3.14 Gravity Field of the Earth 71
the sun in its orbit generates the latitude correction. It’s latitude dependence
is expressed by the equation(Heiskanen and Vening Meinsz 1958)
g(ψ) = 978.049(1 + 0.0052884Sin
2
ψ −0.0000059Sinψ (3.97)
where‘ψ’ is the latitude on the surface of the earth. This is the international
gravity formula. The radius of the spheroidal earth is given by
R(ψ) = 6378.388(1 − 0.0033670Sin
2
ψ +0.0000071Sin
2
2ψ). (3.98)
The normal gravity formula for geodetic reference system is as follows
g(ψ) = 978.0327(1 + 0.0053024 Sin
2
ψ −0.00000071 Sin
2
2ψ). (3.99)
For routine latitude correction needed for geodetic survey as well as for surveys
related with crustal studies the latitude correctio n used is ≈ 1.307 Sin2ψ.
3.14.5 Tidal Correction
Sensitive gravimeters respond to the position of the sun and moon with respect
to the earth and the values of g varies with the tides in the ocean. It may be
a fraction of a milligal but it is measurable.
3.14.6 Isostatic Correction
Isostatic correction originated due to the presence of lateral variation of den-
sity within the earth, s crust. After the said corrections are applied, the
Bouguer anomaly for particular reference plane should have been zero in large
scale mapping and keeping aside the local variations in densities .In re alities
it is was observed that negative Bouguer anomaly exists near the mountains
and positive anomaly exits near the oceans.
Two scientists named G.B. Airy and J.H. Pratt proposed two different
models for the crust. Airy’s model suggests that crust is thick near the moun-
tains and mountains have roots and it is thiner below the ocean bottoms and
here the crust has antiroots. The density of the crust is assumed to be the
same. Pratt assumed a variable density model and this variation in density
has direct relation with the elevation of the ground from the mean sea level.
Depth of the ocean floor from the mean sea level causes increase in density.
Figures 3.23a.b show the Airy and Pratt’s isostatic mo dels.
Isostatic correction is needed only for geodetic survey as well as for surveys
related to crustal studies. For routine exploration survey only free air, Bouguer
and terrain corrections are necessary. Drift correction is an instrument based
correction. Round the clock reading at one point can give the idea about drift
correction to be added or subtracted.