Resolucion Del 1er Examen de Geoestadistica-Vaquerito

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RESOLUCION DEL 1ER EXAMEN DE GEOESTADISTICA

PROBLEMA 1.-

En un proyecto de Exploración, se han perforado 260 sondajes diamantinos, el sondaje 110, tiene el siguiente registro de datos.

DATOS DE INGRESO Y CÁLCULO DE LAS COORDENADAS DEL C. G. DE CADA TESTIGO.

Nº DE

MUESTRA PROFUNDIDAD

CENTRO DE

GRAVEDAD C.G. ESPACIAMIENTO Ley(%)

1 12 6 2.10 2 16 14 8 1.50 3 21 18.5 4.5 0.90 4 26 23.5 5 1.50 5 34 30 6.5 1.30 6 42 38 8 1.60 7 52 47 9 1.40 8 58 55 8 1.20 9 63 60.5 5.5 0.90 10 67 65 4.5 0.80 11 76 71.5 6.5 2.20 12 81 78.5 7 1.90 13 85 83 4.5 1.30 14 92 88.5 5.5 2.50 15 100 96 7.5 1.60 MATRIZ DE DISTANCIAS 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 0 8 12.5 17.5 24 32 41 49 54.5 59 65.5 72.5 77 82.5 90 2 0 4.5 9.5 16 24 33 41 46.5 51 57.5 64.5 69 74.5 82 3 0 5 11.5 19.5 28.5 36.5 42 46.5 53 60 64.5 70 77.5 4 0 6.5 14.5 23.5 31.5 37 41.5 48 55 59.5 65 72.5 5 0 8 17 25 30.5 35 41.5 48.5 53 58.5 66 6 0 9 17 22.5 27 33.5 40.5 45 50.5 58 7 0 8 13.5 18 24.5 31.5 36 41.5 49 8 0 5.5 10 16.5 23.5 28 33.5 41 9 0 4.5 11 18 22.5 28 35.5 10 0 6.5 13.5 18 23.5 31 11 0 7 11.5 17 24.5 12 0 4.5 10 17.5 13 0 5.5 13 14 0 7.5 15 0 (Z(x+h)-Z(x))²

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 0 0.36 1.44 0.36 0.64 0.25 0.49 0.81 1.44 1.69 0.01 0.04 0.64 0.16 0.25 2 0 0.36 0 0.04 0.01 0.01 0.09 0.36 0.49 0.49 0.16 0.04 1 0.01 3 0 0.36 0.16 0.49 0.25 0.09 0 0.01 1.69 1 0.16 2.56 0.49 4 0 0.04 0.01 0.01 0.09 0.36 0.49 0.49 0.16 0.04 1 0.01 5 0 0.09 0.01 0.01 0.16 0.25 0.81 0.36 0 1.44 0.09 6 0 0.04 0.16 0.49 0.64 0.36 0.09 0.09 0.81 0 7 0 0.04 0.25 0.36 0.64 0.25 0.01 1.21 0.04 8 0 0.09 0.16 1 0.49 0.01 1.69 0.16 9 0 0.01 1.69 1 0.16 2.56 0.49 10 0 1.96 1.21 0.25 2.89 0.64 11 0 0.09 0.81 0.09 0.36 12 0 0.36 0.36 0.09 13 0 1.44 0.09 14 0 0.81 15 0 H total = 90 m H mínimo = 4.5 m H máximo 50 γ* (9) = 1/(2x24) x * (2.1 - 1.5)² + (2.1 - 0.9)² + (1.5 - 0.9)² + (1.5 - 1.5)² + (0.9 - 1.5)² + (0.9 - 1.3)² + (1.5 - 1.3)² + (1.3 - 1.6)² + (1.6 - 1.4)² + (1.4 - 1.2)² + (1.4 - 0.9)² + (1.2 - 0.9)² + (1.2 - 0.8)² + (0.9 - 0.8)² + (0.9 - 2.2)² + (0.8 - 2.2)² + (0.8 - 1.9)² + (2.5 - 1.6)² γ* (9) = 0.25458 γ* (18) = 1/(2x34) x * (2.1 - 0.9)² + (2.1 - 1.5)² + (1.5 - 1.5)² + (2.1 - 1.3)² + (1.5 - 1.3)² + (0.9 - 1.3)² + (1.5 - 1.6)² + (0.9 - 1.6)² + (1.5 - 1.6)² + (1.5 - 1.4)² + (1.3 - 1.4)² + (1.6 - 1.4)² + (1.3 - 1.2)² + (1.6 - 1.2)² + (1.6 - 0.9)² + (1.4 - 0.9)² + (1.6 - 0.8)² + (0.9 - 1.9)² + (0.8 - 1.9)² + (0.9 - 1.3)² + (0.8 - 1.3)² + (2.2 - 1.3)² + (0.8 - 2.5)² + (2.2 - 2.5)² + (1.9 - 2.5)² + (2.2 - 1.6)² + (1.9 - 1.6)² + (1.3 - 1.6)² γ* (18) = 0.24132 γ* (27) = 1/(2x42) x * (2.1 - 1.5)² + (2.1 - 1.3)² + (1.5 - 1.3)² + (2.1 - 1.6)² + (1.5 - 1.6)² + (0.9 - 1.6)² + (1.5 - 1.6)² + (1.5 - 1.4)² + (0.9 - 1.4)² + (1.5 - 1.4)² + (1.3 - 1.4)² + (0.9 - 1.2)² + (1.5 - 1.2)² + (1.3 - 1.2)² + (1.6 - 1.2)² + (1.5 - 0.9)² + (1.3 - 0.9)² + (1.4 - 2.2)² + (1.2 - 2.2)² + (1.6 - 1.9)² + (1.4 - 1.9)² + (1.2 - 1.9)² + (0.9 - 1.9)² + (0.8 - 1.9)² + (1.4 - 1.3)² + (1.2 - 1.3)² + (0.9 -

