Teori Dan Pengolahan Data Gravitasi
July 25, 2019 | Author: Firdha Firdaus | Category: N/A
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Metode Gravity...
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19
2.4 Eksplorasi Geofisika Metode Gayaberat
Metode gayaberat merupakan metode geofisika yang didasarkan pada pengukuran variasi percepatan gravitasi bumi. Dalam metode ini yang dipelajari adalah variasi percepatan gravitasi bumi akibat variasi rapat massa batuan di bawah permukaan, sehingga dalam pelaksanaannya yang diselidiki adalah perbedaan percepatan gravitasi bumi dari suatu titik observasi terhadap titik observasi lainnya. Metode gayaberat umumnya digunakan dalam eksplorasi mineral, terutama dalam eksplorasi minyak untuk menemukan struktur yang merupakan jebakan minyak ( oil trap). Metode ini dipilih karena kemampuannya dalam membedakan rapat massa suatu material terhadap lingkungan sekitarnya. Dengan demikian struktur bawah permukaan dapat diketahui. Pengetahuan tentang struktur bawah permukaan ini penting untuk perencanaan langkah-langkah eksplorasi baik itu minyak maupun mineral lainnya. Selain itu metode ini juga banyak dipakai dalam aplikasi lainnya, seperti menyelidiki struktur geothermal, keberadaan keberadaan sistem aliran air tanah, dan struktur sesar.
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2.4.1 Konsep Dasar Metode Gayaberat
Pengukuran pada metode gayaberat didasarkan pada hukum gravitasi universal Newton, yang menyatakan bahwa gaya gravitasi antara dua benda titik merupakan gaya tarik-menarik yang besarnya berbanding lurus dengan massa masing-masing benda dan berbanding terbalik dengan kuadrat jarak antar keduanya. � �1
�12
�21
�2
Gambar 2.7 Interaksi gravitasi antara benda titik ti tik bermassa m 1 dan m 2 yang terpisah sejauh r Besarnya gaya gravitasi dapat ditulis secara matematis dengan persamaan:
= =
(2.1)
Dengan F12 = F21 = besar gaya tarik-menarik t arik-menarik antara kedua benda (N) G = konstanta konstanta gravitasi ( 6.672 6.672 x 10
-11
2
2
Nm /kg )
m1 = massa benda 1 (kg) m = massa benda 2 (kg) r
= jarak antara pusat kedua benda (m) Dalam pengukuran gayaberat yang diukur bukanlah gaya gravitasinya F,
melainkan percepatan gravitasinya, g. Hubungan antara gaya gravitasi dengan percepatan gravitasi dijelaskan oleh hukum II newton,
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21
Interaksi antara bumi (dengan massa M) dengan benda di permukaan bumi (dengan massa m) sejauh jarak R dari pusat kedua benda juga memenuhi hukum tersebut, maka persamaan di atas menjadi:
= = =
(2.3)
Menurut persamaan di atas, besar percepatan gravitasi di semua tempat di permukaan bumi adalah sama, tetapi kenyataannya tidaklah demikian. Hal ini disebabkan oleh beberapa faktor, diantaranya bentuk muka bumi yang elipsoidal, rotasi bumi, bentuk relief permukaan bumi yang bermacam-macam, dan juga perbedaan distribusi rapat massa di bawah permukaan bumi.
