11 306 083

Ujian Akhir Semester

Geostatistika

Disusun

Oleh :

Ardi Siahaan 11 306 083

PROGRAM STUDI JURUSAN TEKNIK PERTAMBANGAN

FAKULTAS TEKNOLOGI MINERAL

INSTITUT TEKNOLOGI MEDAN

2015

DIKETAHUI SEBUAH PENGUKURAN DALAM RUANGAN SEBAGAI BERIKUT,

No Utara Timur

Elevas

i

11

175.8

8 99.06

131.7

9

12

176.5

5

124.7

4

128.2

8

13

178.6

8

148.8

5

123.8

1

14

198.3

9 28.34

126.8

6

15 199.7 76.47 126.3

No Utara Timur

Elevas

i

1

124.1

7 49.59 139.71

2

124.4

4 62.75 140.78

3

124.7

2 75.92 142.85

4

124.4

1 25.53 134.69

5

124.9

2 25.90 133.16

6

124.9

2 75.19 137.88

7

154.3

9 51.31 136.26

8

174.3

7 24.60 130.07

9

174.8

2 50.54 132.96

10

175.1

9 75.30 133.66

8 8

16

200.0

8

150.5

2

119.4

8

17

200.0

8

123.4

3

124.4

8

18

200.1

6

123.4

3

124.9

6

19 201 50.1

126.8

3

20

201.6

3

101.3

1

124.7

3

No Utara Timur Elevasi

31 251.51 22.83 116.68

No Utara Timur

Elevas

i

21 225.6 99.47 120.6

22

225.7

4

124.9

1 119.3

23

225.8

8 75.35 120.87

24

225.9

8 48.76 120.32

25

228.0

9 24.21 120.37

26 249.3 152.8 112.18

27

249.7

3

125.2

2 115

28

249.9

4 75 113.84

29 250.5 98.61 115.11

30

251.2

7 51.31 114.58

32 274.22 76.41 105.68

33 274.24 100.23 112.38

34 275.49 150.31 108.86

35 275.51 23.85 111.56

36 275.76 54.19 104.82

37 276.29 126.42 112.06

38 298.9 99.56 107.32

39 299.11 124.94 106.99

40 300.58 75.07 99.7

No Utara Timur Elevasi

41 301.46 147.62 103.47

42 301.95 48.27 95.56

43 323.13 150.75 96.75

44 324.11 99.4 100.35

45 325.7 73.69 93.48

46 326.08 124.65 99.49

47 326.37 50.32 91.39

48 110.5 10.5 140

49 330 155 90

50 288.17 64.63 102.26

Diminta

1. Tenttukan jumlah pasangan untuk tiap lag (jumlah lag = 20, 25, 30, 40), jlaskan

artinya

2. Tampilkan grafik semi-variogram untuk tiap lag. Deskripsikan arti dari setiap grafik

3. Menurut anda, jumlah lag mana yang sesuai dengan model variogram teoristisnya,?

Tuliskan alasanya, dan sebutkan model variogram yang anda usulkan (pilih)

4. Estimasi parameter estimatornya (Nugget (co), Sill (c) dan range (a)), berikan

alasannya

5. Estimasi distribusi nilai-nilai ruang (grid) yang di maksud. Tampilkan dalam bentuk

velktor kolom (X, Y, Z) misalnya spreadsheet seperti *,xls

6. Gambarkan isoline (bentuk kontur) dari distribusi nilai-nilai tersebut

7. Gambarkan pula bentuk tiga dimensinya

8. Dengan menggunakan metode lainnya (selain Geostatika dan IDW ) estimasi nilai

celah-celah ruang pada titik yang sama seperti grid jawaban sebelumnya,Jelaskan

mengapa anda memilih metode tersebut lengkapi dengan alasan pemilihan/penentuan

nilai-nilai estimator prosesnya

9. Gambarkan peta konturnya dari distribusi nilai-nilai yang diperoleh (jawaban nomor 8

) jelaskan pola sebaran nya

10. Jelaskan perbedaan dari kedua hasil estimasi yang diperoleh ( jawab 6-7 dan jawab

no 9)

Jawaban dibuat dalam bentuk file * doc ver 97-2003,lalu kirim ke

Geostat_itm@yahoo.com.