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1.3)² + (0.8 - 1.3)² + (1.2 - 2.5)² + (0.9 - 2.5)² + (0.8 - 2.5)² + (2.2 - 2.5)² + (0.9 - 1.6)² + (0.8 - 1.6)² + (2.2 - 1.6)² + (1.9 - 1.6)² γ* (27) = 0.22881 γ* (36) = 1/(2x50) x * (2.1 - 1.5)² + (2.1 - 1.3)² + (1.5 - 1.3)² + (2.1 - 1.6)² + (1.5 - 1.6)² + (0.9 - 1.6)² + (1.5 - 1.6)² + (1.5 - 1.4)² + (0.9 - 1.4)² + (1.5 - 1.4)² + (1.3 - 1.4)² + (0.9 - 1.2)² + (1.5 - 1.2)² + (1.3 - 1.2)² + (1.6 - 1.2)² + (1.5 - 0.9)² + (1.3 - 0.9)² + (1.4 - 2.2)² + (1.2 - 2.2)² + (1.6 - 1.9)² + (1.4 - 1.9)² + (1.2 - 1.9)² + (0.9 - 1.9)² + (0.8 - 1.9)² + (1.4 - 1.3)² + (1.2 - 1.3)² + (0.9 - 1.3)² + (0.8 - 1.3)² + (1.2 - 2.5)² + (0.9 - 2.5)² + (0.8 - 2.5)² + (2.2 - 2.5)² + (0.9 - 1.6)² + (0.8 - 1.6)² + (2.2 - 1.6)² + (1.9 - 1.6)² γ* (36) = 0.244 γ* (45) = 1/(2x59) x * (2.1 - 1.3)² + (2.1 - 1.6)² + (1.5 - 1.6)² + (2.1 - 1.4)² + (1.5 - 1.4)² + (0.9 - 1.4)² + (1.5 - 1.4)² + (2.1 - 1.2)² + (1.5 - 1.2)² + (0.9 - 1.2)² + (1.5 - 1.2)² + (1.3 - 1.2)² + (2.1 - 0.9)² + (1.5 - 0.9)² + (0.9 - 0.9)² + (1.5 - 0.9)² + (1.3 - 0.9)² + (1.6 - 0.8)² + (2.1 - 2.2)² + (1.5 - 2.2)² + (0.9 - 2.2)² + (1.5 - 2.2)² + (1.3 - 2.2)² + (1.6 - 2.2)² + (1.4 - 2.2)² + (1.5 - 1.9)² + (0.9 - 1.9)² + (1.5 - 1.9)² + (1.3 - 1.9)² + (1.6 - 1.9)² + (1.4 - 1.9)² + (1.2 - 1.9)² + (0.9 - 1.3)² + (1.5 - 1.3)² + (1.3 - 1.3)² + (1.6 - 1.3)² + (1.4 - 1.3)² + (1.2 - 1.3)² + (0.9 - 1.3)² + (1.5 - 2.5)² + (1.3 - 2.5)² + (1.6 - 2.5)² + (1.4 - 2.5)² + (1.2 - 2.5)² + (0.9 - 2.5)² + (0.8 - 2.5)² + (1.3 - 1.6)² + (1.6 - 1.6)² + (1.4 - 1.6)² + (1.2 - 1.6)² + (0.9 - 1.6)² + (0.8 - 1.6)² + (2.2 - 1.6)² γ* (45) = 0.25407 γ* (54) = 1/(2x56) x * (2.1 - 1.6)² + (2.1 - 1.4)² + (1.5 - 1.4)² + (0.9 - 1.4)² + (2.1 - 1.2)² + (1.5 - 1.2)² + (0.9 - 1.2)² + (1.5 - 1.2)² + (2.1 - 0.9)² + (1.5 - 0.9)² + (0.9 - 0.9)² + (1.5 - 0.9)² + (1.3 - 0.9)² + (2.1 - 0.8)² + (1.5 - 0.8)² + (0.9 - 0.8)² + (1.5 - 0.8)² + (1.3 - 2.2)² + (1.6 - 2.2)² + (2.1 - 1.9)² + (1.5 - 1.9)² + (0.9 - 1.9)² + (1.5 - 1.9)² + (1.3 - 1.9)² + (1.6 - 1.9)² + (1.4 - 1.9)² + (2.1 - 1.3)² + (1.5 - 1.3)² + (0.9 - 1.3)² + (1.5 - 1.3)² + (1.3 - 1.3)² + (1.6 - 1.3)² + (1.4 - 1.3)² + (1.2 - 1.3)² + (1.5 - 2.5)² + (0.9 - 2.5)² + (1.5 - 2.5)² + (1.3 - 2.5)² + (1.6 - 2.5)² + (1.4 - 2.5)² + (1.2 - 2.5)² + (0.9 - 2.5)² + (0.9 - 1.6)² + (1.5 - 1.6)² + (1.3 - 1.6)² + (1.6 - 1.6)² + (1.4 - 1.6)² + (1.2 - 1.6)² + (0.9 - 1.6)² + (0.8 - 1.6)² γ* (54) = 0.25946

