphically inactive, such that persistent older
surfaces are common. As an initial condition, the
model strategy takes a topography that is tacked
to the present topography of these remnant
surfaces and that smoothly drapes across the pre-
sent river canyons. The difference between this
and the present topography is, therefore, mostly
the canyon. The model then simply morphs
between this initial landscape and the modern:
10% of the canyon relief is in place by a certain
age, 30% by some other age, and so on. The ther-
mal history of a rock that emerges at the sur-
face at any sample site can then be assessed.
Such models also require assumptions about the
boundary conditions at the base of the model: in
Schildgen's work, she assumed a particular basal
temperature and gradient in that temperature
associated with position of the section with
respect to the subducting slab. Comparing the
modeled apatite He ages with those measured in
numerous samples in vertical transects through
the canyon walls suggests that the canyon was
cut in the interval 9-5 Ma (Fig. 11.29B).
Dynamic topography
At the broadest continental scale, the elevation
of the Earth's surface can be significantly
affected by stresses imposed on the lithosphere
by motion of the mantle in what has been
dubbed “dynamic topography.” The passage of
lithospheric slabs beneath a site, the dropping
of drips of anomalously heavy crust, the impact
of mantle plumes with the base of the litho-
sphere, all these can raise or lower the Earth's
surface by on the order of 1 km vertically over
length scales of thousands of kilometers. It has,
for example, been argued that the interior of
North America was pulled downward while the
Farallon slab was subducting beneath it and
has bobbed upward subsequent to the pas-
sage of that slab more deeply into the mantle.
The geological evidence for this lies largely in
the relative sea-level pattern recorded in the
Cretaceous seaway (marine) sediments, and the
present 1-km elevation of a large fraction of that
old seaway - see, e.g., Mitrovica
et al.
(1989)
and Forte
et al.
(2007) for discussion of the
resulting state of stress in the continental
