Materil Gravity

8/3/2019 Materil Gravity

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GEOPHYSICSGEOPHYSICSFORFOR

GEOLOGISTGEOLOGISTANDAND

ENGINEERENGINEER

hidartan


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GEOLOGIC

FIELD

STUDY

SEISMIC

SURVEYS

ELECTRIC

AND

OTHERWELL

SURVEYS

SAMPLECUTTINGS

ANDCORES

GEOLOGIC

CROSSSECTIONS

Mapping,measuring,andd

escribingsections

Systematiccollectio

nsofsamples

anddetailedfacie

sdescription

Generalcorrelationan

dinterpretation

Detailcorrelationandinterpretation

Generalusesincorrelationand

gross-faciesde

termination

Detailedanalysesof

curveshapes

andfaciesboundaries

Generalrock-type

determination

Detailed-facie

sanalysis

Generalregionalstratigra

phyandstructure

Detailcor

relation

DETERMINA TION OF B A SIN

TY PE AND STRUCTURE

DEV ELOPMENT OF TIME -

STRA TIGRA PHIC FRAMEWORK

DETECTION OF

UNCONFORMITIES

ENVIRONMENTA L - FA CIES

A NA LY SIS

RECONSTRUCTION OF

PALEOGEOGRAPHY

PREDICTION O F

STRA TIGRA PHIC TRA P

EXPLORATION TOOL S A ND TECHNIQUES

(e.g

.,numberofsands>20'thick)

PALEOGEOGRAPHICMAPS

(e.g.,isolith,three-component,ratio,etc)

FACIES-DISTRIBUTIONMAPS

GRAVITYSURVEYS

MAGNETICSURVEYS

R

EMOTE-SENSINGSURVEYS

SPECIAL-PURPOSEMAPS

ISOPACHMAPS

PETROGRAPHICANALYSIS

GEOCHEMICALANALYSIS

PALEONTOLOGY-AGE

DETERMINATIONOFENVIRONMENTALFACIES

PAL

EONTOLOGIC-ENVIRONMENT

E

F

AERIALPHOTOGRAPHYCANALYSIS

PROCEDURALSTAGES

A

B

C

D

X

X

X

X

X

X X X X X X X X X X

X X X X X X X X

X

X X X X X X X X X X X X X X

XXXX

XXXXX

X

X

X

X

X

X

X

X

X

X

X

X

X

XX X

X

X

X

PRIHADI SA / 2002


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GRAVITYGRAVITY


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MAIN FIELD EQUIPMENTSMAIN FIELD EQUIPMENTS

Gravimeter : 1 unit La Coste and Romberg.

Positioning : 2 set GPS-Receivers LEICA

Elevation : 3 set Paulin Altimeter

Communication : 2 unit SSB radios ( 1 unit at

field, 1 unit at head office),

4 unit Handy talky,2vehicles

Data Processing: Laptop PC, printer, softwares,diskettes, calculator

Crew : Geophysicist,Geodetic, 2 operator

6 lokal labor Hidartan


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DATA ACQUISITION PLANDATA ACQUISITION PLAN

1. Calibration

Calibration of the gravimeter is carried out several

times : before and after a trip and every two weeks.

2. Base Station

The gravity base station in every location is

established by tying the base station to the nearest

standard base station to the location.

3. Data Acquisition Methods

hidartan


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hidartanCONTOH METODA PENGUKURAN


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D a y 1D a y 2

CONTOH METODA PENGUKURANHidartan


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F i e l d D a t a S t a t i o nM o d e m5 6 . 6 k b p s

T e l e p h o n e N e t

F i e l d D a t ai n A S C I I F o r m a t

T r a n s c e i v e r P r o t o c o l

b y Z m o d e m o r K e r m i tS o f t w a r e

T r a n s c e i v e r P r o t o c o lb y Z m o d e m o r K e r m i tS o f t w a r e

F i e l d D a t a

i n S p r e a d S h e e tF o r m a t S o f t w a r e

f i l t e r

D a t a M e d i a s t o r a g eH a r d i s k 4 0 G b .