Jawab :

Lag 20 x(zi) x(z+h) x(zi)-x x(z+h)-xi x(zi)-x^2 x(z+h)-xi^2 Hasil kali91.4 93.5 -27.1 -26.1 736.6 680.2 500996.793.5 100.4 -25.1 -19.2 627.5 369.0 231563.5

100.4 99.5 -18.2 -20.1 330.5 402.8 133132.099.5 90.0 -19.0 -29.6 362.5 873.8 316769.190.0 96.8 -28.5 -22.8 814.0 520.3 423500.796.8 95.6 -21.8 -24.0 474.4 576.0 273236.295.6 99.7 -23.0 -19.9 527.6 394.4 208104.099.7 107.3 -18.8 -12.2 354.6 149.8 53120.7

107.3 107.0 -11.2 -12.6 125.7 158.0 19855.5107.0 103.5 -11.5 -16.1 133.2 258.9 34476.5103.5 102.3 -15.1 -17.3 226.8 299.3 67880.0102.3 111.6 -16.3 -8.0 264.7 64.0 16941.6111.6 104.8 -7.0 -14.7 48.6 217.3 10555.1104.8 105.7 -13.7 -13.9 188.0 192.7 36212.1105.7 112.4 -12.9 -7.2 165.1 51.6 8512.5112.4 112.1 -6.2 -7.5 37.8 56.3 2127.5112.1 108.9 -6.5 -10.7 41.9 114.5 4792.7108.9 116.7 -9.7 -2.9 93.5 8.3 775.6116.7 114.6 -1.8 -5.0 3.4 24.8 84.9114.6 113.8 -4.0 -5.7 15.6 32.7 510.5113.8 115.1 -4.7 -4.5 22.0 19.8 435.6115.1 115.0 -3.4 -4.6 11.7 20.8 243.2115.0 112.2 -3.5 -7.4 12.5 54.5 678.7112.2 120.4 -6.3 0.8 40.3 0.7 26.5120.4 120.3 1.8 0.8 3.4 0.6 2.0120.3 120.9 1.8 1.3 3.2 1.7 5.5120.9 206.0 2.3 86.4 5.5 7471.9 40913.0206.0 119.3 87.5 -0.3 7651.0 0.1 517.2119.3 126.9 0.8 7.3 0.6 53.3 31.6126.9 126.8 8.3 7.3 69.4 52.9 3667.4126.8 126.4 8.3 6.8 68.9 46.5 3204.2126.4 124.7 7.8 5.2 61.6 26.7 1647.1124.7 125.0 6.2 5.4 38.4 29.2 1120.9125.0 119.5 6.4 -0.1 41.3 0.0 0.3119.5 130.1 1.0 10.5 0.9 110.5 99.7130.1 133.0 11.5 13.4 133.2 179.6 23912.3133.0 133.7 14.4 14.1 208.2 198.8 41397.2133.7 131.8 15.1 12.2 228.9 149.6 34239.8131.8 128.3 13.3 8.7 175.8 76.0 13369.6128.3 123.8 9.8 4.3 95.1 18.1 1717.1123.8 136.3 5.3 16.7 27.9 278.9 7775.0136.3 134.7 17.7 15.1 314.4 228.9 71960.7134.7 139.7 16.2 20.2 261.1 406.0 106031.0139.7 133.7 21.2 14.1 448.6 199.7 89564.6133.7 139.7 15.2 20.2 229.8 406.0 93314.4139.7 140.8 21.2 21.2 448.6 450.3 201996.0140.8 140.0 22.3 20.4 495.1 417.8 206833.9

Rata-rata 118.5 119.6 Jumlah 16669.2 16343.1 3287851.7

Varian x(zi) = 362.37Varian x(z+h) = 355.29Covariogram = 71475Corelogram = 199.2

Lag 40 x(zi) x(z+h) x(zi)-x x(z+h)-xi x(zi)-x^2 x(z+h)-xi^2 Hasil kali91.39 100.35 -26.66 -19.78 710.65 391.37 278124.6293.48 99.49 -24.57 -20.64 603.59 426.13 257208.45

100.35 90.00 -17.70 -30.13 313.22 908.00 284402.3199.49 96.75 -18.56 -23.38 344.40 546.76 188305.4190.00 95.56 -28.05 -24.57 786.69 603.83 475029.0496.75 99.70 -21.30 -20.43 453.60 417.51 189383.4095.56 107.32 -22.49 -12.81 505.71 164.17 83023.9499.70 106.99 -18.35 -13.14 336.65 172.74 58152.24

