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Practical Geostatistics 2000

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Table 2.1. Calculation of experimental semi-variogram values in two major directions for iron ore example on square grid

Direction	Distance between	Experimental	Number of
	samples (ft)	semi-variogram	pairs
East-west	100	1.46	36
	200	3.30	33
	300	4.31	27
	400	6.70	23
North-south	100	5.35	36
	200	9.87	27
	300	18.88	21

Table 2.2. Calculation of semi-variogram in diagonal direction for iron ore

Direction	Distance between	Experimental	Number of
	samples (ft)	semi-variogram	pairs
North-west	141	7.06	32
South-east	282	12.95	21
diagonal	424	30.85	13

Table 2.3. Hypothetical borehole log from lead/zinc deposit --- Zinc values

Depthbelow	Zn(%)
collar(m)
(topofcore)
45.40	8.44
46.92	6.21
48.44	4.01
49.96	3.23
51.48	2.62
53.00	1.20
54.52	1.02
56.04	0.62
57.56	0.20
59.08	0.14
60.60	0.13
62.12	0.24
63.64	0.22
65.16	0.24
66.68	0.22
68.20	0.35

Depthbelow	Zn(%)
collar(m)
(topofcore)
69.72	0.35
71.24	0.34
72.76	0.39
74.28	0.66
75.80	1.40
77.32	4.35
78.84	7.74
80.36	7.06
81.88	4.93
83.40	3.05
84.92	2.42
86.44	1.34
87.96	0.56
89.48	0.53
91.00	0.70
92.52	1.01

Depthbelow	Zn(%)
collar(m)
(topofcore)
94.04	0.95
95.56	1.20
97.08	1.87
98.60	2.56
100.12	4.48
101.64	8.73
103.16	9.64
104.68	15.28
106.20	corelost
107.72	corelost
109.24	corelost
110.76	corelost
112.28	7.56
113.80	6.78
115.32	7.16
116.84	5.51

Depthbelow	Zn(%)
collar(m)
(topofcore)
118.36	2.61
119.88	3.34
121.40	6.80
122.92	3.84
124.44	3.21
125.96	3.90
127.48	3.58
129.00	4.32
130.52	6.00
132.04	2.70
133.56	3.72
135.08	4.80
136.60	6.31
138.12	7.05
139.64	7.24
141.16	8.19

Table 2.4. Calculated experimental semi-variogram from Lead/Zinc deposit

Distance between	Experimental	Number of
samples (m)	semi-variogram	pairs
	(%)²
1.52	1.33	58
3.04	3.09	56
4.56	5.03	54
6.08	6.70	52
7.60	8.26	51
9.12	9.00	50
10.64	9.67	49
12.16	10.46	48
13.68	11.44	47
15.20	11.87	46
16.72	11.39	45
18.24	11.33	44
19.76	10.93	43
21.28	10.48	42
22.80	9.76	41
24.32	9.21	40

Distance between	Experimental	Number of
samples (m)	semi-variogram	pairs
	(%)²
25.84	9.27	39
27.36	11.09	38
28.88	11.70	37
30.40	11.25	36
31.92	9.68	36
33.44	8.60	36
34.96	8.45	36
36.48	9.15	36
38.00	10.15	35
39.52	11.70	34
41.04	13.04	33
42.56	14.03	32
44.08	14.98	31
45.60	15.70	30
47.12	15.94	29
48.64	15.81	28

