calculo variogramas

CALCULO DE VARIOGRAMACALCULO DE VARIOGRAMA

VARIOGRAMAS UNIDIMENCIONALES :

REGULARMENTE DISTRIBUIDOSIREGULARMENTE DISTRIBUIDOS

VARIOGRAMAS BIDIMENCIONALES

VARIOGRAMAS TRIDIMENCIONALES

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

k= 1 n= 12

h= 5( 0.5 - 0.9 )^2 = 1 2

2 3 γ h=1 =1/2*1/(n-k)*∑(z(xi+h)-z(xi))^23 44 55 66 77 88 99 10

10 1111 12

∑

3.8307

0.160.002584.275

γ h=1 =0.0940.96

42.25000.040.010.36

0.20250.040.16

3

k= 2

h= 101 32 43 54 65 76 87 98 109 11

10 12∑ 90.725

4.5363

44.89000.090.250.04

0.1225

0.01

0.06250.3600

0.0144.89 γ h=2 =

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= 3 n= 12

h= 15( 0.5 - 0.9 )^2 = 1 4

2 5 γ h=1 =1/2*1/(n-k)*∑(z(xi+h)-z(xi))^23 64 75 86 97 108 119 12

∑

46.24000.090.01

0.062586.335

0.02250.09

4.79640.09

γ h=3 =39.690.04

5

k= 4

h= 201 52 63 74 85 96 107 118 12

∑

38.44000.01

0.022575.905

37.21000.04

00.16

γ h=4 = 4.7441

0.0225

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

k= 5 n= 12

h= 25( 0.5 - 0.9 )^2 = 1 6

2 7 γ h=1 =1/2*1/(n-k)*∑(z(xi+h)-z(xi))^23 84 95 106 117 12

∑ 86.835

0.0443.56000.0025

42.90250.16

γ h=1 = 6.20250.160.01

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

7

k= 6

h= 301 72 83 94 105 116 12

∑

0.04

0.0025

42.902543.805

0.36000.250.25 γ h=2 = 3.6504

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

8

k= 7 n= 12

h= 35( 0.5 - 0.9 )^2 = 1 8

2 9 γ h=1 =1/2*1/(n-k)*∑(z(xi+h)-z(xi))^23 104 115 12

∑ 0.555

0.01 γ h=1 = 0.05550.0225

0.02250.490.01

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

9

k= 8

h= 401 92 103 114 12

∑ 0.185

0.01000.09

0.0225 γ h=2 = 0.0231

0.0625

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

10

k= 9 n= 12

h= 45( 0.5 - 0.9 )^2 = 1 10

2 11 γ h=1 =1/2*1/(n-k)*∑(z(xi+h)-z(xi))^23 12

∑ 0.435γ h=1 = 0.0725

0.12250.25

0.0625

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

11

k= 10

h= 501 112 12

∑ 0.205

0.2025

γ h=2 = 0.0513

0.0025

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

12

h γ1 3.83072 4.53633 4.79644 4.74415 6.20256 3.65047 0.05558 0.02319 0.0725

10 0.0513

0.0000

1.0000

2.0000

3.0000

4.0000

5.0000

6.0000

7.0000

1 2 3 4 5 6 7 8 9 10

YVARIOGRAMA UNIDIMENCINAL

Series1

h

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

13

VARIOGRAMAS UNIDIMENCIONALES :

IREGULARMENTE DISTRIBUIDOS

γ = (kb) = (1 / 2 x (N - k)) x Σ (z i+ k - zi)2

DATAh = kb (k = 1,2,3,…,N - 1)FORMULA BASICA FINAL

DATOS

% Cu dist.a 8.48 2b 6.23 1.5c 4.38 4.83d 3.25 2.25e 7.39 1.2f 4.53 3.5g 8.91 4.1h 5.37 3.1i 6.23 1.9j 4.25 2.3k 6.22 1.85l 7.89 2

14

Nota : distancia 01 versus 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

15

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

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

Determinacion del rango de las muestrasNota: se busca un numero entero entre todas las distancias o un aproximado si no lo ubieraen 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

interv. 0-5 interv. 5-10 interv. 10-151 5.0625 1.5 1 16.8100 6.33 1 15.6025 13.282 3.4225 4.83 2 27.3529 8.58 2 2.8900 11.783 1.2769 2.25 3 1.1881 9.78 3 20.5209 11.054 9.0601 3.45 4 8.8804 7.08 4 0.9801 14.155 17.1396 1.20 5 1.3456 8.28 5 4.4944 11.906 1.6384 4.70 6 0.0225 6.95 6 8.8804 13.807 8.1796 3.50 7 32.0356 8.80 7 4.0804 10.708 19.1844 4.10 8 2.3104 7.60 8 1.3456 12.609 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 11.4011 1.2544 4.20 11 7.1824 5.00 11 2.8561 13.2512 3.9204 2.30 12 21.7156 7.30 12 1.0404 11.1513 0.0001 4.15 13 7.2361 9.15 Σ 72.6288 149.9614 3.8809 1.85 14 0.7225 6.05 PRM 12.49715 13.2496 3.85 15 6.3504 8.0516 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 = 3.0262PRM 3.06 PRM 7.588

γ = 1/(2 x N) x Σ γ = 1/(2 x N) x Σγ = 3.2290 γ = 4.3595

19

interv. 15-20 interv. 20-25 interv. 25-300.1849 17.38 9.6721 20.48 5.1076 26.537.1824 15.88 5.0625 22.38 0.3481 28.530.7396 18.98 17.8929 24.68 0.0001 25.033.4225 16.05 0.0000 20.88 2.7556 27.030.0169 18.35 3.9204 23.18 Σ 8.2114 107.121.0000 16.10 3.3856 20.20 PRM 26.788.8209 17.95 12.3201 22.20 γ = 1/(2 x N) x Σ

21.5296 19.95 Σ 52.2536 154.00 γ = 1.02641.3689 16.75 PRM 22.000.2500 18.75 γ = 1/(2 x N) x Σ

11.2896 15.25 γ = 3.7324Σ 55.8053 191.39

PRM 17.399γ = 1/(2 x N) x Σγ = 2.5366

20

21

22