2.4.2 Anomali Gayaberat
Pada dasarnya nilai anomali gayaberat adalah selisih antara nilai percepatan gravitasi bumi pada kondisi bumi yang sebenarnya dengan nilai percepatan gravitasi bumi pada kondisi teoritik bumi. Pada kondisi bumi yang sebenarnya terdapat faktor-faktor yang mempengaruhi nilai percepatan gravitasi bumi seperti efek rotasi bumi, variasi topografi bumi, dan variasi densitas secara lateral maupun vertikal. Sedangkan percepatan gravitasi bumi secara teoritik mengasumsikan mengasumsikan bahwa bumi berbentuk sferoid dan massa bumi homogen. Saat ini diketahui bahwa nilai percepatan gravitasi bumi di permukaan bumi dipengaruhi oleh lima faktor yaitu:
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22
•
Topografi di sekitar titik pengukuran
•
Interaksi bumi dengan matahari dan bulan (pasang-surut), dan
•
Variasi rapat massa batuan di bawah permukaan bumi Faktor yang disebutkan terakhir adalah satu-satunya faktor yang signifikan
dalam eksplorasi gayaberat dan pada umumnya memiliki nilai yang sangat kecil dibandingkan dibandingkan kombinasi keempat faktor lainnya. Besar anomali gayaberat sangat kecil dibandingkan dengan rata-rata percepatan gravitasi bumi di permukaan, sehingga satuan pengukuran yang biasa digunakan adalah dalam mGal, dan dalam pengukurannya memerlukan alat ukur yang sangat sensitif. Karena nilai anomali yang dibutuhkan dalam eksplorasi gayaberat adalah anomali akibat variasi rapat massa di bawah permukaan, maka dilakukan koreksi-koreksi untuk mereduksi anomali akibat faktor-faktor yang lain.
2.4.3 Gravimeter
Dalam pengukuran gayaberat, perbedaan percepatan gravitasi bumi di suatu tempat dengan tempat lainnya relatif kecil, maka diperlukan suatu alat ukur yang sangat sensitif untuk mengukur perbedaan tersebut. Alat yang digunakan dalam pengukuran gayaberat dinamakan gravimeter yang memiliki ketelitian sangat tinggi, lebih kecil dari 0.01 mgal. Tipe gravimeter yang biasa digunakan dalam eksplorasi gayaberat didasarkan pada sistem massa-pegas sederhana, seperti yang ditunjukkan oleh gambar 2.8.
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23
�
�
� �
∆
�� �(�+∆�)
Gambar 2.8 Prinsip kerja gravimeter stabil
Gaya gravitasi akan menarik massa ke arah pusat bumi dan membuat pegas meregang. Dengan menggunakan hukum Hooke dapat ditunjukkan bahwa besarnya perubahan percepatan gravitasi sebanding dengan perubahan panjang akibat pengaruh gaya gravitasi pada beban.
∆ = ∆ ∆ = ∆
(2.4)
Dan
∆ = ( )∆ Dengan m = massa beban (kg) k = konstanta elastisitas pegas (N/m)
(2.5)
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Salah satu gravimeter yang menggunakan prinsip kerja seperti ini adalah gravimeter La Coste & Romberg. Gravimeter Lacoste & Romberg yang digunakan memiliki skala pembacaan dari 0 hingga 7000 mgal, dengan ketelitian 0.01 mgal dan koreksi drift rata-rata kurang dari 1 mgal setiap bulan. Dalam penggunaannya penggunaannya gravimeter ini memerlukan suhu yang relatif tetap, karenanya alat ini dilengkapi dengan thermostat agar suhu alat tetap terjaga.