D a t a P r o c e s s i n g ,I m p l e m e n t a t i o n ,

a n d D e s k t o p P u b l i s h i n

O f f i c e D a t a S t a t i o n

O f f i c e D a t a S t a t i o

F i e l d D a t a S t a t i o n

M o d e m5 6 . 6 k b p s

M o d e m5 6 . 6 k b p s

M o d e m5 6 . 6 k b p s

P C P I V - 1 G h

P C P I V - 1 G h

DESIGN OF REMOTE DATA COMMUNICATION SYSTEMDESIGN OF REMOTE DATA COMMUNICATION SYSTEM


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DATA PROCESSINGDATA PROCESSING

The data obtained from the sites are sentdirectly to the base camp and processed.

11. DATA REDUCTION. DATA REDUCTION

22. GRAVITY PROFILES. GRAVITY PROFILES

3.3. GRAVITY MAPGRAVITY MAP

4.4. MODELINGMODELING


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GRAVITY PROFILES

* Station Coordinate

* Station Elevation

* Gravity Value

DATA ACQUISITION* Gravity Measurement

* GPS Positioning

DRIFT and TIDAL

CORRECTION

* FREE AIR CORRECTION

* BOUGUER CORRECTION

TERRAIN CORRECTION* Inner (Field Processing)

* Outer (Head Office Processing)

* Bouguer Anomaly

* Complete Bouguer Anomaly

hidartan

GRAVITYGRAVITY

DATADATA

PROCESSINGPROCESSING

FLOWFLOW

CHARTCHART


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Hidartan

11. DATA REDUCTION. DATA REDUCTION

The gravity data reduction consists of two types

of correction which are internal and external

correction.

The internal corrections are drift and tidal

corrections.

The external corrections are ellipsoid gravityvalue, free air, bouguer, and terrain corrections.


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DRIFT CORRECTIONDRIFT CORRECTION is applied to eliminate the

effect of spring fatigue of the La Coste instrument.

This correction is derived by double check thestarting base station at appropriate time interval.

TIDAL CORRECTIONTIDAL CORRECTION is applied to eliminate

gravity of the sun and moon which are time

function due to relative motion among earth,

moon and sun. The tidal correction had beencalculated in advance using computer by applying

the Longmans formula.

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ELLIPSOID EARTH GRAVITYELLIPSOID EARTH GRAVITY reference has to be

applied to produce an earth gravity value at the

mean sea level as a function of location latitude.

This reference implies an homogenous mass

distribution of the ellipsoid earth model.

The ellipsoid model in the IUGG 1979 formula is :

gg = 978.03185 (1 + 0.005278895 sin= 978.03185 (1 + 0.005278895 sin22 ++

0.000023462 sin0.000023462 sin44

) , mgal) , mgalwhere

g

= theoretical gravity as function of

= latitude of the observation point.Hidartan


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FREE-AIR CORRECTIONFREE-AIR CORRECTION (FAC) is applied toestimate the earth gravity at certain altitude of an

observation above mean sea level.

The free air correction formula is calculated foraverage earth radius at elevation h in meters.

FAC = - 0.3086 h, mgalFAC = - 0.3086 h, mgal

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BOUGUER CORRECTIONBOUGUER CORRECTION (BCBC) is applied to estimate the

earth gravity at elevation h above sea level with earth mass

of density (gr./cm3) fill up the space of thickness h.

This theoretical Bouguer correction can be written as:BCBC == 2h2h Gh =Gh = 0.041870.04187 hh, mgalwhere :G = 6.67 x 10-9 Cgs unit

= the chosen density in gr./cm3

H = altitude of observation point in meters.

BOUGUER ANOMALYBOUGUER ANOMALY (BABA) is the difference between the

observation gravity value (gobs

) and the expected earth

normal gravity at an observation point.

