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GRAVITY DATA PROCESSING

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GRAVITY DATAAround 2200 gravity observes that consists of :

1. Bouguer anomaly land gravity observes

random distribution

2. Free-air anomaly satelite data

regular grid with 3-4 km space

Objectives :To create Maps of Bouguer anomaly,

Regional anomaly,

Residual anomaly and

Second vertical derivative

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Gravity datadistribution

Satelite data

Surface

measurement

data

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BOUGUER ANOMALYBouguer correction (off-shore data) :

BA= gobs- ge FC BCgobs= observe gravity at stationge= Ellipsoid gravity value at stationFC = free-air correction at stationBC = Bouguer correcction

Off-shore data ( free-air anomaly), Bouguer anomaly is :

BA= FAA + BCDepth of sea water is estimated from bath-y-metric data

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REGIONAL-RESIDUAL ANOMALYa. POLYNOMIAL TREND SURFACE ANALYSIS:

g (xi,yi) = c1+ c2xi+ c3yi+c4xi2

+ c5xiyi+ c6yi2

i = 1,2,3., n = station numberg(xi,yi) = Bouguer anomaly at xi,yi

xi,yi = station coordinatec1, c2, c3, , c6 = polynomial constant

In matrix

6

2

1

2

2

22

2

11

2

1

.

.

.........1

................

................

........1

........1

.

.

c

cc

yx

yx

yx

g

gg

iii

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b. MOVING AVERAGE WINDOW FILTER :

N

i

N

j

reg

N

jigNNg

1 1

2

),(

2

1,

2

1

Equation for N x N window width :

The residual anomaly :

REGIONAL AND RESIDUAL ANOMALY

),(),(),( jigjigjig regres

Window width (n) estimation spectral analysis

ckS

n

.

2

kc= reg-res cut-off frequency

S = grid spacing

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Spectral analysis of Bouguer anomaly for

estimating window size of moving filter

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Spectral analysis of gravity anomaly for

estimating window size of moving filter

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c. SECOND VERTICAL DERIVATIVE

0),,(2

zyxg

Laplaces Eq. :

SVD can be derived through convolution between

SVD filter and gravity anomaly

REGIONAL-RESIDUAL ANOMALY

0),,(),,(),,(

2

2

2

2

2

2

z

zyxg

y

zyxg

x

zyxg

2

2

2

2

2

2 ),,(),,(),,(

y

zyxg

x

zyxg

z

zyxg

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Amplitude response of Some Second

Vertical Derivative filter