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CUADRO DE RESULTADOS h Rango N(h) ∑N(h) h ∑(Z(x+h)-Z(x))² γ*(h) 9 4.5 13.5 24 206 8.5833 12.22 0.25458 18 9 27 34 596 17.529 16.41 0.24132 27 13.5 40.5 42 1059.5 25.226 19.22 0.22881 36 18 54 50 1729 34.58 24.4 0.244 45 22.5 67.5 59 2443 41.407 29.98 0.25407 54 27 81 56 2718.5 48.545 29.06 0.25946

GRAFICO DEL VARIOGRAMA EXPERIMENTAL

0.225 0.23 0.235 0.24 0.245 0.25 0.255 0.26 0.265 0 8 16 24 32 40 48 56 64 γ*( h) h (m)

VARIOGRAMA EXPERIMENTAL

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GRAFICO DE DISPERSION PARA EL 2DO PUNTO DE VARIOGRAMA

ANALISIS DEL PUNTO 2

RANGO 9 27 N° DE PARES 34 Z (X) Z (X+h) 2.1 0.9 2.1 1.5 1.5 1.5 2.1 1.3 1.5 1.3 0.9 1.3 1.5 1.6 0.9 1.6 1.5 1.6 1.5 1.4 1.3 1.4 1.6 1.4 1.3 1.2 1.6 1.2 1.6 0.9 1.4 0.9 1.6 0.8 1.4 0.8 1.2 0.8 1.4 2.2 1.2 2.2 0.9 2.2 1.2 1.9 0.9 1.9 0.8 1.9 0.9 1.3 0.8 1.3 2.2 1.3 0.8 2.5 2.2 2.5 1.9 2.5 2.2 1.6 1.9 1.6 1.3 1.6