BABA = gobs - (g - FAC + BC)

where the magnitude in the bracket is the expected earth normal

gravity.

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h

A

B

M

BOUGUER EFFECTBOUGUER EFFECT

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PRIHADI SA / 2002

Pengukuran gaya berat sering dilakukan pada

daerah dengan topografi yang cukup bervariasi.

Koreksi terrain harus dihitung untuk

menghilangkan efek relief permukaan bumiterhadap nilai anomali Bouguer yang dihitung.

Koreksi ini dihitung sebagai efek gaya berat yang

ditimbulkan oleh suatu badan massa tiga

dimensional yaitu adanya bukit dan lembah disekitar stasion pengukuran gaya berat.

TERRAIN CORRECTIONTERRAIN CORRECTION


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INNER ZONE CORRECTIONINNER ZONE CORRECTION

To apply this correction, a simple topographicsurvey has to be performed at every gravity

station along a radius of 35 and 68 meterswhich may be done before or after gravity reading.

Such survey should include the nature of localmorphology and the distance to the gravity station

which affects the observation.

The correction was directly calculated at the fieldby using a certain gravity terrain inner correction

chart.

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OUTER ZONE CORRECTIONOUTER ZONE CORRECTION

This correction was done by using the HammerChart, usually based on a topographic map of 1 :

250.000 scale.

Applying the terrain correction, the Bouguer

Anomaly (BA) can be refined to be a Complete

Bouguer Anomaly (CBA) following this formula :

CBA = gCBA = gobsobs - (g- (g - FAC + BC - TC)- FAC + BC - TC)

or

CBA = BA + TC

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Hidartan

Metoda konvensional untuk menghitung koreksi

terrain adalah dengan menggunakan Hammer

Chart dan peta topografi berskala tertentu.

Sekarang ini perhitungan koreksi terrain

dilakukan dengan bantuan komputer, salah

satunya adalah Metoda Integrasi Numerik.

METODA PERHITUNGAN KOREKSI TERRAINMETODA PERHITUNGAN KOREKSI TERRAIN


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Projection

System Similar to

the Map

Y

N

Gravity

Observation

Station

Position X, Y, Z

Transformation

of the Coordinate

Topographic

Map

Digitizing,

Gridding and

Merging

Terrain Correction

TERRAIN CORRECTION CALCULATION FLOW CHARTTERRAIN CORRECTION CALCULATION FLOW CHART

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N W


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Hidartan

65

m

R I V E R

H I L L R O C K

A

B

C

D

B

Sketch measurement topographic for Terrain Correction


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Dua persoalan terlebih dahulu harus dipecahkan untuk dapat

melakukan komputasi koreksi terrain.

Pertama adalah bagaimana menghitung efek gaya berat

yang ditimbulkan oleh suatu badan massa tiga dimensidengan bentuk yang tak beraturan.

Efek gaya berat yang disebabkan oleh massa bervolume V

terhadap suatu titik dengan koordinat (Xo,Yo,Zo) dapat

dihitung dengan persamaan :

Hidartan

( )g X Y Z ZR dx dy dzv0 0 03 2

, ,/

=

( ) ( ) ( )R X X Y Y Z Z2 0 2 0 2 0 2= + +

dengan : : konstanta gravitasi

: densitas

(1)


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Kesulitan utama dalam memecahkan persamaan

integral di atas disebabkan karena batas-batas

integralnya, yang berupa permukaan bumi,bentuknya tidak beraturan.

Pada metoda konvensional, persamaan

dipecahkan secara analitik dengan pendekatan

yang menggunakan bentuk-bentuk geometrisederhana seperti silinder, kerucut, dan

sebagainya.

Dengan komputer, kita dapat menghitungpersamaan integral secara numerik yang batas

integralnya dapat mendekati bentuk permukaan

bumi secara lebih teliti.

