Metode Hagiwara

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METODE HAGIWARA

Dicky Aditya || Farhan Ahmadi || Nur Wahyu M

Yogyakarta, November 2014



Lintasan Gelombang refraksi :

A A’’ – P” P dan B B” – P”’ P

Shoot point Shoot pointReciever



Menurut hukum snellius pada 2 batas medium yang berbedamaka didapat rumus :

Berdasarkan penjalaran gelombang dan hukum snellius,

didapat :



Apabila ditinjau dari berbagai sumber pada shootpoint (a-b) reciever (P) :



Dari persamaan tersebut, didapat persamaan travel time :



-Nilai V1 didapat pada grafik penjalaran gelombanglangsung

- Nilai V2 didapat pada grafik jarak (x) vs T’AP

Y = MX + C



Dari persamaan TAP, TBP, dan TAB maka diperoleh hubungan :

Dari persamaan diatas dapat ditentukan ketebalan (Hp):



Contoh Pengolahan data 1

x(m) 2,5 162,5

Travel Time

TAP TBP TAB TP T'AP V1 V2 Hpforward reverse

2.5 0

5 7.7 186.1 58.99 186.1 58.99 186.1 188.48 56.6125 30.68375 360.1065 1148.106 10.73497

10 23.1 181.5 63.17 181.5 63.17 181.5 188.48 56.1925 35.07375 360.1065 1148.106 10.65533

15 38.5 173.9 67.35 173.9 67.35 173.9 188.48 52.7725 40.96375 360.1065 1148.106 10.00683

20 53.8 169.1 71.53 169.1 71.53 169.1 188.48 52.1525 45.45375 360.1065 1148.106 9.889261

25 69.2 164.6 75.71 164.6 75.71 164.6 188.48 51.8325 49.79375 360.1065 1148.106 9.828582

30 81.2 159.4 79.89 159.4 79.89 159.4 188.48 50.8125 54.48375 360.1065 1148.106 9.635167

35 85 153.7 84.07 153.7 84.07 153.7 188.48 49.2925 59.42375 360.1065 1148.106 9.346942

40 88.3 148.2 88.3 148.2 88.3 148.2 188.48 48.0225 64.28875 360.1065 1148.106 9.106122

45 91.7 143.5 91.7 143.5 91.7 143.5 188.48 46.7225 68.33875 360.1065 1148.106 8.859613

50 96.1 138.7 96.1 138.7 96.1 138.7 188.48 46.3225 72.93875 360.1065 1148.106 8.783765

55 100.3 133.8 100.3 133.8 100.3 133.8 188.48 45.6225 77.48875 360.1065 1148.106 8.651029

60 104.4 129.3 104.4 129.3 104.4 129.3 188.48 45.2225 81.78875 360.1065 1148.106 8.57518

65 108.9 124.2 108.9 124.2 108.9 124.2 188.48 44.6225 86.58875 360.1065 1148.106 8.461407

70 112.6 119.2 112.6 119.2 112.6 119.2 188.48 43.3225 90.93875 360.1065 1148.106 8.214899

75 116.8 114.9 116.8 114.9 116.8 114.9 188.48 43.2225 95.18875 360.1065 1148.106 8.195936

80 121.5 110.5 121.5 110.5 121.5 110.5 188.48 43.5225 99.73875 360.1065 1148.106 8.252823

85 126 106.4 126 106.4 126 106.4 188.48 43.9225 104.0388 360.1065 1148.106 8.328672

90 131 101.6 131 101.6 131 101.6 188.48 44.1225 108.9388 360.1065 1148.106 8.366596

95 135.1 96.1 135.1 96.1 135.1 96.1 188.48 42.7225 113.7388 360.1065 1148.106 8.101125

100 138.6 91.5 138.6 91.5 138.6 91.5 188.48 41.6225 117.7888 360.1065 1148.106 7.892541

105 143.3 87.5 143.3 87.5 143.3 87.5 188.48 42.3225 122.1388 360.1065 1148.106 8.025277

110 148.2 83 148.2 83 148.2 83 188.48 42.7225 126.8388 360.1065 1148.106 8.101125

115 152.7 77.7 152.7 77.7 152.7 77.7 188.48 41.9225 131.7388 360.1065 1148.106 7.949428

120 156.1 72.4 156.1 72.4 156.1 72.4 188.48 40.0225 136.0888 360.1065 1148.106 7.589146



