Sample Problem on Absolute Gravity Reductions
An absolute gravimeter located ฯ = 23ยฐ-45โ-38โ, ฮป=121ยฐ37โ45โ at the middle of an island 50m from the
shore with an elevation of 16.37 m above mean sea level. Observation took place on August 5,2024 at 10
AM local time when sea level was 3.4 meters above msl and the moon is at zenith above the gravimeter.
A mean reading of 981.3859235 Gal was recorded with atmospheric pressure of 750 mm Hg. Determine
the reduced gravimeter reading.
Solution
1. Gravitational attraction of the Moon
๐ฟ๐๐๐ก๐ก๐ =๐บ๐
(๐โ๐
)2=3.55 ๐๐บ๐๐ = 3550ฮผ๐บ๐๐
G=universal gravitation constant= G = 6.6743 x 10-11 m3 kg -1s-2
m=mass of the Moon= 7.342 x 1022 kg
R=mean radius of the Earth=6,371,000 m
d=371,629,000 m
2. Crustal deformation
๐ฟ๐๐๐๐ =๐บ๐
๐
2โ๐บ๐
(๐
+๐ฟโ)2=92.5 ฮผ๐บ๐๐
R=6,371,000 m
r=0.30 m
3. Ocean loading
๐ฟ๐๐=๐บ๐๐ฅ๐ผ(โ๐ง2
2+๐12โโ๐ง1
2+๐12)=41.3๐๐บ๐๐
ฯ=1,030 kg/m3
ฮฮฑ =2ฯ
Z1=12.97
Z2=16.37
r1=50 m
4. Atmospheric reduction
ฮดgP = โ0.36ฮผGal/millibar = โ3.6ฮผGal/kPa
1013.25 mbar = 760 mm Hg
ฮดgp=4.8 ฮผGal
5. Polar motion
๐ฟ๐๐ =โ1.164 ๐ฅ108(2๐๐2sin๐cos๐(๐ฅcos๐โ๐ฆsin๐))= 7ฮผ๐บ๐๐
a=6,378,137 m
ฯ=7.292115x10-5
ฯ = 23ยฐ-45โ-38โ,