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INTEGRASI NUMERIKINTEGRASI NUMERIK

Apabila persamaan (1) ditulis dalam koordinat silinder maka

bentuknya adalah sebagai berikut :

Hidartan

g r rZRo o

o

h

r

r

( , )/

=

3 2

1

2

1

2

R r z

h Z r Z o

2 2 2= +

= ( , )

dengan Zo

: elevasi stasiun

(2)


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Bentuk ini lebih sesuai digunakan, karena

koreksi terrain biasanya dihitung untuk daerah

yang berbentuk lingkaran dalam radiusbeberapa kilometer dari titik stasiun.

Lebih lanjut persamaan (2) dapat

disederhanakan menjadi persamaan (3) :

( ) ( )g r r rr

r h

dr do or

r

,

=

+

2 1

2 21

2

1

2

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Suku kedua dapat dihitung secara numerik apabila nilai h

dapat diketahui pada titik-titik sampel integrasi.

Teknik integrasi yang digunakan adalah metoda Quadratur

Gauss dengan bentuk umum :

( )G d d W W Gi j i jj

n

i

m

, ,=

=

=

111

1

1

1

Wi, W

j: koefisien bobot

i,

j : titik sampel integrasi

Dalam hal ini G(i,

j) merupakan fungsi dari beda elevasi h

yang harus dihitung untuk sembarang titik dengan teknik

interpolasi. Hidartan


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Hidartan

Untuk mendapatkan nilai elevasi di setiap titik padadaerah integrasi, dilakukan interpolasi.

Teknik ini hanya memerlukan nilai elevasi pada titik -

titik tertentu, kemudian dihitung fungsi hampiran

sehingga elevasi dapat dihitung :h = f(x,y).

Teknik interpolasi berupa pencocokan permukaan

(surface fitting) yang tingkat ketelitiannya bervariasi

untuk tiap metodanya.Seperangkat data elevasi dan persamaan

pencocokan permukaannya merupakan satu model

topografi.

MODEL TOPOGRAFIMODEL TOPOGRAFI


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Model topografi yang digunakan dibangun berdasarkan data

elevasi pada titik-titik kasa (grid).

Metoda pencocokan permukaan yang digunakan adalah

persamaan multi-quadric dengan persamaan :

Z X Y C X X Y Yj j jj

n

( , )

/

= +

=

2 2 1 2

1

Persamaan ini menyatakan bahwa elevasi suatu titik di dalam

daerah data adalah kombinasi linier dari fungsi-fungsi

permukaan kerucut, yang titik puncaknya merupakan elevasititik-titik yang diketahui.

Fungsi Z(x,y) adalah permukaan yang smooth dan melalui

setiap titik data.

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Koefisien kerataan (flatness coefficient) Cj

didapat dari pemecahan persamaan linier

berikut :[A] C = Z

dimana :

i j j i j ix x y y=

+

2 2 1 2/

i = 1,2,3, ... n

j = 1,2,3, ... n

Zi

: elevasi yang diketahui

Hidartan

Y-axis PRIHADI SA / 2002


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A

B

C D

E

FGH

X-axis

P (0,0,0)

Z-axis

Z Bottom

Z Top

Contour at depth Z

Body M

PRIHADI SA / 2002

Penentuan gravity pada satu titik dari suatu bentuk tiga dimensi yang tak beraturan


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HIdartan

22. GRAVITY PROFILES. GRAVITY PROFILES

Gravity profile will be produced for each line using

its reduced data to present the trend of gravity

values along the line.

33. GRAVITY MAP. GRAVITY MAP

Consists of CBA/BA anomaly map, regional

gravity map, residual gravity map.