107.32 103.47 -10.73 -16.66 115.09 277.66 31955.37106.99 102.26 -11.06 -17.87 122.28 319.44 39061.42103.47 111.56 -14.58 -8.57 212.52 73.50 15619.30102.26 104.82 -15.79 -15.31 249.26 234.49 58448.69111.56 105.68 -6.49 -14.45 42.09 208.89 8793.01104.82 112.38 -13.23 -7.75 174.98 60.11 10517.87105.68 112.06 -12.37 -8.07 152.97 65.17 9969.40112.38 108.86 -5.67 -11.27 32.13 127.08 4082.62112.06 116.68 -5.99 -3.45 35.86 11.92 427.52108.86 114.58 -9.19 -5.55 84.42 30.84 2603.14116.68 113.84 -1.37 -6.29 1.87 39.60 74.11114.58 115.11 -3.47 -5.02 12.03 25.23 303.45113.84 115.00 -4.21 -5.13 17.71 26.35 466.55115.11 112.18 -2.94 -7.95 8.63 63.25 545.97115.00 120.37 -3.05 0.24 9.29 0.06 0.52112.18 120.32 -5.87 0.19 34.43 0.03 1.20120.37 120.87 2.32 0.74 5.39 0.54 2.93120.32 206.00 2.27 85.87 5.16 7373.14 38060.04120.87 119.30 2.82 -0.83 7.96 0.69 5.53206.00 126.86 87.95 6.73 7735.55 45.25 350053.40119.30 126.83 1.25 6.70 1.57 44.85 70.30126.86 126.38 8.81 6.25 77.65 39.03 3030.34126.83 124.73 8.78 4.60 77.12 21.13 1629.81126.38 124.96 8.33 4.83 69.42 23.30 1617.53124.73 119.48 6.68 -0.65 44.65 0.43 19.04124.96 130.07 6.91 9.94 47.78 98.74 4717.57119.48 132.96 1.43 12.83 2.05 164.53 337.39130.07 133.66 12.02 13.53 144.53 182.98 26445.78132.96 131.79 14.91 11.66 222.37 135.89 30216.59133.66 128.28 15.61 8.15 243.73 66.37 16177.54131.79 123.81 13.74 3.68 188.84 13.52 2553.21128.28 136.26 10.23 16.13 104.69 260.08 27228.78123.81 134.69 5.76 14.56 33.20 211.91 7035.42136.26 139.71 18.21 19.58 331.68 383.26 127118.15134.69 133.69 16.64 13.56 276.96 183.79 50902.40139.71 139.71 21.66 19.58 469.24 383.26 179841.28133.69 140.78 15.64 20.65 244.67 426.30 104303.40139.71 140.00 21.66 19.87 469.24 394.70 185208.83

Rata-rata 118.05 120.13 Jumlah 16163.53 15647.82 3153074.82

Varian x(zi) = 359.19Varian x(z+h) = 347.73Covariogram = 70068Corelogram = 198.26

