Geoscience Reference
In-Depth Information
The technique of cell declustering is another commonly
used declustering technique (Journel
1983
; Deutsch
1989
).
Cell declustering works as follows:
1. Divide the volume of interest into a grid of cells
l
=
1, …, L
.
2. Count the occupied cells
L
o
and the number of data in
each occupied cell
n
lo
,
lo
=
1, …, L
o
.
3. Weight each data according to the number of data falling
in the same cell, for example, for datum
i
falling in cell
l
,
the cell declustering weight is:
=
1
n
l
w
i
·
L
o
The weights are greater than zero and sum to one. Each oc-
cupied cell is assigned the same weight. An unoccupied cell
simply receives no weight.
Figure
2.12
illustrates the cell declustering procedure.
The area of interest is divided into a grid of
L
= 36 cells, with
L
o
= 33 occupied cells. The number of data in each occupied
cell is established by arbitrarily moving data on the grid
boundaries to the right and down.
The weights depend on the cell size and the origin of the grid
network. It is important to note that the cell size for declustering
is
not
the cell size for geologic modeling; it simply defines an
intermediate grid that allows assigning a declustering weight.
When the cell size is very small, each datum is in its own
cell and receives an equal weight. When the cell size is very
large, all data fall into one cell and are equally weighted.
Choosing the optimal grid origin, cell shape, and size re-
quires some sensitivity studies. It is common to choose the
cell size so that there is approximately one datum per cell in
the sparsely sampled areas or, if available, to choose it ac-
cording to an underlying, quasi-homogeneous sampling grid.
The sensitivity of the results to small changes in the
cell size should be checked. If the results change by a large
amount, then most likely the declustering weights are chang-
ing for one or two anomalously high or low grades.
Since it is generally known whether over-sampling oc-
curs in high- or low-valued areas, the weights can be selected
such that they give the minimum or maximum declustered
mean of the data. The declustered mean versus a range of
cell sizes should be plotted, and the size with the lowest
(Fig.
2.13
, data clustered in high-valued areas) or highest
(data clustered in low-valued areas) chosen. Care should
be taken not to over-fit the minimum. The correct cell size
should be approximately the spacing of the data in sparsely
sampled areas. This qualitative check can be used to ensure
that a too-large or too-small cell size is not chosen.
The shape of the cells depends on the geometric configu-
ration of the data, as it is adjusted to conform to the major
directions of preferential sampling. For example, if the sam-
ples are more closely spaced in the X direction than in the Y
direction, the cell size in the X direction should be reduced.
Fig. 2.11
An example of 122 samples with their polygonal areas of
influence
2.3.1
Declustering
Data are rarely collected randomly. Drill holes are often
drilled in areas of greatest interest, for example high grade
areas that will be mined early in the production schedule.
This practice of collecting more samples in areas of high
grade should not be changed because it leads to the greatest
number of data in portions of the study area that are the most
important. There is a need, however, to adjust the histograms
and summary statistics to be representative of the entire vol-
ume of interest.
Declustering
techniques assign each datum a weight
based on closeness to surrounding data
wi, i
=
1, …, n
. These
weights are greater than 0 and sum to 1. The experimental
distribution and all summary statistics are calculated with the
weights instead of a constant
1/n
.
The polygonal declustering method (Fig.
2.11
; Isaaks
and Srivastava
1989
) is perhaps the simplest, and assigns
each weight proportional to the area or volume of interest of
each sample. Studies have shown that this approach works
well when the limits to the area of interest are well defined
and the ratio of the largest to smallest weight is less than
10 to 1.
The nearest-neighbor declustering technique is com-
monly used in resource estimation, and is like the polygonal
method. The difference is that it is applied to a regular grid
of blocks or grid nodes. The closest datum of the set being
declustered is assigned to each block. Because it works on
the same blocks that are used to estimate resources, it is more
practical in resource estimation.