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GRAFICO DE DISPERSION PARA EL 5TO PUNTO DE VARIOGRAMA

ANALISIS DEL PUNTO 5 RANGO 22.5 67.5 N° DE PARES 59 Z (X) Z (X+h) Z (X) Z (X+h) 2.1 1.3 2.1 2.2 2.1 1.6 1.5 2.2 1.5 1.6 0.9 2.2 2.1 1.4 1.5 2.2 1.5 1.4 1.3 2.2 0.9 1.4 1.6 2.2 1.5 1.4 1.4 2.2 2.1 1.2 1.5 1.9 1.5 1.2 0.9 1.9 0.9 1.2 1.5 1.9 1.5 1.2 1.3 1.9 1.3 1.2 1.6 1.9 2.1 0.9 1.4 1.9 1.5 0.9 1.2 1.9 0.9 0.9 0.9 1.3 1.5 0.9 1.5 1.3 1.3 0.9 1.3 1.3 1.6 0.9 1.6 1.3 2.1 0.8 1.4 1.3 1.5 0.8 1.2 1.3 0.9 0.8 0.9 1.3 1.5 0.8 1.5 2.5 1.3 0.8 1.3 2.5 1.6 0.8 1.6 2.5 1.4 2.5 1.2 2.5 0.9 2.5 0.8 2.5 1.3 1.6 1.6 1.6 1.4 1.6 1.2 1.6 0.9 1.6 0.8 1.6 2.2 1.6

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PROBLEMA 2.-

Calcular el variograma experimental, en las direcciones Norte–Sur y Este-Oeste, para la formación de muestreo dada en la siguiente tabla. Modelar el variograma en una de las direcciones.

DATOS DE ENTRADA ESTE NORTE % 30 80 1 40 80 1 50 80 2 60 80 2 70 80 3 80 80 5 90 80 4 100 80 6 110 80 7 120 80 8 130 80 7 140 80 9 150 80 9 160 80 11 170 80 10 PLANO DE UBICACIÓN 150 2 140 3 130 5 120 7 110 9 100 8 90 7 80 1 1 2 2 3 5 4 6 7 8 7 9 9 11 10 70 4 60 2 50 3 40 3 30 4 20 3 10 3 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 VARIOGRAMA EXPERIMENTAL EN LA DIRECCION ESTE – OESTE (VARIOGRAMA A 0°)

x y % 100 10 3 100 20 3 100 30 4 100 40 3 100 50 3 100 60 2 100 70 4 100 90 7 100 100 8 100 110 9 100 120 7 100 130 5 100 140 3 100 150 2

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γ* (10) = 1/(2x14) x * (1 - 1)² + (1 - 2)² + (2 - 2)² + (2 - 3)² + (3 - 5)² + (5 - 4)² + (4 - 6)² + (6 - 7)² + (7 - 8)² + (8 - 7)² + (7 - 9)² + (9 - 9)² + (9 - 11)² + (11 - 10)² ] γ* (10) = 0.8214 γ* (20) = 1/(2x13) x * (1 - 2)² + (1 - 2)² + (2 - 3)² + (2 - 5)² + (3 - 4)² + (5 - 6)² + (4 - 7)² + (6 - 8)² + (7 - 7)² + (8 - 9)² + (7 - 9)² + (9 - 11)² + (9 - 10)² ] γ* (20) = 1.4231 γ* (30) = 1/(2x12) x * (1 - 2)² + (1 - 3)² + (2 - 5)² + (2 - 4)² + (3 - 6)² + (5 - 7)² + (4 - 8)² + (6 - 7)² + (7 - 9)² + (8 - 9)² + (7 - 11)² + (9 - 10)² ] γ* (30) = 2.9167 γ* (40) = 1/(2x11) x * (1 - 3)² + (1 - 5)² + (2 - 4)² + (2 - 6)² + (3 - 7)² + (5 - 8)² + (4 - 7)² + (6 - 9)² + (7 - 9)² + (8 - 11)² + (7 - 10)² ] γ* (40) = 4.7727 γ* (50) = 1/(2x10) x * (1 - 5)² + (1 - 4)² + (2 - 6)² + (2 - 7)² + (3 - 8)² + (5 - 7)² + (4 - 9)² + (6 - 9)² + (7 - 11)² + (8 - 10)² ] γ* (50) = 7.4500 γ* (60) = 1/(2x9) x * (1 - 4)² + (1 - 6)² + (2 - 7)² + (2 - 8)² + (3 - 7)² + (5 - 9)² + (4 - 9)² + (6 - 11)² + (7 - 10)² ] γ* (60) = 10.3333 γ* (70) = 1/(2x8) x [ (1 - 6)² + (1 - 7)² + (2 - 8)² + (2 - 7)² + (3 - 9)² + (5 - 9)² + (4 - 11)² + (6 - 10)² ] γ* (70) = 14.9375 γ* (80) = 1/(2x7) x * (1 - 7)² + (1 - 8)² + (2 - 7)² + (2 - 9)² + (3 - 9)² + (5 - 11)² + (4 - 10)² ]

