11 306 083
TRANSCRIPT
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
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