Step - 1

• Buat forward - reverse travel time,kemudian plot grafiknya

x(m) 2,5 162,5

Travel Time

forward reverse

2.5 0

5 7.7 186.1 58.99 186.1

10 23.1 181.5 63.17 181.5

15 38.5 173.9 67.35 173.9

20 53.8 169.1 71.53 169.125 69.2 164.6 75.71 164.6

30 81.2 159.4 79.89 159.4

35 85 153.7 84.07 153.7

40 88.3 148.2 88.3 148.2

45 91.7 143.5 91.7 143.5

50 96.1 138.7 96.1 138.7

55 100.3 133.8 100.3 133.8

60 104.4 129.3 104.4 129.3

65 108.9 124.2 108.9 124.2

70 112.6 119.2 112.6 119.2

75 116.8 114.9 116.8 114.9

80 121.5 110.5 121.5 110.5

85 126 106.4 126 106.4

90 131 101.6 131 101.6

95 135.1 96.1 135.1 96.1

100 138.6 91.5 138.6 91.5

105 143.3 87.5 143.3 87.5

y = 2.7668x - 4.4719

y = 0.8365x + 54.815

y = -2.788x + 454.13

y = -0.9742x + 188.63

0

50

100

150

200

250

0 50 100 150 200

S

h

oo

t

p

o

i

n

t

jarak

jarak vs SP1-3

slope 1 sp1slope2 sp1

slope 1 sp3

slope 2 sp 3

Linear (slope 1 sp1)

Linear (slope2 sp1)

Linear (slope 1 sp3)

Linear (slope 2 sp 3)



Step - 2

TAP TBP TAB TP

58.99 186.1 188.48 56.6125

63.17 181.5 188.48 56.1925

67.35 173.9 188.48 52.7725

71.53 169.1 188.48 52.1525

75.71 164.6 188.48 51.8325

79.89 159.4 188.48 50.8125

84.07 153.7 188.48 49.2925

88.3 148.2 188.48 48.0225

91.7 143.5 188.48 46.7225

96.1 138.7 188.48 46.3225

100.3 133.8 188.48 45.6225

104.4 129.3 188.48 45.2225

108.9 124.2 188.48 44.6225112.6 119.2 188.48 43.3225

116.8 114.9 188.48 43.2225

121.5 110.5 188.48 43.5225

126 106.4 188.48 43.9225

131 101.6 188.48 44.1225

135.1 96.1 188.48 42.7225

138.6 91.5 188.48 41.6225

143.3 87.5 188.48 42.3225

Tentukan TAP, TBP, TAB

TAP = Travel time ForwardTBP = Travel time Reverse



Step - 3

T'AP V1 V2 Hp

30.68375 360.1065 1148.106 10.73497

35.07375 360.1065 1148.106 10.65533

40.96375 360.1065 1148.106 10.00683

45.45375 360.1065 1148.106 9.889261

49.79375 360.1065 1148.106 9.828582

54.48375 360.1065 1148.106 9.635167

59.42375 360.1065 1148.106 9.346942

64.28875 360.1065 1148.106 9.106122

68.33875 360.1065 1148.106 8.859613

72.93875 360.1065 1148.106 8.783765

77.48875 360.1065 1148.106 8.651029

81.78875 360.1065 1148.106 8.57518

86.58875 360.1065 1148.106 8.46140790.93875 360.1065 1148.106 8.214899

95.18875 360.1065 1148.106 8.195936

99.73875 360.1065 1148.106 8.252823

104.0388 360.1065 1148.106 8.328672

108.9388 360.1065 1148.106 8.366596

113.7388 360.1065 1148.106 8.101125

117.7888 360.1065 1148.106 7.892541

122.1388 360.1065 1148.106 8.025277

Tentukan T’AP, V1, V2, Hp

Grafik X vs T’AP

y = 0.9058x + 27.281

0

20

40

60

80

100

120140

160

180

200

0 50 100 150 200

T

'

A

P

Jarak(X)

X vs T'AP

Series1

Linear (Series1)

Utk mencari V2



-15

-13

-11

-9

-7

-5

-3

-1

1

5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140 145 150 155 160

Series2

Series1

v1=360.10 m/s

v2=1148.10 m/s

Contoh model lapisan pengolaha data 1



Pengolahan data 2 stepnya sama kayak

yang pengolahan data 1



Pengolahan data 3

Xloc 2.5 97.5

travel time

elevasi beda tinggi TAP TBP TAB TP T'AP V1 V2 Hp profile interface

forward reverse

2.5 0

5 7.2 102.4 24.46 102.4 100 -1 24.46 102.4 101.1038 25.75625 11.58188 408.8737 1162.791 5.62473 93.37526988