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γ* (80) = 19.0714 γ* (90) = 1/(2x6) x * (1 - 8)² + (1 - 7)² + (2 - 9)² + (2 - 9)² + (3 - 11)² + (5 - 10)² ] γ* (90) = 22.6667 CUADRO DE RESULTADOS h N(h) [Z(x+h)-Z(x)]^2 Y*(h) 0° 10 14 23 0.8214 20 13 37 1.4231 30 12 70 2.9167 40 11 105 4.7727 50 10 149 7.4500 60 9 186 10.3333 70 8 239 14.9375 80 7 267 19.0714 90 6 272 22.6667

VARIOGRAMA EXPERIMENTAL EN LA DIRECCION NORTE - SUR (VARIOGRAMA A 90°)

0.00 5.00 10.00 15.00 20.00 25.00 0 20 40 60 80 100 Y* (h ) 0 ° h (m)

VARIOGRAMA EXPERIMENTAL A 0°

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γ* (10) = 1/(2x14) x * (3 - 2)² + (5 - 3)² + (7 - 5)² + (9 - 7)² + (8 - 9)² + (7 - 8)² + (6 - 7)² + (4 - 6)² + (2 - 4)² + (3 - 2)² + (3 - 3)² + (4 - 3)² + (3 - 4)² + (3 - 3)² ] γ* (10) = 0.9643 γ* (20) = 1/(2x13) x * (5 - 2)² + (7 - 3)² + (9 - 5)² + (8 - 7)² + (7 - 9)² + (6 - 8)² + (4 - 7)² + (2 - 6)² + (3 - 4)² + (3 - 2)² + (4 - 3)² + (3 - 3)² + (3 - 4)² ] γ* (20) = 3.0385 γ* (30) = 1/(2x12) x * (7 - 2)² + (9 - 3)² + (8 - 5)² + (7 - 7)² + (6 - 9)² + (4 - 8)² + (2 - 7)² + (3 - 6)² + (3 - 4)² + (4 - 2)² + (3 - 3)² + (3 - 3)² ] γ* (30) = 5.5833 γ* (40) = 1/(2x11) x [ (9 - 2)² + (8 - 3)² + (7 - 5)² + (6 - 7)² + (4 - 9)² + (2 - 8)² + (3 - 7)² + (3 - 6)² + (4 - 4)² + (3 - 2)² + (3 - 3)² ] γ* (40) = 7.5455 γ* (50) = 1/(2x10) x * (8 - 2)² + (7 - 3)² + (6 - 5)² + (4 - 7)² + (2 - 9)² + (3 - 8)² + (3 - 7)² + (4 - 6)² + (3 - 4)² + (3 - 2)² ] γ* (50) = 7.9000 γ* (60) = 1/(2x9) x * (7 - 2)² + (6 - 3)² + (4 - 5)² + (2 - 7)² + (3 - 9)² + (3 - 8)² + (4 - 7)² + (3 - 6)² + (3 - 4)² ] γ* (60) = 7.7778 γ* (70) = 1/(2x8) x * (6 - 2)² + (4 - 3)² + (2 - 5)² + (3 - 7)² + (3 - 9)² + (4 - 8)² + (3 - 7)² + (3 - 6)² ] γ* (70) = 7.4375 γ* (80) = 1/(2x7) x * (4 - 2)² + (2 - 3)² + (3 - 5)² + (3 - 7)² + (4 - 9)² + (3 - 8)² + (3 - 7)² ]