2.4.4 Koreksi-Koreksi Gayaberat 2.4.4.1 Koreksi Apungan (Drift Correction)
Koreksi ini dilakukan untuk menghilangkan pengaruh perubahan kondisi alat (gravimeter) terhadap nilai pembacaan. Koreksi apungan muncul karena gravimeter selama digunakan untuk melakukan pengukuran, mengalami goncangan sehingga akan menyebabkan bergesernya pembacaan titik nol pada alat tersebut. Koreksi ini dilakukan dengan cara melakukan pengukuran dengan metode looping (gambar 2.9), yaitu dengan pembacaan ulang pada titik amat acuan (base station) dalam satu kali looping, sehingga nilai penyimpangannya diketahui. Besarnya koreksi drift dirumuskan sebagai berikut:
= ( − ) untuk titik amat stasiun1 dimana,
DC
= koreksi drift pada pada titik amat amat stasiun1 stasiun1
gA
= harga percepatan gravitasi titik amat acuan pada saat t A
(2.6)
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tA = waktu pengamatan di titik amat acuan pada saat saat awal tA’ = waktu pengamatan pengamatan di titik amat acuan acuan pada saat saat t A’ Tb = waktu pengamatan pengamatan di di titik amat stasiun1 stasiun1
Gambar 2.9 Pola pengukuran metode gayaberat
2.4.4.2 Koreksi Pasang Surut (Tidal Correction)
Koreksi pasang surut dilakukan untuk menghilangkan efek gayaberat benda-benda di luar bumi seperti Matahari dan Bulan. Alat gravimeter sangat peka sehingga pengaruh gaya tarik matahari dan bulan sangat berpengaruh pada
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26
Hasil ini kemudian ditambahkan dengan koreksi drift untuk memperoleh anomali gayaberat observasi.
dengan
= +
(2.8)
adalah anomali gayaberat observasi yang telah dikoreksi drift dan
pasang surut, T adalah koreksi pasang surut.
2.4.4.3 Koreksi Lintang ( Latitude Latitude Correction)
Koreksi ini diperlukan karena perputaran bumi mengakibatkan perbedaan percepatan gravitasi bumi pada setiap lintang. Untuk menghitung koreksi lintang digunakan rumus sebagai berikut:
= 978.03185(1+0.005278895 + 0.00002346 00023462 2) dengan
(2.9)
adalah nilai percepatan gravitasi teoritik pada posisi titik amat dan
adalah koordinat lintang.
2.4.4.4 Koreksi Udara Bebas (Free Air Correction)
Koreksi
udara
bebas
dilakukan
untuk
menghilangkan
perbedaan
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27
Setelah dilakukan koreksi tersebut maka akan didapatkan anomali udara bebas di topografi yang dapat dinyatakan dengan persamaan:
∆ = − ( − ))
dengan: �g
(2.11)
= anomali udara bebas di topografi (mgal)
gobs = percepatan gravitasi observasi di topografi (mgal)
= percepatan gravitasi teoritis pada posisi titik amat (mgal)
FAC = koreksi koreksi udara udara bebas bebas (mgal) (mgal)
2.4.4.5 Koreksi Bouguer (Bouguer Correcion)
Koreksi Bouguer merupakan koreksi yang dilakukan dil akukan untuk menghilangkan perbedaan percepatan gravitasi bumi akibat perbedaan ketinggian di setiap titik amat, dengan tidak mengabaikan massa di bawahnya. Massa ini dianggap sebagai lempeng massa (slab) tak hingga dengan tebal h (meter) dan rapat massa ρ (gr/cc). Slab horizontal mengasumsikan pengukuran berada pada suatu bidang mendatar
dan mempunyai massa batuan dengan rapat massa tertentu. Koreksi ini dihitung menggunakan menggunakan persamaan:
= 0.04193 �ℎ
(2.12)
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28
Anomali gayaberat setelah diaplikasikan koreksi udara bebas dan koreksi bouguer disebut simple bouguer anomaly (SBA):
= − = − � 0.3085 085 � ℎ −0. − 0.04192 � � ℎ
(2.13)
Dengan nilai SBA dalam mgal.
2.4.4.6 Koreksi Medan (Terrain Correction)
Daerah yang memiliki topografi relatif datar cukup melakukan koreksi sampai mendapatkan nilai SBA, sedangkan untuk daerah dengan topografi berundulasi diperlukan koreksi medan (TC). Koreksi ini diterapkan sebagai akibat dari pendekatan slab horizontal tak berhingga, padahal kenyataannya permukaan bumi tidak datar, berundulasi sesuai dengan topografinya.
