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90 CH 5 MODELING SPATIAL CONTINUITY
representing different categories (rock types, sedimentary facies, and fractures). These
objects are then moved around to match the data by Markov chain simulation, which
is discussed in Chapter 6. This technique has mostly been used to model sedimentary
objects in reservoirs or aquifers, but many other applications can be envisioned, such as
for example the simulation of gold veins.
Before “simulating” the objects, it is necessary to define the object model. The first task
is to establish the various types of objects (sinuous, elliptic, cubic) and their dimensions
(width, thickness or width to thickness ratio, vertical cross section parameters, sinuosity,
etc.) which can be constant or varying according to a user specified distribution function.
Next it is necessary to specify their mutual spatial relationship: erosion of one object by
another, embedding, and attraction/repulsion of objects.
For example, in the case of channel type system (fluvial or submarine) various sources
of information can be considered to define the object model:
r
Outcrop studies of analog systems are probably the best source of information, although
there is a possibility of bias that comes up when inferring 3D object properties from 2D
outcrops (smaller 3D objects are less likely to occur in 2D sections).
r
Data from the site itself may provide information on object geometry, or may at least
help in relating object shape parameters from outcrop data to the objects shapes being
simulated.
5.4 3D Training Image Models
In many cases, it is not possible to capture spatial complexity by a few variogram pa-
rameters or even by a limited set of object shapes. The 3D training image approach is
a relatively new tool for modelers to communicate the spatial continuity style, explicitly
as a full 3D image, not as a set of parameters, whether variogram ranges or distributions
of object dimensions. The 3D training image is not an Earth model; it is a conceptual
rendering of the major variations that may exist in the studied area. The aim is then to
build 3D Earth models that mimic the spatial continuity of the 3D training image, and
at the same time constrain such Earth model to data. This topic is covered in the next
chapter. In this way the training image is much like a “texture mapping” approach used
in the games industry. A particular pattern is presented, such as in Figure 5.11, then the
trick is to randomize this pattern over the area being modeled. In the Earth Sciences this
must be done in 3D as well as be constrained to data.
Training images may be defined at various scales, from the large 10–100 km basin
scale to the m pore scale. Figure 5.12 shows a training image of a reservoir potential
consisting of channel sand with overbank deposits next to a binary training image of pores
in a sandstone matrix.
Often, many alternative training images are created, reflecting uncertainty about
the understanding of the studied phenomenon. This issue is considered extensively in
Chapters 9 and 10.