10 22 95.6 28.55 95.6 99 0 28.55 95.6 101.1038 23.04625 17.02688 408.8737 1162.791 5.032912 93.96708812

15 33.4 89.6 32.64 89.6 98.3 0.7 32.64 89.6 101.1038 21.13625 22.07188 408.8737 1162.791 4.6158 94.38419987

20 37.8 85.8 36.73 85.8 98.4 0.6 36.73 85.8 101.1038 21.42625 26.01688 408.8737 1162.791 4.679131 94.32086877

25 42.4 82.3 42.4 82.3 98.6 0.4 42.4 82.3 101.1038 23.59625 30.60188 408.8737 1162.791 5.153023 93.84697741

30 48.1 79.8 48.1 79.8 99.2 -0.2 48.1 79.8 101.1038 26.79625 34.70188 408.8737 1162.791 5.851849 93.14815144

35 52.7 76.2 52.7 76.2 99.4 -0.4 52.7 76.2 101.1038 27.79625 38.80188 408.8737 1162.791 6.070232 92.92976832

40 54.3 69.7 54.3 69.7 98.5 0.5 54.3 69.7 101.1038 22.89625 42.85188 408.8737 1162.791 5.000154 93.99984559

45 56.3 63.5 56.3 63.5 97.8 1.2 56.3 63.5 101.1038 18.69625 46.95188 408.8737 1162.791 4.082945 94.91705467

50 58.5 57.6 58.5 57.6 97.1 1.9 58.5 57.6 101.1038 14.99625 51.00188 408.8737 1162.791 3.274928 95.7250722

55 62.1 53 62.1 53 96.9 2.1 62.1 53 101.1038 13.99625 55.10188 408.8737 1162.791 3.056545 95.94345532

60 64.9 47.7 64.9 47.7 96.4 2.6 64.9 47.7 101.1038 11.49625 59.15188 408.8737 1162.791 2.510587 96.48941311

65 69.8 44.4 69.8 44.4 96.7 2.3 69.8 44.4 101.1038 13.09625 63.25188 408.8737 1162.791 2.86 96.14000012

70 73.4 39.8 73.4 39.8 96.5 2.5 73.4 39.8 101.1038 12.09625 67.35188 408.8737 1162.791 2.641617 96.35838324

75 79.7 38 79.7 38 97.4 1.6 79.7 38 101.1038 16.59625 71.40188 408.8737 1162.791 3.624341 95.37565922

80 86.4 36.5 86.4 36.5 98.3 0.7 86.4 36.5 101.1038 21.79625 75.50188 408.8737 1162.791 4.759933 94.24006701

85 91.6 33.5 91.6 28.905 98.7 0.3 91.6 28.905 101.1038 19.40125 81.89938 408.8737 1162.791 4.236905 94.76309458

90 97.8 21.9 97.8 24.47 99.5 -0.5 97.8 24.47 101.1038 21.16625 87.21688 408.8737 1162.791 4.622352 94.37764838

95 103.2 7.3 103.2 20.035 99.9 -0.9 103.2 20.035 101.1038 22.13125 92.13438 408.8737 1162.791 4.833091 94.16690867

97.5 0



Step – 1(sebelum

koreksi)

Xloc 2.5 97.5travel time

elevasi beda tinggiforward reverse

2.5 0

5 7.2 102.4 24.46 102.4 100 -1

10 22 95.6 28.55 95.6 99 0

15 33.4 89.6 32.64 89.6 98.3 0.7

20 37.8 85.8 36.73 85.8 98.4 0.6

25 42.4 82.3 42.4 82.3 98.6 0.4

30 48.1 79.8 48.1 79.8 99.2 -0.2

35 52.7 76.2 52.7 76.2 99.4 -0.4

40 54.3 69.7 54.3 69.7 98.5 0.5

45 56.3 63.5 56.3 63.5 97.8 1.2

50 58.5 57.6 58.5 57.6 97.1 1.9

55 62.1 53 62.1 53 96.9 2.1

60 64.9 47.7 64.9 47.7 96.4 2.6

65 69.8 44.4 69.8 44.4 96.7 2.3

70 73.4 39.8 73.4 39.8 96.5 2.5

75 79.7 38 79.7 38 97.4 1.6

80 86.4 36.5 86.4 36.5 98.3 0.7

85 91.6 33.5 91.6 28.905 98.7 0.3

90 97.8 21.9 97.8 24.47 99.5 -0.5

95 103.2 7.3 103.2 20.035 99.9 -0.9

97.5 0

Tentukan elevasi dan beda tinggi



Step – 2(sebelum

koreksi)

