geodesi fisik perhitungan nilai undulasi di titik p

Jurusan Teknik GeomatikaFakultas Teknik Sipil dan PerencanaanInstitut Teknologi Sepuluh Nopember

Surabaya

PERHITUNGAN NILAI UNDULASI DI TITIK P

A. Data yang Diketahui dari ExcelData yang diketahui adalah sebagai berikut :

Geoid a

(m)6378137

Par

amet

er G

RS

-80

b (m)

6356752.314

e2 0.00669438

e'2

0.006739497

f 0.003352811

R1

6371008.771

ϒa (ms-2) 9.780326772

ϒb (ms-2) 9.832186369

m 0.003449786

Dan data pengukuran akan dilampirkan berikut.

B. Data yang diketahui parameter dari titik P sebagai berikut:

Latitute P -32°

Longitude P 116°Geoid height (EGM96) N

EGM96-30.884 mNormal height hP 996.092 mOrthometric height HP 1026.808

m

C. Perhitungan Nilai Free Air AnomalyFree air anomaly dihitung dengan koreksi free-air ke anomali gravitasi dengan rumus sebagai berikut.

D. Perhitungan Fungsi StokesAdapun fungsi Stokes adalah sebagai berikut :


Surabaya

E. Perhitungan Nilai Konstribusi Tiap TitikAdapun rumus nilai konstribusi tiap titik adalah sebagai berikut :

F. Nilai Undulasi Titik P

Adapun rumus nilai konstribusi tiap titik adalah sebagai berikut :

Hasil perhitungan sebagai berikut :

gGeophysics

(Mgal)S(𝞇) Ni (Stokes)(Meter) Ni (Stokes)(Meter)

189.859 205.7732 -0.000723 -0.000723262.835 224.448 -0.002524 -0.002524335.192 242.5384 -0.001011 -0.001011392.706 257.4687 0.001412 0.001412433.521 266.0908 -0.000133 -0.000133466.301 266.0908 -0.00053 -0.00053478.669 257.4687 -0.000061 -0.000061468.155 242.5384 0.000865 0.000865452.074 224.448 0.001029 0.001029423.628 205.7732 0.000952 0.000952152.135 233.2243 -0.000649 -0.000649227.584 262.0272 -0.002394 -0.002394


Surabaya

302.724 292.763 -0.002858 -0.002858368.277 320.8008 -0.000115 -0.000115419.607 338.3434 0.002239 0.002239456.404 338.3434 0.002551 0.002551477.123 320.8008 0.001176 0.001176478.978 292.763 0.001835 0.001835470.319 262.0272 0.001421 0.001421

448.056 233.2243 0.000906 0.00090695.548 263.4788 -0.00049 -0.00049

177.8 308.0808 -0.001493 -0.001493260.67 362.9283 -0.002808 -0.002808

334.263 422.4233 -0.000891 -0.000891397.344 466.2157 0.003762 0.003762

445.89 466.2157 0.004872 0.004872480.524 422.4233 0.002083 0.002083499.077 362.9283 0.00222 0.00222499.386 308.0808 0.00148 0.00148479.595 263.4788 0.000913 0.000913

35.56 292.1299 -0.002048 -0.002048115.956 357.8431 -0.002472 -0.002472203.156 455.2366 -0.003758 -0.003758

284.48 597.5271 -0.003306 -0.003306359.621 750.8795 0.003792 0.003792424.245 750.8795 0.006808 0.006808472.485 597.5271 0.002438 0.002438507.116 455.2366 0.002838 0.002838525.361 357.8431 0.002213 0.002213515.464 292.1299 0.001398 0.001398-34.014 310.7092 -0.000082 -0.00008244.218 394.4058 -0.0018 -0.0018

135.128 540.7071 -0.0055 -0.0055223.255 854.3728 -0.007867 -0.007867305.197 1766.113 -0.000573 -0.000573380.029 1766.113 0.002419 0.002419443.727 854.3728 -0.001517 -0.001517497.222 540.7071 0.001625 0.001625532.162 394.4058 0.002222 0.002222

536.8 310.7092 0.002552 0.002552-112.864 310.8705 0.003318 0.003318

-31.231 394.6093 0.000582 0.00058263.08 540.9804 -0.005127 -0.005127

153.372 854.7702 -0.009381 -0.009381

Geodesi Fisik {Perhitungan Undulasi Di Titik P} 4


Surabaya

238.097 1766.512 -0.007849 -0.007849318.185 1766.512 -0.007273 -0.007273394.252 854.7702 -0.003106 -0.003106467.227 540.9804 0.000781 0.000781523.194 394.6093 0.001557 0.001557549.789 310.8705 0.002395 0.002395

