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144 CH 8 MODELING STRUCTURAL UNCERTAINTY
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What is the computation time of any physical model applied to an Earth model? Phys-
ical models often require finite element or finite difference codes that do not scale
favorably with computation time (in the order of the number of cells squared or cubed).
Moreover, in modeling response uncertainty (Chapter 10) a physical model may need
to be run on several alternative Earth models. Often some form of upscaling (reducing
the number of cells and assigning upscaled/averaged properties to the larger cells) is
needed to reduce computation time to realistic levels.
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What is the decision goal for which the Earth models are used? Some decision pur-
poses require only crude/coarse models; for example, in getting a rough guess of an ore
body volume in the subsurface, a simple structural model with low grid resolution may
be sufficient. On the other hand, in order to predict transport of a chemically complex
contaminant in a highly heterogeneous soil, many grid cells may be needed to accu-
rately catch the spatial variability as well as chemical and physical interaction of the
contaminant with the highly variable environment.
No specific set of rules exists to choose the grid resolution. In fact, the grid resolution
itself can be considered a source of uncertainty and one may opt to build grids with
various resolutions, then through a sensitivity study (Chapter 10) determine whether or
not this is an impacting factor to the decision goal.
8.6 Modeling Surfaces through Thicknesses
In the previous sections, a fairly general approach to modeling structures was discussed.
This approach has been traditionally applied to subsurface structures but could be ap-
plied to any surface modeling application requiring a representation of both geometry
and topology. In certain applications, such as modeling specific depositional environ-
ments in the subsurface, more specialized forms of modeling can be used that are tailored
to the application and generally less complex. This is the case when modeling sedimen-
tary structures that have not undergone any deformation, or for which the deformation
part has been accounted for by unfolding and unfaulting the structures. Sediments are
deposited on top of each other, that is, in a sequence of depositional layers over a de-
positional plane with periods of erosion that have removed material. A simple way to
represent a surface is to start from a 2D thickness map (Figure 8.11). This thickness vari-
able is basically a 2D variable that can simply be represented on a Cartesian grid. Surfaces
created by depositional events can easily be represented in this fashion. Stacking various
thickness outcomes on top of each other results in a 3D volume, as shown in Figure 8.11.
Erosion is simply a negative thickness. In this way, surfaces can be modeled using the
Cartesian grid-based techniques described in Chapters 5–7.
8.7 Modeling Structural Uncertainty
So far we have concentrated on building a single structural model. Often such models
require a large amount of manual intervention to make them consistent with the ideas the