Geology Reference
In-Depth Information
the comparison, a network is categorized into dense, sparse or near optimal.
The network is iteratively optimized either by discarding, adding or shifting
the measurement points.
The theory of regionalized variable using kriging was used to analyse the
water level from 56 observation wells, with the grid size of 500 m × 500 m.
Following norms are calculated by comparing the
c
(cut off standard
deviation) values with
i
values all over the area.
Mean value of
i
as <
i
>
(1)
No. of grids (M) where
i
>
c
(2)
c
)
2
where
c
(3)
If the network is dense, the value of M and SSD will both be zero and
measurement points can be discarded starting from the location with the
least
Sum of the Squared Difference (SSD) =
&
(
i
-
i
>
i
. If the network is sparse, M and SSD will be non-zero and positive
and their magnitude directly relates to the sparseness of the network. New
measurement points can be added at the highest
i
areas. The monitoring
network need not be dense or sparse but it may not be still optimal as per
the desired accuracy/constraints. In that case values of M and SSD will be
moderately positive and the network could be optimized by shifting the
measurement points.
The following ordinary kriging equation was used in estimation:
n
)
F
F
()
x
=
(4)
i
i
i
1
n
)
+
'
=
,
i
= 1,………
n
(5)
j j
io
j
1
n
)
= 1
(6)
i
i
1
n
)
k
2
=
+
(7)
iio
i
1
where
x
F
is the estimated value of the variable at the point
x
o
and
x
o
is
the spatial coordinate. The , ,
()
2
k
and are the kriging weight, variogram,
kriging variance and Lagrange multiplier respectively. Krignet using ordinary
kriging equation was used to analyze the 56 data points and based on the
norms as shown in Table 1 and after comparing the different norms the
particular well was not considered for monitoring purpose. The criterion for
rejecting a well(s) was that the different norms should not differ much from
the standard situation when all 56 wells were present. The procedure was
repeated by removing a single well, two wells, three wells and four wells
taken at a time (Table 1).