TAP TBP TAB TP T'AP

24.46 102.4 101.1038 25.75625 11.58188

28.55 95.6 101.1038 23.04625 17.02688

32.64 89.6 101.1038 21.13625 22.07188

36.73 85.8 101.1038 21.42625 26.01688

42.4 82.3 101.1038 23.59625 30.60188

48.1 79.8 101.1038 26.79625 34.70188

52.7 76.2 101.1038 27.79625 38.80188

54.3 69.7 101.1038 22.89625 42.85188

56.3 63.5 101.1038 18.69625 46.95188

58.5 57.6 101.1038 14.99625 51.00188

62.1 53 101.1038 13.99625 55.10188

64.9 47.7 101.1038 11.49625 59.15188

69.8 44.4 101.1038 13.09625 63.25188

73.4 39.8 101.1038 12.09625 67.35188

79.7 38 101.1038 16.59625 71.40188

86.4 36.5 101.1038 21.79625 75.50188

91.6 28.905 101.1038 19.40125 81.89938

97.8 24.47 101.1038 21.16625 87.21688

103.2 20.035 101.1038 22.13125 92.13438

Tentukan TAP, TBP, TP, T’AP



Step – 3(sebelum

koreksi)

V1 V2 Hp profile interface

408.8737 1162.791 5.62473 93.37526988

408.8737 1162.791 5.032912 93.96708812

408.8737 1162.791 4.6158 94.38419987

408.8737 1162.791 4.679131 94.32086877

408.8737 1162.791 5.153023 93.84697741

408.8737 1162.791 5.851849 93.14815144

408.8737 1162.791 6.070232 92.92976832

408.8737 1162.791 5.000154 93.99984559

408.8737 1162.791 4.082945 94.91705467

408.8737 1162.791 3.274928 95.7250722

408.8737 1162.791 3.056545 95.94345532

408.8737 1162.791 2.510587 96.48941311

408.8737 1162.791 2.86 96.14000012

408.8737 1162.791 2.641617 96.35838324

408.8737 1162.791 3.624341 95.37565922

408.8737 1162.791 4.759933 94.24006701

408.8737 1162.791 4.236905 94.76309458

408.8737 1162.791 4.622352 94.37764838

408.8737 1162.791 4.833091 94.16690867

Profil Interface = Baseline - Hp



88

90

92

94

96

98

100

102

5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95

Series1

Series2

v1 = 408.87 m/s

v2 = 1162.79 m/s

Contoh model lapisan sebelum koreksi



delta h delta t

Xloc 2.5 97.5

travel time

elevasi TAP TBP TAB TP T'AP V1 V2 Hp profie interface

forward reverse

2.5 0

1 2.4458 5 7.2 102 4. 754235 99.95423 100 26.81 99.95423 102.3213 24. 44298 -7.46726 385.9607 1092.896 5. 041889 93.95811131

0 0 10 22 95.6 22 95.6 99 30.89 95.6 102.3213 24.16875 9.915625 385.9607 1092.896 4.985322 94.01467812

-0.7 -1.712 15 33.4 89.6 35.11204 91.31204 98.3 34.97 91.31204 102.3213 23.96079 23.13164 385.9607 1092.896 4.942425 94.05757522

-0.6 -1.4675 20 37.8 85.8 39.26746 87.26746 98.4 39.05 87.26746 102.3213 23.99621 27.26935 385.9607 1092.896 4.949732 94.05026837

-0.4 -0.9783 25 42.4 82.3 43.37831 83.27831 98.6 43.37831 83.27831 102.3213 24.33536 31.21063 385.9607 1092.896 5.019689 93.9803108

0.2 0 .4892 30 48.1 79.8 47.61085 79.31085 99.2 47.61085 79.31085 102.3213 24.60044 35.31063 385.9607 1092.896 5.074368 93.92563201

0.4 0 .9783 35 52.7 76.2 51.72169 75.22169 99.4 51.72169 75.22169 102.3213 24.62214 39.41063 385.9607 1092.896 5.078843 93.92115717

-0.5 -1.2229 40 54.3 69.7 55.52288 70.92288 98.5 55.52288 70.92288 102.3213 24.12452 43.46063 385.9607 1092.896 4.976197 94.0238025