Density of Common Geologic Material ( Telford et al. 1990 )


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Density range Approximate average

No. Material Type ( Mg / m 3 ) density ( Mg / m 3 )

Unconsolidated Sediment

1. Alluvium 1.96 - 2.00 1.98

2. Clay 1.63 - 2.60 2.21

3. Gravel 1.70 - 2.40 2.00

4. Loess 1.40 - 1.93 1.64

5. Silt 1.80 - 2.20 1.93

6. Soil 1.20 - 2.40 1.92

Sedimentary Rocks

7. Sand 1.70 - 2.30 2.00

8. Sandstone 1.61 - 2.76 2.35

9. Shale 1.77 - 3.20 2.40

10. Limestone 1.93 - 2.90 2.55

11. Dolomite 2.28 - 2.90 2.7012. Chalk 1.53 - 2.60 2.01

13. Halite 2.10 - 2.60 2.22

14. Glacier Ice 0.88 - 0.92 0.90

Igneous Rocks

15. Rhyolite 2.35 - 2.70 2.52

16. Granite 2.50 - 2.81 2.64

17. Andesite 2.40 - 2.80 2.61

18. Syenite 2.60 - 2.95 2.77

19. Basalt 2.70 - 3.30 2.99

20. Gabbro 2.70 - 3.50 3.03

Metamorphic Rocks

21. Schist 2.39 - 2.90 2.64

22. Gneiss 2.59 - 3.00 2.80

23. Phylite 2.68 - 2.80 2.74

24. Slate 2.70 - 2.90 2.79

25. Granulite 2.52 - 2.73 2.65

26. Amphibolite 2.90 - 3.04 2.96

27. Eclogite 3.20 - 3.54 3.37

( from John M. Reynolds, An Introduction to Applied and Environmental Geophysics, 1997 )hidartan

Densities of Minerals and Miscellaneous Materials ( Telford et al, 1990 )


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Density Range Approximate average density

Material Type ( Mg/m 3 ) ( Mg / m 3 )

Metallic minerals

Oxides, Carbonates

A. Manganite 4.2 - 4.4 4.32

B. Chromite 4.2 - 4.6 4.36

C. Magnetite 4.9 - 5.2 5.12

D. Haematite 4.9 - 5.3 5.18

E. Cuprite 5.7 - 6.15 5.92

F. Cassiterite 6.8 - 7.1 6.92

G. Woframite 7.1 - 7.5 7.32

H. Uraninite 8.0 - 9.97 9.17

Copper n.d 8.7

Silver n.d 10.5

Gold 15.6 - 19.4 17.0

Sulphides

A. Malachite 3.9 - 4.03 4.0

B. Stannite 4.3 - 4.52 4.4

C. Pyrrhotite 4.5 - 4.8 4.65

D. Molybdenite 4.4 - 4.8 4.7

E. Pyrite 4.9 - 5.2 5.0

F. Cobaltite 5.8 - 6.3 6.1

G. Galena 7.4 - 7.6 7.5

H. Cinnabar 8.0 - 8.2 8.1

Non-metallic mineralsGypsum 2.2 - 2.6 2.35

Bauxite 2.3 - 2.55 2.45

Kaolinite 2.2 - 2.63 2.53

Baryte 4.3 - 4.7 4.47

Miscellaneous materials

Snow 0.05 - 0.88 n.d

Petroleum 0.6 - 0.9 n.d

Lignite 1.1 - 1.25 1.19

Anthracite 1.34 - 1.8 1.50

No.

1.

2.

3.

4.

5.

6.

7.

8.

9.

12.

13.

10.

11.

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DATA REDUCTION TABLEDATA REDUCTION TABLE

D a te T im e S tat ionR e ad ingG -o b s L at i tud eLo ng itu deE levat ionG -n orm a lC om b. C T erra in C orr .B A C B A

(m ga l) (m ga l) (d eg ree )(degre e ) (m ) (m ga l ) (m ga l ) Inne r O u te r(m ga l )(m ga l

Hidartan

GRAVITY DATA SHEET


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GRAVITY DATA SHEETGRAVITY DATA SHEET

