Geology Reference
In-Depth Information
discretized space as a set of nodes whose
attributes include the elevation of the point, the
thickness of the crust at that point, the amount
of soil or regolith or channel sediment at that
point, and so on. One must prescribe rules that
allow these attributes to change in a physically
reasonable way. In general, these rules simply
represent physical processes, the rate at which
they operate being dependent on other attributes
of the point of concern, such as the distance
from a fault, which might dictate the local
tectonic uplift rate, the local slope, the local
rainfall, and so on. These rules are generally
mathematical representations of differential
equations, the solutions to which require both
initial and boundary conditions. The differential
equations represent abstracts of the physics of
the problem, including the conservation of mass
and of momentum, equations for the response
of crustal materials to stress fields, rate of weath-
ering of bedrock, and so on. We have also seen
in previous chapters the importance of being
able to define how a landscape begins (as a sea
cliff with a known geometry; as a river with a
given profile). In the model world, the effect of
the starting geometry translates into the need to
specify
initial conditions
. In addition, we have
to worry about the edges of the model, that is,
its
boundary conditions
. The numerical model
ends abruptly, but the real space it is meant to
represent is connected to the rest of the world
through exchange of materials and forces.
Models, therefore, differ not only in how the
processes are mimicked, but also in how these
boundary and initial conditions are set up. If
faults are present within the model space and
form internal boundaries to blocks within the
volume, boundary conditions must be applied
to each of the faults.
are appropriate for the given problem and that
capture the essence of the problem. These
model rules evolve as our knowledge of the
physical processes evolves. It is here that
the links must be forged tightly with both the
tectonics and the geomorphic communities.
Because the role of the pattern of precipitation
on the landscape appears to matter significantly,
one must also establish links to the atmospheric
sciences community. Such linkage has indeed
been a thrust of the community in the last
decade, with the development of models of oro-
graphic precipitation (e.g., Roe
et al
., 2003; Roe,
2005) and of observational capabilities that
allow us to document the complex pattern of
precipitation as the atmosphere interacts with
the topography (e.g., Bookhagen and Burbank,
2006, 2010) (Fig. 10.32).
Tectonics
The sophistication of tectonic models varies
widely. The most commonly employed model
for tectonic deformation associated with discrete
faults within some material is based upon the
expected elastic deformation associated with a
dislocation across which no shear stresses are
transmitted. In all such models, the fault plane
or planes must be defined (Fig. 11.1). The full
location requires one point on the fault, the fault
strike and dip, and the vertical and horizontal
extent of the fault plane. The slip on the fault
must also be either determined or specified.
In boundary element models, the slip on any
dislocation within the volume can be calculated
in several ways. The boundary conditions on the
faults within the space can be either displace-
ments (same as specifying the slip on the faults)
or stresses (stress drop can be specified; zero
shear stress can be specified). These latter modes
can be driven by specifying remote stresses on
the volume or by specifying the strain within the
volume. For example, a right-lateral shear strain
within the volume can be imposed by dictating
that the east edge of the block has moved to the
south relative to the west edge of the block. If
the slip is instead specified, it can be defined in
two equivalent ways (Fig. 11.1): either by speci-
fying the fault rake and the total slip, or by
The rules
It is inevitable that any model is a simplification
or idealization of the real world. The “rules”
discussed here are the rules used within the
model and are not necessarily the rules by
which the real world operates. The art of mod-
eling lies in choosing a set of model rules that