-196.971 292.5302 0.005518 0.005518-111.937 358.2961 0.005041 0.005041

-17.316 455.7209 -0.000753 -0.00075370.192 597.9279 -0.005923 -0.005923

150.589 750.9689 -0.002711 -0.002711231.604 750.9689 -0.003244 -0.003244

320.04 597.9279 -0.003797 -0.003797414.968 455.7209 -0.001586 -0.001586496.602 358.2961 0.000056 0.000056547.932 292.5302 0.001225 0.001225

-267.473 263.9638 0.003066 0.003066-185.84 308.5566 0.003525 0.003525

-100.186 363.3304 -0.000055 -0.000055-22.882 422.654 -0.003718 -0.00371851.639 466.2504 -0.001894 -0.001894

136.056 466.2504 -0.003173 -0.003173238.406 422.654 -0.003488 -0.003488350.033 363.3304 -0.001288 -0.001288451.149 308.5566 -0.000386 -0.000386525.361 263.9638 0.000572 0.000572-331.48 233.6894 0.005596 0.005596

-260.361 262.4308 0.004475 0.004475-186.148 293.053 -0.00031 -0.00031-117.193 320.9392 -0.003803 -0.003803

-43.6 338.3615 -0.00273 -0.0027345.764 338.3615 -0.003255 -0.003255

151.207 320.9392 -0.003591 -0.003591265.308 293.053 -0.001483 -0.001483380.954 262.4308 -0.00045 -0.00045479.595 233.6894 0.000869 0.000869

-388.376 206.1782 0.005279 0.005279-329.625 224.7688 0.002229 0.002229-267.782 242.7465 -0.001673 -0.001673-208.721 257.5588 -0.004086 -0.004086-145.023 266.1019 -0.003689 -0.003689

-61.844 266.1019 -0.002933 -0.002933


Surabaya


42.672 257.5588 -0.003465 -0.003465163.576 242.7465 -0.001728 -0.001728295.921 224.7688 0.000226 0.000226418.681 206.1782 0.00139 0.00139

Hasil tersebut di jumlahkan sehingga hasil penjumlahan tersebut akan di jumlahkan dengan undulasi GGM (N GGM). Sehingga hasil nilai undulasi di titik P adalah -30,921828 meter.