Table 2.5. Experimental semi-variogram from 400m adit --- silver values

Distance between	Experimental	Distance between	Experimental	Distance between	Experimental	Distance between	Experimental
samples(m)	semi-variogram	samples(m)	semi-variogram	samples(m)	semi-variogram	samples (m)	semi-variogram
1	0.42	26	8.94	51	10.22	76	12.26
2	0.72	27	8.48	52	9.96	77	11.69
3	0.92	28	7.65	53	11.64	78	12.30
4	1.36	29	7.04	54	11.93	79	11.63
5	1.69	30	6.49	55	12.62	80	12.98
6	2.03	31	7.26	56	11.35	81	15.78
7	1.95	32	7.47	57	10.18	82	17.42
8	2.75	33	7.66	58	10.69	83	16.72
9	3.65	34	9.54	59	10.03	84	17.20
10	4.05	35	10.98	60	9.81	85	17.16
11	3.44	36	10.82	61	10.23	86	14.67
12	3.55	37	10.58	62	11.85	87	14.12
13	3.24	38	10.21	63	11.27	88	14.56
14	3.07	39	10.08	64	13.01	89	16.04
15	4.52	40	8.28	65	13.61	90	17.81
16	5.23	41	8.08	66	14.17	91	20.96
17	6.53	42	9.34	67	11.75	92	22.70
18	6.41	43	9.55	68	9.91	93	23.20
19	5.98	44	9.87	69	10.12	94	24.37
20	5.72	45	10.45	70	9.56	95	23.67
21	5.26	46	10.23	71	10.91	96	21.66
22	6.46	47	8.87	72	11.98	97	21.44
23	7.01	48	9.19	73	12.13	98	22.94
24	7.55	49	10.19	74	11.45	99	22.29
25	8.06	50	10.73	75	12.14	100	22.16

Table 2.6. Spherical semi-variogram model for silver values up to h=75m

Distance between	Theoretical
samples (m)	semi-variogram
0	0.00
5	1.64
10	3.26
15	4.80
20	6.25
25	7.56
30	8.71
35	9.66
40	10.38
45	10.84
50	11.00
>50	11.00

Table 2.7 Attempts to fit exponential models to silver semi-variogram

Distance between	Theoretical semi-variograms
samples (m)	a=33,C=14	a=50,C=14	a=50,C=15	a=50,C=16
5	1.97	1.33	1.43	1.52
10	3.66	2.54	2.72	2.90
15	5.11	3.63	3.89	4.15
20	6.36	4.62	4.95	5.27
25	7.44	5.51	5.90	6.30
30	8.36	6.32	6.77	7.22
35	9.15	7.05	7.55	8.05
40	9.83	7.71	8.26	8.81
45	10.42	8.31	8.90	9.49
50	10.92	8.85	9.48	10.11
55	11.36	9.34	10.01	10.67
60	11.73	9.78	10.48	11.18
65	12.05	10.18	10.91	11.64
70	12.32	10.55	11.30	12.05

Table 2.8 Experimental semi-variogram from a disseminated nickel deposit (logarithm of grade)

Distance between	Experimental	Number of
samples (m)	semi-variogram	pairs
2	0.74	1222
4	1.10	1194
6	1.34	1186
8	1.58	1152
10	1.72	1137
12	1.81	1120
14	1.87	1095
16	1.90	1077
18	1.93	1055
20	1.92	1026
22	1.95	1011
24	2.01	990
26	2.09	969
28	2.16	950
30	2.25	919

Distance between	Experimental	Number of
samples (m)	semi-variogram	pairs
32	2.29	899
34	2.38	886
36	2.35	860
38	2.36	848
40	2.39	825
42	2.48	814
44	2.52	787
46	2.56	779
48	2.55	767
50	2.49	750
52	2.59	736
54	2.61	722
56	2.64	705
58	2.68	689
60	2.62	675

Distance between	Experimental	Number of
samples (m)	semi-variogram	pairs
62	2.52	657
64	2.59	639
66	2.53	628
68	2.47	612
70	2.56	597
72	2.62	582
74	2.64	563
76	2.75	552
78	2.93	539
80	3.06	514

Table 2.9 First attempt to fit a mixture of Spherical models to the experimental nickel semi-variogram (parameters in text)

Distance between	Theoretical	Distance between	Theoretical
samples (m)	semi-variogram	samples (m)	semi-variogram
0	0.00	25	2.36
2	0.77	30	2.42
4	1.12	35	2.48
6	1.44	40	2.52
8	1.73	45	2.54
10	1.96	50	2.55
12	2.12	55	2.55
14	2.20	60	2.55
16	2.23
18	2.26
20	2.29

