Geoscience Reference
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Fig. 11.16 Schematic
example of four square cells
near boundary of artificial
study area illustrating bias
prevention method based on
considering for each cell:
area of exposed bedrock,
area of covered bedrock,
area outside study region,
and combined length of
fractures. Measurements of
fracture intensity are
divided by
w
i
¼
a
i
/
a
to
correct for bias with
a
i
representing area of
exposed bedrock per cell,
and
a
(constant) total cell
area, respectively (Source:
Agterberg et al.
1996a
,
Fig. 2)
bedrock or part of the cell outside the study region (see Fig.
11.16
). The modified
equation also implies that frequency of fractures in the exposed part of a cell is
considered to be representative for the entire cell. This linear extrapolation may
result in the assignation of too much weight to fractures in cells with relatively
small values of
w
i
.
In order to assess this source of uncertainty, it is desirable to carry out the
following type of sensitivity analysis. The entire procedure can be repeated a
number of times, for each
using only those cells with
w
i
greater than a threshold
E
value denoted as
. Estimates then can be regarded as robust if they remain
approximately the same for a range of successive
ʔ
-values. A disadvantage of
introducing a threshold value for
w
i
is that the sample size
n
(
ʔ
E
) is reduced for each
E
.
ʔ
The sample size decreases when
is increased. This, in turn, would result in loss of
precision, especially for relatively small values of
close
to 10, 20, 40, 80, and 160 m) were used for this type of sensitivity analysis. The first
three sets of cells are shown in Fig.
11.17
. The measurements obtained for each cell
(i)
were cell area (
a
i
), exposed area (
s
i
) and total length of all fractures per cell (
E
. Five different cell sizes (
E
ʼ
i
).
The cells were constructed by using the Voronoi tessellation procedure in a GIS for
points on a regular grid with spacing equal to
. Cells near the edges of the study
E
2
representing the standard cell size. The
variable cell area was used only to determine relative exposed cell area (
s
i
/
a
i
) for
comparison with successive
area are larger or smaller than
a
¼
E
-values.
Bias correction was applied after setting
w
i
¼
ʔ
2
. Thus, measure-
ments for cells with areas greater than standard cell size were reduced (relatively
few of such cells occur at the contact between granite and other rocks;
cf
. Fig.
11.14a
), and those for smaller cells were increased, before raising them
to successive powers (
q
). The analysis was repeated several times, for each
s
i
/
a
with
a
¼
E
,
E
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