Geology Reference
In-Depth Information
Clarification: It may be clarified that can not take values greater than
or equal to 2. It can be 1.9 or 1.999, but cannot be equal to 2 or more.
4. Calculation of Experimental Variograms
Regular Grids in One Direction
Question 4.1
1 3 5 7 9 8 6 4 2
Case I I--------I--------I--------I------- I--------I-------I--------I--------I
5 1 9 2 3 7 8 4 6
Case II I--------I--------I--------I------- I--------I-------I--------I--------I
The above figures represent the value of Z ( x ) at each point. Calculate the
experimental variograms in both the cases.
Answer
The theoretical formula for the variogram is
1
>
?
2
()
h
EZx
(
h
)
Zx
()
.
2
1
)
/
0
2
()
h
Z x
(
h
)
Z x
(),
But to calculate practically
where N
2
N
represents the number of pairs and h represents the lag. The variograms
for the cases are calculated using the formula and presented in Table 5.
The distance lag and the number of pairs for both the cases are same
since the measurement points are same.
Table 5: Variograms of two data sets having same mean and variance
h
( h ) -Case I
( h ) -Case II
Number of pairs
1
1.81
10.44
8
2
6.43
8.29
7
3
11.92
4.58
6
4
14.80
5.40
5
5
10.50
11.75
4
6
5.83
4.50
3
7
2.50
6.50
2
8
0.50
0.50
1
It may be noted that though both data sets are numeral from 1 to 9
with the same mean and variance but have different variograms.
Question 4.2
10 12 36 72 91 38 31 50 69 07 21 18 71 08 40 82
I --- I --- I --- I --- I --- I --- I --- I --- I --- I --- I --- I --- I --- I --- I--- I
Calculate the experimental Variogram for the above distribution.
 
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