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Higher
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Figure 2.45
Cell-based models. (a) The model comprises a series of voxels of the same size, with the magnitude of the physical property
speci
ed for each voxel; (b) 2D or 2.5D version of (a) depending on length L; (c) 3D cell-based model where one dimension of each cell is
varied; and (d) 2D or 2.5D version of (c) depending on length L. The shading depicts variation in the magnitude of the physical property.
direction, usually the vertical (
Fig. 2.45 c
and
d
). This kind
of model is commonly used to simulate basement topog-
raphy or sedimentary basins where all the cells are ascribed
the same physical property value and the data modelled by
adjusting the variable dimension.
Cell size and the number of cells are of fundamental
importance in cell-based models. They determine the reso-
lution of the model and the computational effort required
to obtain the response. A sufficient number of sufficiently
small cells are required to model the shorter-wavelength
variations in the observed geophysical response, and to
adequately represent areas where physical property vari-
ations are more complex. However, too many cells results
in a large number of model parameters and demands
greater computational resources. Often smaller cells are
used in the near-surface, becoming larger with depth where
less resolution is acceptable. The cell size may also vary
laterally, being smaller where more detail is required in the
central part of the model or where the data suggest more
complex structure.
shape- and cell-based models can represent a homoge-
neous subsurface, or can be arranged into 1-, 2- and 3D
forms. The dimensionality should re
ect the geological
complexity being modelled, which must be justi
ed in
terms of the available knowledge of the local geology, and
the distribution and quality of the geophysical data.
The model response is usually computed above the
surface, and topography may be included in the model. It
is also possible to compute responses at locations below the
surface, which is the requirement when modelling down-
hole data.
Half-space model
The simplest representation of the subsurface is a homoge-
neous volume with a
flat upper surface, known as a half-
space (the other half of the space being the air which, for
practical purposes, is a medium with homogeneous phys-
ical properties) (
Fig. 2.46a
). This model depicts those situ-
ations where the ground
s physical properties are invariant
in all directions, including to great depth, i.e. there are no
physical property contrasts except at the ground
'
-
air inter-
face. It is an important model for calculating the back-
ground response of the host rocks of a potential target, and
forms part of the response of discrete bodies in electrical
and electromagnetic data
2.11.1.3
1D, 2D and 3D models
In addition to selecting the type of model to use, the
interpreter must also decide the number of directions, or
dimensions, in which the model is to be defined. Both
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