calculo de variogramas unidimensionales con distancias regulares e irregulares

1. CALCULO DE VARIOGRAMACALCULO DE VARIOGRAMA
VARIOGRAMAS
UNIDIMENCIONALES :
REGULARMENTE DISTRIBUIDOS
IREGULARMENTE DISTRIBUIDOS

2. VARIOGRAMAS
UNIDIMENCIONALES :
REGULARMENTE DISTRIBUIDOS
1 2 3 4 5 6 7 8 9 10 11 12
5 mt 5 mt 5 mt
0.5 0.3 0.2 0.8 0.4 0.450.45 0.9 0.7 0.3 0.6 7
2

3. 3
k= 1 h= 5 N= 12 k= 2 h= 10 N= 12 k= 3 h= 15 N= 12
( 0.9 - 0.45 )^2 = ( 0.7 - 0.5 )^2 = ( 0.3 - 0.5 )^2 =
( 0.7 - 0.9 )^2 ( 0.3 - 0.9 )^2 ( 0.6 - 0.9 )^2
( 0.3 - 0.7 )^2 ( 0.6 - 0.7 )^2 ( 7 - 0.7 )^2
( 0.6 - 0.3 )^2 ( 7 - 0.3 )^2 ( 0.5 - 0.3 )^2
( 7.0 - 0.6 )^2 ( 0.5 - 0.6 )^2 ( 0.3 - 0.6 )^2
( 0.5 - 7 )^2 ( 0.3 - 7 )^2 ( 0.2 - 7 )^2
( 0.3 - 0.5 )^2 ( 0.2 - 0.5 )^2 ( 0.8 - 0.5 )^2
( 0.2 - 0.3 )^2 ( 0.8 - 0.3 )^2 ( 0.4 - 0.3 )^2
( 0.8 - 0.2 )^2 ( 0.4 - 0.2 )^2 ( 0.5 - 0.2 )^2
( 0.4 - 0.8 )^2 ( 0.5 - 0.8 )^2
( 0.5 - 0.4 )^2
∑ ∑ ∑
γ= γ= γ=
0.160
40.960
0.040
0.203
0.040
0.123
90.725
4.53625
0.360
0.003
84.275
42.250
0.160
0.090
0.010
0.063
0.360
0.010
44.890
0.010
44.890
0.090
0.250
0.040
46.240
0.090
0.010
0.063
86.335
0.023
0.090
39.690
0.040
0.090
4.79643.83068

4. 1 2 3 4 5 6 7 8 9 10 11 12
5 mt 5 mt 5 mt
0.5 0.3 0.2 0.8 0.4 0.450.45 0.9 0.7 0.3 0.6 7
4
k= 4 h= 20 N= 12 k= 5 h= 25 N= 12 k= 6 h= 30 N= 12
( 0.6 - 0.45 )^2 = ( 7 - 0.5 )^2 = ( 0.5 - 0.5 )^2 =
( 7 - 0.9 )^2 ( 0.5 - 0.9 )^2 ( 0.3 - 0.9 )^2
( 0.5 - 0.7 )^2 ( 0.3 - 0.7 )^2 ( 0.2 - 0.7 )^2
( 0.3 - 0.3 )^2 ( 0.2 - 0.3 )^2 ( 0.8 - 0.3 )^2
( 0.2 - 0.6 )^2 ( 0.8 - 0.6 )^2 ( 0.4 - 0.6 )^2
( 0.8 - 7 )^2 ( 0.4 - 7 )^2 ( 0.5 - 7 )^2
( 0.4 - 0.5 )^2 ( 0.5 - 0.5 )^2
( 0.5 - 0.3 )^2
∑ ∑ ∑
γ= γ= γ=
0.250
0.000 0.010 0.250
0.160 0.040 0.040
0.023 42.903 0.003
37.210 0.160 0.360
0.040 0.160
3.6504
0.023
75.905 86.835 43.805
42.903
0.010 0.003
38.440 43.560
4.74406 6.2025

5. 5
k= 7 h= 35 N= 12 k= 8 h= 40 N= 12 k= 9 h= 45 N= 12
( 0.3 - 0.45 )^2 = ( 0.2 - 0.5 )^2 = ( 0.8 - 0.5 )^2 =
( 0.2 - 0.9 )^2 ( 0.8 - 0.9 )^2 ( 0.4 - 0.9 )^2
( 0.8 - 0.7 )^2 ( 0.4 - 0.7 )^2 ( 0.5 - 0.7 )^2
( 0.4 - 0.3 )^2 ( 0.5 - 0.3 )^2
( 0.5 - 0.6 )^2
∑ ∑ ∑
γ= γ= γ=
k= 10 h= 50 N= 12 k= 11 h= 55 N= 12
( 0.4 - 0.45 )^2 = ( 0.5 - 0.5 )^2 =
( 0.5 - 0.9 )^2
∑ ∑
γ= γ=
0.023 0.063 0.123
0.023
0.490 0.010 0.250
0.010 0.090 0.063
0.05125 0
0.203
0.435
0.0555 0.02313 0.0725
0.003 0.000
0.555 0.185
0.205 0.000
0.010 0.023

6. 1 2 3 4 5 6 7 8 9 10 11 12
5 mt 5 mt 5 mt
0.5 0.3 0.2 0.8 0.4 0.450.45 0.9 0.7 0.3 0.6 7
6
Resumen
k h
1 5
2 10
3 15
4 20
5 25
6 30
7 35
8 40
9 45
10 50
11 55
0.0513
0.0000
6.2025
3.6504
0.0555
0.0231
0.0725
γ
3.8307
4.5363
4.7964
4.7441
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
5 10 15 20 25 30 35 40 45 50 55
Títulodeleje
Título del gráfico
Series1

7. VARIOGRAMAS
UNIDIMENCIONALES :
IREGULARMENTE DISTRIBUIDOS
γ = (kb) = (1 / 2 x (N - k)) x Σ (z i+ k - zi)2
DATA
h = kb (k = 1,2,3,…,N - 1)
FORMULA BASICA FINAL
DATOS
% Cu dist.
a 8.48 2
b 6.23 1.5
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 7

8. Nota : distancia 01versus las demas distancias
muestra a 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
(z i+k - zi)
2
8

9. muetrad dista muetrae dista muetraf 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
9

10. muetrag dista muetrah dista muetrai 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
muetraj dista muetrak dista muetral 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
10

11. 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 05metros
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
11

12. 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
12

13. 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/(2x 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/(2x N) x Σ
11.2896 15.25 γ = 3.7324
Σ 55.8053 191.39
PRM 17.399
γ = 1/(2x N) x Σ
γ = 2.5366
13

14. 14