The document discusses the calculation of unidimensional and irregularly distributed variograms. It provides sample data with copper concentration values and distances. It then calculates the variogram values (γ) for different lags (h) using the basic formula, and plots the results on a graph with lag distance on the x-axis and variogram value on the y-axis. The variogram values level off with increasing lag distance, indicating the sample data is irregularly distributed.

1. CALCULO DE VARIOGRAMA
CALCULO DE VARIOGRAMA
VARIOGRAMAS
UNIDIMENCIONALES :
REGULARMENTE DISTRIBUIDOS
IREGULARMENTE DISTRIBUIDOS
VARIOGRAMAS BIDIMENCIONALES
VARIOGRAMAS
TRIDIMENCIONALES

2. VARIOGRAMAS
UNIDIMENCIONALES :
REGULARMENTE DISTRIBUIDOS
1 2 3 4 5 6 7 8 9 10 11 12
0.45 0.9 0.7 0.3 0.6 7 0.5 0.3 0.2 0.8 0.4 0.45
5 mt 5 mt 5 mt
2

3. k= 1 n= 12
h= 5
( 0.5 - 0.9 )^2 = 0.2025 1 2
0.04 2 3 γ h=1 =1/2*1/(n-k)*∑(z(xi+h)-z(xi))^2
0.16 3 4
0.09 4 5 γ h=1 = 3.8307
40.96 5 6
42.2500 6 7
0.04 7 8
0.01 8 9
0.36 9 10
0.16 10 11
0.0025 11 12
∑ 84.275
3

4. 1 2 3 4 5 6 7 8 9 10 11 12
0.45 0.9 0.7 0.3 0.6 7 0.5 0.3 0.2 0.8 0.4 0.45
5 mt 5 mt 5 mt
k= 2
h= 10
0.0625 1 3
0.3600 2 4
0.01 3 5
44.89 4 6 γ h=2 = 4.5363
0.01 5 7
44.8900 6 8
0.09 7 9
0.25 8 10
0.04 9 11
0.1225 10 12
∑ 90.725
4

5. k= 3 n= 12
h= 15
( 0.5 - 0.9 )^2 = 0.0225 1 4
0.09 2 5 γ h=1 =1/2*1/(n-k)*∑(z(xi+h)-z(xi))^2
39.69 3 6
0.04 4 7 γ h=3 = 4.7964
0.09 5 8
46.2400 6 9
0.09 7 10
0.01 8 11
0.0625 9 12
∑ 86.335
5

6. 1 2 3 4 5 6 7 8 9 10 11 12
0.45 0.9 0.7 0.3 0.6 7 0.5 0.3 0.2 0.8 0.4 0.45
5 mt 5 mt 5 mt
k= 4
h= 20
0.0225 1 5
37.2100 2 6
0.04 3 7
0 4 8 γ h=4 = 4.7441
0.16 5 9
38.4400 6 10
0.01 7 11
0.0225 8 12
∑ 75.905
6

7. 1 2 3 4 5 6 7 8 9 10 11 12
0.45 0.9 0.7 0.3 0.6 7 0.5 0.3 0.2 0.8 0.4 0.45
5 mt 5 mt 5 mt
k= 5 n= 12
h= 25
( 0.5 - 0.9 )^2 = 42.9025 1 6
0.16 2 7 γ h=1 =1/2*1/(n-k)*∑(z(xi+h)-z(xi))^2
0.16 3 8
0.01 4 9 γ h=1 = 6.2025
0.04 5 10
43.5600 6 11
0.0025 7 12
∑ 86.835
7

8. 1 2 3 4 5 6 7 8 9 10 11 12
0.45 0.9 0.7 0.3 0.6 7 0.5 0.3 0.2 0.8 0.4 0.45
5 mt 5 mt 5 mt
k= 6
h= 30
0.0025 1 7
0.3600 2 8
0.25 3 9
0.25 4 10 γ h=2 = 3.6504
0.04 5 11
42.9025 6 12
∑ 43.805
8

9. 1 2 3 4 5 6 7 8 9 10 11 12
0.45 0.9 0.7 0.3 0.6 7 0.5 0.3 0.2 0.8 0.4 0.45
5 mt 5 mt 5 mt
k= 7 n= 12
h= 35
( 0.5 - 0.9 )^2 = 0.0225 1 8
0.49 2 9 γ h=1 =1/2*1/(n-k)*∑(z(xi+h)-z(xi))^2
0.01 3 10
0.01 4 11 γ h=1 = 0.0555
0.0225 5 12
∑ 0.555
9

10. 1 2 3 4 5 6 7 8 9 10 11 12
0.45 0.9 0.7 0.3 0.6 7 0.5 0.3 0.2 0.8 0.4 0.45
5 mt 5 mt 5 mt
k= 8
h= 40
0.0625 1 9
0.0100 2 10
0.09 3 11
0.0225 4 12 γ h=2 = 0.0231
∑ 0.185
10