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29
lembah yang merupakan merupakan massa kosong kosong dengan pendulum pendulum gravimeter. Gaya tarik tersebut dapat dapat diuraikan menjadi menjadi komponen gaya gaya vertikal vertikal dan horizontal, horizontal, pada metoda gayaberat yang digunakan adalah komponen gaya vertikal (Gambar 2.11). Karena komponen gaya horizontal (koreksi medan) bersifat mengurangi nilai gayaberat terukur, maka koreksi medan harus ditambahkan pada SBA, sehingga anomalinya menjadi Complete Bouguer Anomaly (CBA).
= +
(2.14)
Perhitungan koreksi medan (TC) dapat dilakukan dengan menggunakan Hammer chart seperti pada Gambar 2.12 yang dikembangkan oleh Sigmund
Hammer. Berdasarkan besarnya radius dari titik pengukuran gayaberat, Hammer chart dapat dikelompokkan menjadi (Hammer, 1939):
1. Inner Inner zone zone Memiliki radius yang tidak terlalu besar sehingga beda elevasi bisa didapatkan dari pengamatan langsung di lapangan. Dapat dibagi menjadi beberapa zona : • Zona B : radius radius 6,56 – 54,6 ft, dibag dibagii menjadi menjadi 4 kompartemen kompartemen • Zona C : radius radius 54,6 – 175 ft, dibagi dibagi menjadi menjadi 6 komparteme kompartemen n
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• Zona Zona F : radi radi s 1280 – 2936 ft, dibagi dibagi menjadi menjadi 8 kompa komparte rte men • Zona Zona G : radi radius 2936 2936 – 5018 ft, ft, dibagi dibagi menjadi menjadi 12 kompa komparr temen • Zona Zona H : radi radius 5018 5018 – 8578 ft, ft, dibagi dibagi menjadi menjadi 12 kompar kompartemen • Zona Zona I : radi radi s 8578 8578 – 14662 14662 ft, dibag dibagii menjadi menjadi 12 komp rtemen • Zona Zona J : radi radi s 14662 14662 – 21826 21826 ft, dibagi dibagi menjad menjadii 16 kom kom artemen • Zona K sa sampai M : masing-masing dibagi menjadi 16 ko partemen
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31
Gambar 2.13 Cincin melingkar yang terbagi ke dalam delapan kompartemen untuk menghitung koreksi medan
Hammer melakukan pendekatan efek gayaberat dalam suatu cincin seperti pada Gambar 2.13. Jika cincin memiliki ketebalan atau beda elevasi z, jari-jari luar RL, dan jari-jari dalam R D, maka persamaan yang menyatakan gaya tarik gravitasi pada titik ditengah cincin untuk tiap t iap kompartemen, yaitu :
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32
2.4.4.7 Anomali Bouguer Lengkap (Complete Bouguer Anomaly)
Anomali Bouguer (CBA) suatu titik amat didefinisikan sebagai penyimpangan harga percepatan gravitasi pengamatan (G obs) terhadap harga percepatan gravitasi normal (
) di titik tersebut. Anomali bouguer di titik amat
pada ketinggian h merupakan anomali kumulatif akibat semua penyebab anomali yang berada di bawah ketinggian titik amat, dengan persamaan sebagai berikut:
= − + − − + + = +
(2.16)
2.4.5 Moving Average Average
Metode moving average merupakan salah satu cara untuk memisahkan anomali regional-residual dengan noise. Metode moving average dilakukan dengan cara merata-ratakan nilai anomali, proses perata-rataan dilakukan untuk tiap titik pengamatan pengamatan dan bergerak bergerak dari satu titik ke titik lainnya. Hasil Hasil metode
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33
dihitung dengan merata-ratakan semua nilai ∆gbouguer di dalam sebuah kotak persegi dengan titik pusat adalah titik yang akan dihitung harga ∆gR.
