Geostatistics
Assignment 1: Geostatistical Methods
Willem Botha
U19013711
PMW 410
Prof. Malan
Department of Mining Engineering
Faculty of Engineering, the Built Environment and Information Technology
University of Pretoria
16 May 2023
Geostatistics
UNIVERSITY OF PRETORIA
FACULTY OF ENGINEERING, BUILT ENVIRONMENT AND INFORMATION TECHNOLOGY
DEPARTMENT OF MINING ENGINEERING
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I (full names)
WILLEM JOHANNES BOTHA
Student number U9013711
Topic of work
Geostatistics
Declaration
1.
I understand what plagiarism is and am aware of the University’s policy in this regard.
2.
I declare that this ASSIGNMENT (e.g. essay, report, project, assignment, dissertation, thesis etc) is my own
original work. Where other people’s work has been used (either from a printed source, internet or any other
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3.
I have not used another student’s past written work to hand in as my own.
4.
I have not allowed, and will not allow, anyone to copy my work with the intention of passing it off as his or her own
work.
Signature
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Geostatistics
Table of Contents
LIST OF FIGURES ................................................................................................................ 3
1.
2.
Grade distributions ...................................................................................................... 4
1.1.
Polygon Method ................................................................................................................ 4
1.2.
Standard Block Model ....................................................................................................... 5
1.3.
Inverse Distance Weighted (IDW) method ........................................................................ 6
Conclusion ................................................................................................................... 8
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Geostatistics
LIST OF FIGURES
Figure 1: Grade distribution of the property. .................................................................................... 4
Figure 2: Semi variogram of the data given. .................................................................................... 6
Figure 3: IDW method (A) vs the standard block model (B)............................................................. 8
LIST OF TABLES
Table 1: Standard block model grade distribution............................................................................ 5
Table 2: Variogram data inputs. ...................................................................................................... 6
Table 3: Grade distribution using IDW formulas. ............................................................................. 7
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Geostatistics
1.
Grade distributions
1.1.
Polygon Method
Figure 1: Grade distribution of the property.
The polygon method used above in figure 1 indicates that the grade for each polygon is dependent
on the spacing between known exploration holes.
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Geostatistics
1.2.
Standard Block Model
Table 1: Standard block model grade distribution
3.2
4.0
4.0
4.0
4.0
8.0
8.0
8.0
8.0
8.0
3.2
2.8
2.8
4.0
8.0
8.0
8.0
8.0
8.0
8.0
3.2
2.8
2.8
2.8
8.9
8.9
8.9
9.0
8.0
8.0
3.2
2.8
2.8
2.8
7.0
7.0
6.5
6.5
6.5
4.2
5.0
5.0
5.0
6.9
7.0
7.0
6.5
6.5
4.2
4.2
5.0
5.0
5.0
6.9
6.9
6.9
6.5
6.5
4.2
4.2
9.2
9.2
9.2
6.9
6.9
6.4
3.2
3.2
3.2
4.2
9.2
9.2
9.8
9.8
6.4
6.4
6.4
3.2
3.0
3.0
9.3
9.3
9.3
6.7
6.7
6.4
3.2
3.2
3.0
3.0
9.3
9.3
93
6.7
6.7
6.7
3.2
3.2
3.0
3.0
Each block is assigned the grade value of the nearest known grade. Furthermore, if two adjacent
grade values are present, the lowest value was used.
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Geostatistics
1.3.
Inverse Distance Weighted (IDW) method
To speed up the process of IDW, I calculated the semi variogram for the data. The sill values gave
me a cut-off distance where beyond that point the distance will have no effect on the grade
distribution of an unknown point. The following equation was used to determine the values in table
1 and 2:
1
у∗ (ℎ) = 2𝑁(ℎ) ∑𝑢𝑖−𝑢𝑗(𝑍(𝑢𝑖 ) − 𝑍(𝑢𝑗 ))
(1)
Table 2: Variogram data inputs.
Distance (h)y
100
200
300
400
500
600
700
у*(h)
0.81
3.479
0.34
10.73
16.7725
9.05
12.5
Distance (h)x
100
200
300
400
500
600
700
у*(h)
0.02
0.203
6.778
4.225
13.03
11.981
18.3325
The values in Table 1 yielded the values in figure 2.
Variogram
20
Variance
15
10
5
Y direction
X direction
0
0
100
200
300
400
500
600
700
800
-5
Distance
Figure 2: Semi variogram of the data given.
The variogram yielded a hole effect for the values in the Y-direction, however a linear model is
evident for the X-direction. The cut of value in the y-direction was determined at 500m, whereas the
cut of range in the X-direction was determined at 700m. Thus, a radius (R-value) was determined at
860m around every point.
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Geostatistics
Table 3: Grade distribution using IDW formulas.
5.56
5.62
5.42
4
6.14
6.65
6.72
6.76
6.82
6.58
5.33
5.43
5.21
5.75
6.4
8
6.9
7
8
6.73
3.2
5.34
2.8
5.89
6.55
8.9
6.99
9
6.88
6.57
5.1
5.7
6.2
6.12
6.48
6.71
6.7
6.68
6.5
6.3
5.86
5
6.6
6.34
6.48
7
6.4
6.5
6.12
5.9
6.51
6.6
7
6.54
6.9
6.38
6.12
5.85
5.7
4.2
6.94
9.2
7.1
6.42
6.5
6.24
5.8
3.2
5.34
5.52
7
7.5
9.8
6.59
6.5
6.4
5.76
5.26
5.29
5.46
7.2
9.3
7.3
6.42
6.7
6.25
5.6
3.2
3
5.24
7
7.22
6.95
6.19
6.55
6.11
5.73
5.3
5.21
5.12
Figure 3: Colour contour of the grade distribution.
The colour contour clearly indicated the value of reef that is present in the mining lease area.
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Geostatistics
2.
Conclusion
The mining lease are indicated goo distribution of values across the property. The most reliable
model is surely the IDW method, as this method includes the influence of values across the whole
property.
A
B
Figure 3: IDW method (A) vs the standard block model (B).
Using the standard block model may lead us astray. It is clear that for the block model the blue areas
(8-10 g/t) are over a greater area, which will lead to over estimations when calculating the financial
model.
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