Gravity Method

ByDr. Amin E. Khalil

M1M2 R

2

21

r

MMGF

Newton 2nd law

gMF hence

2

212

r

MMGgM

Then

2r

MGg

r

R = radius of the earth

6371

km

Earth is considered as sphere and hence radius is constant.

Ideal

RealEarth is not sphere and hence radius is not constant.

Hence correction must be applied

Why corrections?

Because many factors affect the value of g. As an example:•Earth flattening.•Surface relief.• anomalous masses inside the earth

We want to focus on

Anomalous masses

We need first to define reference surface

Geoid

What is geoid? It is equipotential surface where the g is always constant. The equipotential surface is usually taken as the sea level. However, due to some heterogeneity in the earth Geoid may differ slightly from Sea level.

Reduction

Reduction is carried out to correct for:•Latitude•Elevation•Excess mass•Terrain•Drift•Isostacy•Earth’s rotation

Latitude Corrction

The earth is flattened, i.e the radius at the equator is longer than at the poles.

gn = 978031.85 (1.0 + 0.005278895 sin2(lat) + 0.000023462 sin4(lat)) (mGal)

Elevation Correction

geoid

+h

-h

gfa = gobs - gn+ 0.3086h (mGal)

Bouguer Correction

+m

-m

gb = gobs - gn + 0.3086h - 0.04193r h (mGal)