Lampiran data Pengukuran Tiap Titik

𝜆 𝜙 TinggiOrthometrik

ObservedGravity

g EGM

(meter) (mGal) (mGal)115.55 -31.55 615.228 979,161.977 -93.495

115.65 -31.55 851.700 979,082.418 -94.324

115.75 -31.55 1086.170 979,021.846 -87.807

115.85 -31.55 1272.540 978,984.827 -74.494

115.95 -31.55 1404.800 978,958.021 -56.032

116.05 -31.55 1511.020 978,945.287 -34.875

116.15 -31.55 1551.100 978,955.255 -13.845

116.25 -31.55 1517.030 978,986.820 4.375

116.35 -31.55 1464.920 979,016.982 17.699

116.45 -31.55 1372.740 979,052.725 24.964

115.55 -31.65 492.985 979,205.945 -95.855

115.65 -31.65 737.472 979,125.696 -95.921

115.75 -31.65 980.958 979,056.972 -89.040

115.85 -31.65 1193.380 979,011.709 -75.755

115.95 -31.65 1359.710 978,983.708 -57.625

116.05 -31.65 1478.950 978,968.269 -36.954

116.15 -31.65 1546.090 978,965.232 -16.385

116.25 -31.65 1552.100 978,983.262 1.560

116.35 -31.65 1524.040 979,004.644 14.913

116.45 -31.65 1451.900 979,033.406 22.560

115.55 -31.75 309.618 979,270.814 -96.338

115.65 -31.75 576.151 979,187.156 -95.516

115.75 -31.75 844.686 979,109.514 -88.132

115.85 -31.75 1083.160 979,053.506 -74.744

115.95 -31.75 1287.570 979,015.913 -56.847

116.05 -31.75 1444.880 978,989.376 -36.614

116.15 -31.75 1557.110 978,970.714 -16.526

116.25 -31.75 1617.230 978,970.635 1.064

116.35 -31.75 1618.230 978,982.595 14.313


Surabaya


116.45 -31.75 1554.100 979,009.252 22.176

115.55 -31.85 115.230 979,336.551 -94.832

115.65 -31.85 375.750 979,258.075 -92.988

115.75 -31.85 658.314 979,177.919 -84.939

115.85 -31.85 921.840 979,112.277 -71.290

115.95 -31.85 1165.330 979,062.826 -53.501

116.05 -31.85 1374.740 979,021.056 -33.646

116.15 -31.85 1531.060 978,988.678 -14.060

116.25 -31.85 1643.280 978,972.775 3.059

116.35 -31.85 1702.400 978,967.442 16.008

116.45 -31.85 1670.330 978,984.115 23.829

115.55 -31.95 -110.221 979,422.410 -91.690

115.65 -31.95 143.286 979,343.921 -88.733

115.75 -31.95 437.874 979,257.673 -79.879

115.85 -31.95 723.444 979,184.333 -65.812

115.95 -31.95 988.974 979,126.843 -48.000

116.05 -31.95 1231.460 979,072.824 -28.454

116.15 -31.95 1437.870 979,025.838 -9.391

116.25 -31.95 1611.220 978,992.441 7.134

116.35 -31.95 1724.440 978,971.891 19.560

116.45 -31.95 1739.470 978,976.661 27.039

115.55 -32.05 -365.730 979,521.646 -87.606

115.65 -32.05 -101.202 979,437.219 -83.518

115.75 -32.05 204.408 979,344.454 -73.776

115.85 -32.05 496.992 979,267.647 -59.171

115.95 -32.05 771.540 979,205.765 -41.215

116.05 -32.05 1031.060 979,145.236 -21.900

116.15 -32.05 1277.550 979,088.071 -3.360

116.25 -32.05 1514.020 979,034.730 12.474

116.35 -32.05 1695.380 978,992.338 24.177

116.45 -32.05 1781.560 978,975.407 31.029

115.55 -32.15 -638.273 979,624.251 -83.387

115.65 -32.15 -362.724 979,540.759 -78.252

115.75 -32.15 -56.112 979,445.001 -67.613

115.85 -32.15 227.453 979,366.527 -52.396

115.95 -32.15 487.974 979,309.046 -34.196

116.05 -32.15 750.499 979,246.673 -15.022

116.15 -32.15 1037.070 979,174.771 3.033

116.25 -32.15 1344.680 979,097.095 18.135

116.35 -32.15 1609.210 979,029.038 28.987

116.45 -32.15 1775.540 978,986.740 35.000

115.55 -32.25 -866.730 979,701.139 -79.726


Surabaya


115.65 -32.25 -602.202 979,625.370 -73.719

115.75 -32.25 -324.647 979,542.501 -62.253

115.85 -32.25 -74.147 979,474.565 -46.402

115.95 -32.25 167.334 979,422.123 -27.874

116.05 -32.25 440.881 979,354.785 -8.738

116.15 -32.25 772.542 979,269.009 8.922

116.25 -32.25 1134.260 979,175.325 23.333

116.35 -32.25 1461.920 979,085.902 33.307

116.45 -32.25 1702.400 979,019.332 38.384

115.55 -32.35 -1074.140 979,785.269 -77.032

115.65 -32.35 -843.683 979,715.615 -70.391

115.75 -32.35 -603.203 979,639.972 -58.225

115.85 -32.35 -379.758 979,579.378 -41.762

115.95 -32.35 -141.283 979,527.543 -22.843

116.05 -32.35 148.297 979,456.233 -3.624

116.15 -32.35 489.978 979,367.015 13.779

116.25 -32.35 859.716 979,271.361 27.625

116.35 -32.35 1234.460 979,167.407 36.807

116.45 -32.35 1554.100 979,077.020 40.981

115.55 -32.45 -1258.510 979,853.288 -75.351

115.65 -32.45 -1068.130 979,789.757 -68.338

115.75 -32.45 -867.731 979,727.983 -55.636

115.85 -32.45 -676.349 979,679.199 -38.616

115.95 -32.45 -469.938 979,636.361 -19.261

116.05 -32.45 -200.401 979,574.743 0.165

116.15 -32.45 138.276 979,485.721 17.486

116.25 -32.45 530.057 979,383.049 30.958

116.35 -32.45 958.915 979,265.380 39.528

116.45 -32.45 1356.710 979,150.352 42.947

geodesi fisik perhitungan nilai undulasi di titik p

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