Hidartan

COMBINE GRAVITY DATA SHEETCOMBINE GRAVITY DATA SHEET Hidartan


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COMBINE GRAVITY DATA SHEETCOMBINE GRAVITY DATA SHEET

HidartanDENSITYDENSITY


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DENSITY

DETERMINATIONDETERMINATION


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Hidartan


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Hidartan

1 4 8


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6 9 6 6 9 8 7 0 0 7 0 2 7 0 4 7 0 6 7 0 8 7 1 0 7 1 2

1 3 2

1 3 4

1 3 6

1 3 8

1 4 0

1 4 2

1 4 4

1 4 6

L H D - 4 , 8 , 9 , 1 0L H D - 6

L H D - 7L H D - 5L H D - 1

L H D - 2

L H D - 3

GRAVITASI

ANOMALI

BOUGUER

rapat massa = 2.67 gr/cm3

U

2 km

Hidartan

1 4 8


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6 9 6 6 9 8 7 0 0 7 0 2 7 0 4 7 0 6 7 0 8 7 1 0 7 1 2

1 3 2

1 3 4

1 3 6

1 3 8

1 4 0

1 4 2

1 4 4

1 4 6

L H D - 1

L H D - 2

L H D - 3

L H D - 4 , 8 , 9 , 1 0

L H D - 5

L H D - 6

L H D - 7L H D - 5 L H D - 7

GRAVITASI

ANOMALI

REGIONAL

POLINOM FIT

ORDE - 2

U

2 km

Hidartan

1 4 8


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6 9 6 6 9 8 7 0 0 7 0 2 7 0 4 7 0 6 7 0 8 7 1 0 7 1 2

1 3 2

1 3 4

1 3 6

1 3 8

1 4 0

1 4 2

1 4 4

1 4 6

L H D - 1L H D - 5 L H D - 7

L H D - 4 , 8 , 9 , 1 0L H D - 6

L H D - 3

L H D - 2

GRAVITASIANOMALI SISA

U

2 km

Hidartan

1 0 . 0


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1 3 2 1 3 6 1 4 0 1 4 4 1 4 8

- 5 . 0

0 . 0

5 . 0

A

N

O

M

A

L

I

S

IS

A

(M

G

A

L

)

- 3 . 0

- 2 . 0

- 1 . 0

0 . 0

1 . 0

E

L

E

V

A

S

I

(K

M

)

L H D - 4 L H D - 5 L H D - 2 L H D - 3

S E L A T A N U T A R A

a n d e s i t b a s a l t i k t e r u b a h ( 2 . 5 g r / c c )

t u f f a , i g n i m b r i t e ( 2 . 0 g r / c c )

a n d e s i t ( 2 . 6 g r / c c )

s e d i m e n ( 2 . 2 g r / c c )

a n d e s i t ( 2 . 6 7 g r / c c )

i n t r u s i d i o r i t ( 2 . 9 g r / c c )

d a t a

p e r h i t u n g a n

GRAVITASI

PROFIL

ANOMALI

SISA

DANMODEL

2-DIMENSI

Hidartan

1 0 . 0


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6 9 6 7 0 0 7 0 4 7 0 8 7 1 2

- 5 . 0

0 . 0

5 . 0

A

N

O

M

A

L

I

S

IS

A

(M

G

A

L

)

- 3 . 0

- 2 . 0

- 1 . 0

0 . 0

1 . 0

E

L

E

V

A

S

I

(K

M

)

B A R A T T I M U R

L H D - 1 L H D - 5L H D - 7

d a t a

p e r h i t u n g a n

a n d e s i t b a s a l t i k t e r u b a h ( 2 . 5 g r / c c )

t u f f a , i g n i m b r i t e ( 2 . 0 g r / c c )

a n d e s i t ( 2 . 6 g r / c c )

a n d e s i t ( 2 . 6 7 g r / c c )

i n t r u s i d i o r i t ( 2 . 9 g r / c c )

GRAVITASI

PROFIL

ANOMALI

SISA

DANMODEL

2-DIMENSI

PRIHADI SA / 2002


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Materil Gravity