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γ* (80) = 6.5000 CUADRO DE RESULTADOS h N(h) [Z(x+h)-Z(x)]^2 Y*(h) 90° 10 14 27 0.9643 20 13 79 3.0385 30 12 134 5.5833 40 11 166 7.5455 50 10 158 7.9000 60 9 140 7.7778 70 8 119 7.4375 80 7 91 6.5000 90 6 74 6.1667 VARIOGRAMA EXPERIMENTAL A 90°

MODELAMIENTO DEL VARIOGRAMA EXPERIMENTAL A 90°

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 0 20 40 60 80 100 Y* (h ) 90 ° h (m)

VARIOGRAMA EXPERIMENTAL A 90°

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PARAMETROS C0= 0 C1= 10 a= 53 S 8 MODELO ESFERICO 0.0000 1.0000 2.0000 3.0000 4.0000 5.0000 6.0000 7.0000 8.0000 9.0000 0 20 40 60 80 100 γ*( h) h (m)

MODELAMIENTO DEL VARIOGRAMA

EXPERIMENTAL

γ*(h) ESFERICO

MODELAMIENTO:

h γ*(h) MODELO ESFERICO 10 0.9643 0.79660391 20 3.0385 3.39169919 30 5.5833 5.58377721 40 7.5455 7.17132935 50 7.9000 7.95284698 60 7.7778 8 70 7.4375 8 80 6.5000 8                               

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PROBLEMA N° 03.- Los siguientes datos en % corresponden a un muestreo efectuado en

un yacimiento de salitre, cuya malla empleada fue de 5 x 5 metros.

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 70 65 60 55 50 45 40 35 22 22 19 16 17 30 28 25 18 18 13 11 9 25 21 18 24 21 20 13 14 20 16 20 21 23 12 11 17 15 20 15 15 19 15 19 17 12 16 10 18 16 14 13 14 13 10 10 18 5 20 19 16 10 12 13 19 0 11 18 22

VARIOGRAMA EXPERIMENTAL EN LA DIRECCION ESTE – OESTE (VARIOGRAMA A 0°)

γ* (5) = 1/(2x34) x * (22 - 22)² + (22 - 19)² + (16 - 17)² + (28 - 25)² + (18 - 18)² + (18 - 13)² + (11 - 9)² + (21 - 18)² + (24 - 21)² + (21 - 20)² + (20 - 13)² + (16 - 20)² + (20 - 21)² + (21 - 23)² + (12 - 11)² + (11 - 17)² + (20 - 15)² + (15 - 15)² + (15 - 19)² + (19 - 15)² + (15 - 19)² + (19 - 17)² + (17 - 12)² + (18 - 16)² + (16 - 14)² + (14 - 13)² + (13 - 14)² + (13 - 10)² + (10 - 10)² + (10 - 18)² + (19 - 16)² + (10 - 12)² + (13 - 19)² + (18 - 22)² ] γ* (5) = 6.235294 γ* (10) = 1/(2x27) x * (22 - 22)² + (22 - 19)² + (16 - 17)² + (28 - 25)² + (18 - 18)² + (18 - 13)² + (11 - 9)² + (21 - 18)² + (24 - 21)² + (21 - 20)² + (20 - 13)² + (16 - 20)² + (20 - 21)² + (21 - 23)² + (12 - 11)² + (11 - 17)² + (20 - 15)² + (15 - 15)² + (15 - 19)² + (19 - 15)² + (15 - 19)² + (19 - 17)² + (17 - 12)² + (18 - 16)² + (16 - 14)² + (14 - 13)² + (13 - 14)² + (13 - 10)² + (10 - 10)² + (10 - 18)² + (19 - 16)² + (10 - 12)² + (13 - 19)² + (18 - 22)² ] γ* (10) =11.66667