Table 2.10 Final attempt to fit a mixture of Spherical models to the experimental Nickel semi-variogram (parameters in text)

Distance between	Theoretical	Distance between	Theoretical
samples (m)	semi-variogram	samples (m)	semi-variogram
0	0.00	20	2.03
2	0.74	25	2.14
4	1.05	30	2.24
6	1.34	35	2.33
8	1.58	40	2.40
10	1.75	45	2.46
12	1.85	50	2.51
14	1.89	55	2.54
16	1.94	60	2.55
18	1.99

Table 3.1 Hypothetical borehole log fom Lead/Zinc deposit ---

core has been sectioned in three alternative ways, 1.52m, 3.04m and 4.56m

Depth below collar (m)	1.52m	3.04m	4.56m
(top of core)
45.40	8.44	7.32	6.22
46.92	6.21
48.44	4.01	3.62
49.96	3.23		2.35
51.48	2.62	1.91
53.00	1.20
54.52	1.02	0.82	0.61
56.04	0.62
57.56	0.20	0.17
59.08	0.14		0.17
60.60	0.13	0.18
62.12	0.24
63.64	0.22	0.23	0.23
65.16	0.24
66.68	0.22	0.28
68.20	0.35		0.35
69.72	0.35	0.34
71.24	0.34
72.76	0.39	0.52	0.82
74.28	0.66
75.80	1.40	2.87
77.32	4.35		6.38
78.84	7.74	7.40
80.36	7.06
81.88	4.93	3.99	3.47
83.40	3.05
84.92	2.42	1.88
86.44	1.34		0.81
87.96	0.56	0.54
89.48	0.53
91.00	0.70	0.85	0.89
92.52	1.01

Depth below collar (m)	1.52m	3.04m	4.56m
(top of core)
94.04	0.95	1.07
95.56	1.20		1.88
97.08	1.87	2.21
98.60	2.56
100.12	4.48	6.60	7.62
101.64	8.73
103.16	9.64	12.46
104.68	15.28		---
106.20	core lost	---
107.72	core lost
109.24	core lost	---	---
110.76	core lost
112.28	7.56	7.17
113.80	6.78		6.48
115.32	7.16	6.33
116.84	5.51
118.36	2.61	2.97	4.25
119.88	3.34
121.40	6.80	5.32
122.92	3.84		3.65
124.44	3.21	3.55
125.96	3.90
127.48	3.58	3.95	4.63
129.00	4.32
130.52	6.00	4.35
132.04	2.70		3.74
133.56	3.72	4.26
135.08	4.80
136.60	6.31	6.68	6.87
138.12	7.05
139.64	7.24	7.71
141.16	8.19

Table 3.2 Experimental semi-variogram values calculated from the three different core section lengths

Distance between samples	Experimental semi-variograms
	1.52m	3.04m	4.56m
1.52	1.33
3.04	3.09	2.67
4.56	5.03		3.40
6.08	6.70	6.08
7.60	8.26
9.12	9.00	8.32	5.91
10.64	9.67
12.16	10.46	9.50
13.68	11.44		6.55
15.20	11.87	11.01
16.72	11.39
18.24	11.33	10.32	6.68
19.76	10.93
21.28	10.48	9.18
22.80	9.76		5.71
24.31	9.21	8.75
25.84	9.27
27.36	11.09	10.62	7.21
28.88	11.70
30.40	11.25	10.10
31.92	9.68		4.93
33.44	8.60	7.80
34.96	8.45
36.48	9.15	8.12	4.28
38.00	10.15
39.52	11.70	11.55
41.04	13.04		8.64
42.56	14.03	13.18
44.08	14.98
45.60	15.70	14.18	10.01
47.12	15.94
48.64	15.81	14.20

Distance between samples	Experimental semi-variograms
	1.52m	3.04m	4.56m
1.52	1.33
3.04