11. 1 2 3 4 5 6 7 8 9 10 11 12
0.45 0.9 0.7 0.3 0.6 7 0.5 0.3 0.2 0.8 0.4 0.45
5 mt 5 mt 5 mt
k= 9 n= 12
h= 45
( 0.5 - 0.9 )^2 = 0.1225 1 10
0.25 2 11 γ h=1 =1/2*1/(n-k)*∑(z(xi+h)-z(xi))^2
0.0625 3 12
γ h=1 = 0.0725
∑ 0.435
11

12. 1 2 3 4 5 6 7 8 9 10 11 12
0.45 0.9 0.7 0.3 0.6 7 0.5 0.3 0.2 0.8 0.4 0.45
5 mt 5 mt 5 mt
k= 10
h= 50
0.0025 1 11
0.2025 2 12
γ h=2 = 0.0513
∑ 0.205
12

13. 1 2 3 4 5 6 7 8 9 10 11 12
0.45 0.9 0.7 0.3 0.6 7 0.5 0.3 0.2 0.8 0.4 0.45
5 mt 5 mt 5 mt
h γ
1 3.8307 VARIOGRAMA UNIDIMENCINAL
2 4.5363
7.0000
3 4.7964
4 4.7441 6.0000
5 6.2025
6 3.6504 5.0000
7 0.0555
Y
8 0.0231 4.0000
9 0.0725 Series1
3.0000
10 0.0513
2.0000
1.0000
0.0000 h
1 2 3 4 5 6 7 8 9 10
13

14. VARIOGRAMAS
UNIDIMENCIONALES :
IREGULARMENTE DISTRIBUIDOS
DATOS
DATA
h = kb (k = 1,2,3,…,N - 1) % Cu dist.
FORMULA BASICA FINAL a 8.48 2
b 6.23 1.5
γ = (kb) = (1 / 2 x (N - k)) x Σ (z i+ k - zi)2 c 4.38 4.83
d 3.25 2.25
e 7.39 1.2
f 4.53 3.5
g 8.91 4.1
h 5.37 3.1
i 6.23 1.9
j 4.25 2.3
k 6.22 1.85
l 7.89 2 14

15. Nota : distancia 01 versus las demas distancias
2
muestra a (z i+ k - zi) dista muestra b dista muestra c dista
( 6.23 - 8.48 )2 = 5.0625 1.5 ( 4.38 - 6.23 )2 = 3.4225 4.83 ( 3.25 - 4.38 )2 = 1.2769 2.25
( 4.38 8.48 )2 = 16.8100 6.33 ( 3.25 - 6.23 )2 = 8.8804 7.08 ( 7.39 - 4.38 )2 = 9.0601 3.45
( 3.25 8.48 )2 = 27.3529 8.58 ( 7.39 - 6.23 )2 = 1.3456 8.28 ( 4.53 - 4.38 )2 = 0.0225 6.95
( 7.39 8.48 )2 = 1.1881 9.78 ( 4.53 - 6.23 )2 = 2.8900 11.78 ( 8.91 - 4.38 )2 = 20.5209 11.05
( 4.53 8.48 )2 = 15.6025 13.28 ( 8.91 - 6.23 )2 = 7.1824 15.88 ( 5.37 - 4.38 )2 = 0.9801 14.15
( 8.91 8.48 )2 = 0.1849 17.38 ( 5.37 - 6.23 )2 = 0.7396 18.98 ( 6.23 - 4.38 )2 = 3.4225 16.05
( 5.37 8.48 )2 = 9.6721 20.48 ( 6.23 - 6.23 )2 = 0.0000 20.88 ( 4.25 - 4.38 )2 = 0.0169 18.35
( 6.23 8.48 )2 = 5.0625 22.38 ( 4.25 - 6.23 )2 = 3.9204 23.18 ( 6.22 - 4.38 )2 = 3.3856 20.20
( 4.25 8.48 )2 = 17.8929 24.68 ( 6.22 - 6.23 )2 = 0.0001 25.03 ( 7.89 - 4.38 )2 = 12.3201 22.20
( 6.22 8.48 )2 = 5.1076 26.53 ( 7.89 - 6.23 )2 = 2.7556 27.03
( 7.89 8.48 )2 = 0.3481 28.53
15

16. muetra d dista muetra e dista muetra f dista
( 7.39 - 3.25 )2 = 17.1396 1.20 ( 4.53 - 7.39 )2 = 8.1796 3.50 ( 8.91 - 4.53 )2 = 19.1844 4.10
( 4.53 - 3.25 )2 = 1.6384 4.70 ( 8.91 - 7.39 )2 = 2.3104 7.60 ( 5.37 - 4.53 )2 = 0.7056 7.20
( 8.91 - 3.25 )2 = 32.0356 8.80 ( 5.37 - 7.39 )2 = 4.0804 10.70 ( 6.23 - 4.53 )2 = 2.8900 9.10
( 5.37 - 3.25 )2 = 4.4944 11.90 ( 6.23 - 7.39 )2 = 1.3456 12.60 ( 4.25 - 4.53 )2 = 0.0784 11.40
( 6.23 - 3.25 )2 = 8.8804 13.80 ( 4.25 - 7.39 )2 = 9.8596 14.90 ( 6.22 - 4.53 )2 = 2.8561 13.25
( 4.25 - 3.25 )2 = 1.0000 16.10 ( 6.22 - 7.39 )2 = 1.3689 16.75 ( 7.89 - 4.53 )2 = 11.2896 15.25
( 6.22 - 3.25 )2 = 8.8209 17.95 ( 7.89 - 7.39 )2 = 0.2500 18.75
( 7.89 3.25 )2 = 21.5296 19.95
16