Gambar 2.14 Ilustrasi moving average dua dimensi dengan lebar windows 5x5
Persamaannya Persamaannya diberikan oleh: (2.18)
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34
dikonversikan ke dalam nilai lebar windows untuk digunakan pada proses moving average , untuk menghilangkan noise dari data anomali bouguer. Penghilangan noise ini penting untuk proses analisa SVD yang bersifat high pass filter atau
meninggikan anomali dengan frekuensi tinggi, sehingga bila
noise tidak
dihilangkan terlebih dahulu maka akan menghasilkan pola anomali yang tidak tepat. Analisis spektrum dilakukan dengan cara mentransformasi Fourier lintasan yang telah ditentukan pada peta kontur CBA. Secara umum, suatu transformasi Fourier adalah menyusun kembali/mengurai suatu bentuk gelombang sembarang ke dalam gelombang sinus dengan frekuensi bervariasi, dengan hasil penjumlahan gelombang-gelombang sinus tersebut adalah bentuk gelombang aslinya. Untuk analisis lebih lanjut, amplitudo gelombang-gelombang sinus tersebut ditampilkan sebagai fungsi dari frekuensinya. Secara matematis hubungan antara gelombang
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35
dengan U = potensial gayaberat µ = anomali rapat massa γ = konstanta gayaberat r = jarak sehingga persamaannya menjadi:
||() () = 2 ||
(2.21)
Berdasarkan persamaan (2.21), transformasi Fourier untuk anomali gayaberat
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36
Agar mendapatkan estimasi lebar windows yang tepat untuk pemisahan noise dari sinyal, amplitudo A pada persamaan (2.23) dilogaritmakan sehingga
memberikan hasil persamaan linier. Komponen bilangan gelombang k menjadi berbanding lurus dengan amplitudo.
= + + �� − ′||
(2.24)
Dari persamaan diatas, dibuat grafik antara ln A terhadap k untuk mengklasifikasikan mengklasifikasikan anomali (gambar 2.15). Melalui regresi linier diperoleh nilai k pada batas antara sinyal residual dengan noise yang kemudian digunakan sebagai
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37
2.4.7 Teknik Gradien 2.4.7.1 Gradien Horisontal (Horizontal Derivative)
Gradien horisontal anomali gayaberat adalah perubahan nilai anomali gayaberat dari satu titik ke titik lainnya secara horisontal dengan jarak tertentu. gradien horisontal memiliki karakteristik tajam berupa nilai maksimum pada batas kontak benda anomali (gambar 2.16), sehingga digunakan untuk menunjukkan batas suatu struktur geologi berdasarkan anomali gayaberat.
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38
gayaberat yang lebih rendah dibandingkan sekitarnya ( low anomaly). Seperti halnya model tabular, FHD memiliki nilai maksimum pada batas struktur, sementara nilai minimumnya berada pada titik yang memiliki nilai minimum anomali gayaberat. Gravity anomaly FHD
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39
turunan horisontal pertama (FHD) dari
(,)
pada titik
i, j diberikan oleh
persamaan:
(,) ≈ ,, ∆ (,) ≈ ,, ∆
(2.28)
(2.29)
Dalam pelaksanaannya gradien horisontal dilakukan dalam domain bilangan gelombang. Sesuai dengan sifat diferensiasi transformasi Fourier, maka persamaan (2.34) dan (2.35) dapat dinyatakan dengan
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40
∇ = 0
, atau
+ + = 0 Sehingga SVD diberikan oleh persamaan:
(2.32)
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BAB III PENGUKURAN DAN PENGOLAHAN DATA
3.1
Pengukuran Gayaberat
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27
dan
m × ∆g k
∆s =
Dengan m = massa beban (kg)
(3.2)
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29
3.3
Pengolahan Data Gayaberat
Pengukuran gayaberat dilapangan secara umumnya merupakan pengambilan data mentah yang harus diolah untuk memperoleh gambaran anomali yang dicari, yaitu anomali Bouguer. Anomali Bouguer yaitu harga pengamatan gayaberat yang
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Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
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