Lag 60 x(zi) x(z+h) x(zi)-x x(z+h)-xi x(zi)-x^2 x(z+h)-xi^2 Hasil kali91.39 99.49 -25.81 -21.56 666.20 464.92 309730.7993.48 90.00 -23.72 -31.05 562.68 964.23 542552.14100.35 96.75 -16.85 -24.30 283.95 590.59 167698.9199.49 95.56 -17.71 -25.49 313.68 649.84 203839.8590.00 99.70 -27.20 -21.35 739.89 455.91 337321.2396.75 107.32 -20.45 -13.73 418.24 188.57 78866.4895.56 106.99 -21.64 -14.06 468.33 197.74 92607.2199.70 103.47 -17.50 -17.58 306.28 309.13 94679.80107.32 102.26 -9.88 -18.79 97.63 353.14 34477.76106.99 111.56 -10.21 -9.49 104.26 90.10 9393.85103.47 104.82 -13.73 -16.23 188.54 263.48 49675.48102.26 105.68 -14.94 -15.37 223.23 236.30 52749.00111.56 112.38 -5.64 -8.67 31.82 75.20 2392.96104.82 112.06 -12.38 -8.99 153.29 80.86 12394.16105.68 108.86 -11.52 -12.19 132.73 148.64 19729.80112.38 116.68 -4.82 -4.37 23.24 19.11 444.24112.06 114.58 -5.14 -6.47 26.43 41.89 1107.02108.86 113.84 -8.34 -7.21 69.57 52.01 3618.57116.68 115.11 -0.52 -5.94 0.27 35.31 9.58114.58 115.00 -2.62 -6.05 6.87 36.63 251.59113.84 112.18 -3.36 -8.87 11.30 78.71 889.11115.11 120.37 -2.09 -0.68 4.37 0.47 2.03115.00 120.32 -2.20 -0.73 4.84 0.54 2.60112.18 120.87 -5.02 -0.18 25.21 0.03 0.84120.37 206.00 3.17 84.95 10.04 7216.16 72473.33120.32 119.30 3.12 -1.75 9.73 3.07 29.86120.87 126.86 3.67 5.81 13.46 33.73 454.12206.00 126.83 88.80 5.78 7885.28 33.39 263252.32119.30 126.38 2.10 5.33 4.41 28.39 125.08126.86 124.73 9.66 3.68 93.30 13.53 1262.11126.83 124.96 9.63 3.91 92.72 15.27 1416.06126.38 119.48 9.18 -1.57 84.26 2.47 208.21124.73 130.07 7.53 9.02 56.69 81.32 4610.06124.96 132.96 7.76 11.91 60.20 141.80 8536.90119.48 133.66 2.28 12.61 5.19 158.96 825.69130.07 131.79 12.87 10.74 165.61 115.30 19096.03132.96 128.28 15.76 7.23 248.35 52.24 12974.75133.66 123.81 16.46 2.76 270.90 7.61 2060.63131.79 136.26 14.59 15.21 212.84 231.28 49226.76128.28 134.69 11.08 13.64 122.75 186.00 22830.23123.81 139.71 6.61 18.66 43.68 348.12 15205.99136.26 133.69 19.06 12.64 363.25 159.72 58017.83134.69 139.71 17.49 18.66 305.87 348.12 106479.28139.71 140.78 22.51 19.73 506.66 389.19 197188.86133.69 140.00 16.49 18.95 15418.04 14899.01 2850709.10

Rata-rata 117.57 120.57 Jumlah 30836.09 29798.03 5701418.20

Varian x(zi) = 700.82Varian x(z+h) = 677.228Covariogram = 129577.7Corelogram = 188.08

h n(h) µ1 µ2 S1^2 S2^2 s(h) r(h)20 47 118.53 119.57 362.37 355.29 71475 199.240 46 118.05 120.13 359.19 347.73 70068 198.2660 45 117.57 120.57 700.82 677.23 129577.70 188.08

15 20 25 30 35 40 45 50 55 60 650

20000

40000

60000

80000

100000

120000

140000

Covariogram

Covariogram

15 20 25 30 35 40 45 50 55 60 65182184186188190192194196198200202

Corelogram

Corelogram

No Timur Utara Elevasi

1 49.59 124.17 139.71

2 62.75 124.44 140.78

3 75.92 124.72 142.85

4 25.53 124.41 134.69

5 25.9 124.92 133.16

6 75.19 124.92 137.88

7 51.31 154.39 136.26

8 24.6 174.37 130.07

9 50.54 174.82 132.96

10 75.3 175.19 133.66

11 99.06 175.88 131.79

12 124.74 176.55 128.28

13 148.85 178.68 123.81

14 28.34 198.39 126.86

15 76.47 199.78 126.38

16 150.52 200.08 119.48

17 123.43 200.08 124.48

18 123.43 200.16 124.96

19 50.1 201 126.83

20 101.31 201.63 124.73

21 99.47 225.6 120.6

22 124.91 225.74 119.3

23 75.35 225.88 120.87

24 48.76 225.98 120.32

25 24.21 228.09 120.37

26 152.8 249.3 112.18

27 125.22 249.73 115

28 75 249.94 113.84

29 98.61 250.5 115.11

30 51.31 251.27 114.58

31 22.83 251.51 116.68

32 76.41 274.22 105.68

33 100.23 274.24 112.38

34 150.31 275.49 108.86

35 23.85 275.51 111.56

36 54.19 275.76 104.82

37 126.42 276.29 112.06

38 99.56 298.9 107.32

39 124.94 299.11 106.99

40 75.07 300.58 99.7

41 147.62 301.46 103.47

42 48.27 301.95 95.56

43 150.75 323.13 96.75

44 99.4 324.11 100.35

45 73.69 325.7 93.48

46 124.65 326.08 99.49

47 50.32 326.37 91.39

48 10.5 110.5 140

49 155 330 90

50 64.63 288.17 102.26