-1.2 -2.9349 45 56.3 63.5 59.23492 66.43492 97.8 59.23492 66.43492 102.3213 23.34859 47.56063 385.9607 1092.896 4.816146 94.18385442

-1.9 -4.647 50 58.5 57.6 63.14695 62.24695 97.1 63.14695 62.24695 102.3213 23.07266 51.61063 385.9607 1092.896 4.759229 94.24077063

-2.1 -5.1361 55 62.1 53 67.23611 58.13611 96.9 67.23611 58.13611 102.3213 23.05096 55.71063 385.9607 1092.896 4.754755 94.24524547

-2.6 -6.359 60 64.9 47.7 71.25899 54.05899 96.4 71.25899 54.05899 102.3213 22.99673 59.76063 385.9607 1092.896 4.743567 94.25643257

-2.3 -5.6253 65 69.8 44.4 75.42526 50.02526 96.7 75.42526 50.02526 102.3213 23.12927 63.86063 385.9607 1092.896 4.770907 94.22909317

-2.5 -6.1144 70 73.4 39.8 79.51441 45.91441 96.5 79.51441 45.91441 102.3213 23.10758 67.96063 385.9607 1092.896 4.766432 94.23356801

-1.6 -3.9132 75 79.7 38 83.61322 41.91322 97.4 83.61322 41.91322 102.3213 23.2052 72.01063 385.9607 1092.896 4.786569 94.21343123

-0.7 -1.712 80 86.4 36.5 88.11204 38.21204 98.3 88.11204 38.21204 102.3213 24.00282 76.11063 385.9607 1092.896 4.951096 94.04890448

-0.3 -0.7337 85 91.6 33.5 92.33373 34.23373 98.7 92.33373 33.76 102.3213 23.77248 80.44749 385.9607 1092.896 4.903583 94.09641738

0.5 1 .2229 90 97.8 21.9 96.57712 20.67712 99.5 96.57712 29.64 102.3213 23.89587 84.62918 385.9607 1092.896 4.929034 94.07096599

0.9 2 .2012 95 103 7. 3 100.9988 5.098811 99.9 100.9988 25. 52 102.3213 24. 19756 88.90003 385.9607 1092.896 4. 991265 94.00873516

97.5 0

Setelah koreksi



delta h delta tXloc 2.5 97.5

travel time

elevasiforward reverse

2.5 0

1 2.4458 5 7.2 102 4.754235 99.95423 100

0 0 10 22 95.6 22 95.6 99

-0.7 -1.712 15 33.4 89.6 35.11204 91.31204 98.3

-0.6 -1.4675 20 37.8 85.8 39.26746 87.26746 98.4

-0.4 -0.9783 25 42.4 82.3 43.37831 83.27831 98.6

0.2 0.4892 30 48.1 79.8 47.61085 79.31085 99.2

0.4 0.9783 35 52.7 76.2 51.72169 75.22169 99.4

-0.5 -1.2229 40 54.3 69.7 55.52288 70.92288 98.5

-1.2 -2.9349 45 56.3 63.5 59.23492 66.43492 97.8

-1.9 -4.647 50 58.5 57.6 63.14695 62.24695 97.1

-2.1 -5.1361 55 62.1 53 67.23611 58.13611 96.9

-2.6 -6.359 60 64.9 47.7 71.25899 54.05899 96.4

-2.3 -5.6253 65 69.8 44.4 75.42526 50.02526 96.7

-2.5 -6.1144 70 73.4 39.8 79.51441 45.91441 96.5

-1.6 -3.9132 75 79.7 38 83.61322 41.91322 97.4

-0.7 -1.712 80 86.4 36.5 88.11204 38.21204 98.3

-0.3 -0.7337 85 91.6 33.5 92.33373 34.23373 98.7

0.5 1.2229 90 97.8 21.9 96.57712 20.67712 99.5

0.9 2.2012 95 103 7.3 100.9988 5.098811 99.9

97.5 0

Step – 1(sebelum

koreksi)

Delta h = baseline - Hp

Delta t = (1000*deltah)/V1

Forward & reverse = Shoot point- delta h

Plot Grafik

Kemudian, tentukan Tap, Tbp, T’ap, V1, V2,

Hp, Profile Interface



90

91

92

93

94

95

96

97

98

99

100

101

5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95

Series1

Series2

Model lapisan setelah koreksi



Terima Kasih

Metode Hagiwara

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