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γ* (15) = 1/(2x28) x * (19 - 22)² + (13 - 18)² + (11 - 13)² + (24 - 18)² + (20 - 24)² + (13 - 21)² + (21 - 16)² + (23 - 20)² + (12 - 23)² + (17 - 12)² + (15 - 20)² + (19 - 15)² + (15 - 15)² + (19 - 19)² + (17 - 15)² + (12 - 19)² + (16 - 12)² + (14 - 18)² + (13 - 16)² + (14 - 14)² + (13 - 14)² + (10 - 13)² + (18 - 10)² + (19 - 20)² + (10 - 16)² + (13 - 12)² + (18 - 11)² ] γ* (15) = 16.60714 γ* (20) = 1/(2x23) x * (16 - 19)² + (18 - 25)² + (11 - 18)² + (9 - 13)² + (24 - 21)² + (21 - 18)² + (13 - 24)² + (14 - 13)² + (23 - 16)² + (12 - 21)² + (11 - 23)² + (19 - 20)² + (15 - 15)² + (19 - 15)² + (17 - 19)² + (12 - 15)² + (16 - 17)² + (13 - 18)² + (14 - 16)² + (13 - 13)² + (10 - 14)² + (18 - 13)² + (16 - 20)² + (10 - 19)² + (12 - 16)² + (13 - 10)² + (19 - 12)² + (22 - 11)² ] γ* (20) = 18.13043 γ* (25) = 1/(2x21) x * (16 - 22)² + (17 - 19)² + (18 - 28)² + (18 - 25)² + (11 - 18)² + (9 - 18)² + (21 - 21)² + (20 - 18)² + (14 - 20)² + (12 - 20)² + (11 - 21)² + (17 - 23)² + (15 - 20)² + (19 - 15)² + (17 - 15)² + (12 - 19)² + (16 - 19)² + (14 - 18)² + (13 - 14)² + (10 - 13)² + (10 - 14)² + (12 - 19)² + (19 - 10)² ] γ* (25) = 17.80952 γ* (30) = 1/(2x16) x * (16 - 22)² + (17 - 22)² + (18 - 28)² + (13 - 25)² + (9 - 18)² + (20 - 21)² + (13 - 18)² + (14 - 21)² + (12 - 16)² + (11 - 20)² + (17 - 21)² + (19 - 20)² + (17 - 15)² + (12 - 15)² + (16 - 15)² + (13 - 16)² + (10 - 14)² + (10 - 13)² + (18 - 14)² ] γ* (30) = 21.4375

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CUADRO DE RESULTADOS h N(h) [Z(x+h)-Z(x)]² Y*(h) 0° 5 34 424 6.235294 10 27 630 11.66667 15 28 930 16.60714 20 23 834 18.13043 25 21 748 17.80952 30 16 686 21.4375

GRAFICO DEL VARIOGRAMA EXPERIMENTAL A 0°

0 5 10 15 20 25 0 5 10 15 20 25 30 35 40 Y* (h ) 0 ° h (m)

VARIOGRAMA EXPERIMENTAL A 0°

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VARIOGRAMA EXPERIMENTAL EN LA DIRECCION NORTE - SUR (VARIOGRAMA A 90°) h N(h) [Z(x+h)-Z(x)]² Y*(h) 90° 5 37 441 5.959459 10 30 571 9.516667 15 21 770 18.33333 20 18 622 17.27778 25 11 394 17.90909 30 7 287 20.5

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CALCULO DEL VARIOGRAMA OMNIDIRECCIONAL

h Y*(h) 0° Y*(h) 90° Y*(h) omni

10 6.2353 5.9595 6.0915 20 11.6667 9.5167 10.5351 30 16.6071 18.3333 17.3469 40 18.1304 17.2778 17.7561 50 17.8095 17.9091 17.8438 60 21.4375 20.5000 21.1522 70 23.6250 18.0000 23.0000 0.0 5.0 10.0 15.0 20.0 25.0 0 5 10 15 20 25 30 35 40 Y* (h ) h (m)

VARIOGRAMA OMNIDIRECCIONAL

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MODELAMIENTO DEL VARIOGRAMA OMNIDIRECCIONAL

MODELO ESFERICO:

MODELAMIENTO:

h Y*(h) omni ESFERICO

5 6.091549296 6.307094266 10 10.53508772 11.88532556 15 17.34693878 16.0058309 20 17.75609756 17.93974733 25 17.84375 18 30 21.15217391 18 35 23 18 0.0 5.0 10.0 15.0 20.0 25.0 0 5 10 15 20 25 30 35 40 Y* (h ) h (m)

MODELAMIENTO DEL VARIOGRAMA

OMNIDIRECCIONAL

Y*(h) omni ESFERICO PARAMETROS C0= 0 C1= 18 a= 21 S 18                                    a h si s a h si a h a h s h 3 3 2 1 2 3



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