17. muetra g dista muetra h dista muetra i dista
( 5.37 - 8.91 )2 = 12.5316 3.10 ( 6.23 - 5.37 )2 = 0.7396 1.90 ( 4.25 - 6.23 )2 = 3.9204 2.30
( 6.23 - 8.91 )2 = 7.1824 5.00 ( 4.25 - 5.37 )2 = 1.2544 4.20 ( 6.22 - 6.23 )2 = 0.0001 4.15
( 4.25 - 8.91 )2 = 21.7156 7.30 ( 6.22 - 5.37 )2 = 0.7225 6.05 ( 7.89 - 6.23 )2 = 2.7556 6.15
( 6.22 - 8.91 )2 = 7.2361 9.15 ( 7.89 - 5.37 )2 = 6.3504 8.05
( 7.89 - 8.91 )2 = 1.0404 11.15
muetra j dista muetra k dista muetra l dista
( 6.22 - 4.25 )2 = 3.8809 1.85 ( 7.89 - 6.22 )2 = 2.7889 2.00
( 7.89 - 4.25 )2 = 13.2496 3.85
17

18. Determinacion del rango de las muestras
Nota: se busca un numero entero entre todas las distancias o un aproximado si no lo ubiera
en este caso es 05 metros
Pareo γ* Dp
[ 0 - 5 ] 16.00 3.2290 3.055
[ 5 - 10 ] 16.00 4.3595 7.588
[ 10 - 15 ] 12.00 3.0262 12.497
[ 15 - 20 ] 11.00 2.5366 17.399
[ 20 - 25 ] 7.00 3.7324 22.00
[ 25 - 30 ] 4.00 1.0264 26.78
18

19. interv. 0-5 interv. 5-10 interv. 10-15
1 5.0625 1.5 1 16.8100 6.33 1 15.6025 13.28
2 3.4225 4.83 2 27.3529 8.58 2 2.8900 11.78
3 1.2769 2.25 3 1.1881 9.78 3 20.5209 11.05
4 9.0601 3.45 4 8.8804 7.08 4 0.9801 14.15
5 17.1396 1.20 5 1.3456 8.28 5 4.4944 11.90
6 1.6384 4.70 6 0.0225 6.95 6 8.8804 13.80
7 8.1796 3.50 7 32.0356 8.80 7 4.0804 10.70
8 19.1844 4.10 8 2.3104 7.60 8 1.3456 12.60
9 12.5316 3.10 9 0.7056 7.20 9 9.8596 14.90
10 0.7396 1.90 10 2.8900 9.10 10 0.0784 11.40
11 1.2544 4.20 11 7.1824 5.00 11 2.8561 13.25
12 3.9204 2.30 12 21.7156 7.30 12 1.0404 11.15
13 0.0001 4.15 13 7.2361 9.15 Σ 72.6288 149.96
14 3.8809 1.85 14 0.7225 6.05 PRM 12.497
15 13.2496 3.85 15 6.3504 8.05
16 2.7889 2.00 16 2.7556 6.15 γ = 1/(2 x N) x Σ
Σ 103.330 48.88 Σ 139.504 121.40 γ= 3.0262
PRM 3.06 PRM 7.588
γ = 1/(2 x N) x Σ γ = 1/(2 x N) x Σ
γ = 3.2290 γ= 4.3595
19

20. interv. 15-20 interv. 20-25 interv. 25-30
0.1849 17.38 9.6721 20.48 5.1076 26.53
7.1824 15.88 5.0625 22.38 0.3481 28.53
0.7396 18.98 17.8929 24.68 0.0001 25.03
3.4225 16.05 0.0000 20.88 2.7556 27.03
0.0169 18.35 3.9204 23.18 Σ 8.2114 107.12
1.0000 16.10 3.3856 20.20 PRM 26.78
8.8209 17.95 12.3201 22.20 γ = 1/(2 x N) x Σ
21.5296 19.95 Σ 52.2536 154.00 γ= 1.0264
1.3689 16.75 PRM 22.00
0.2500 18.75 γ = 1/(2 x N) x Σ
11.2896 15.25 γ = 3.7324
Σ 55.8053 191.39
PRM 17.399
γ = 1/(2 x N) x Σ
γ = 2.5366
20

21. 21

22. 22