Gravity measurement is known, however the value measured can seem to show slight variation at different locations and situations, even in the same observation point at different times. Just keep reading this post to know why this occurs.
There are two (2) major categories of factors that affecting gravitational acceleration as briefly described here below
1: Temporal based variation
Are the changes in the observed gravity that are time dependent.
They are observed from gravity itself.
i/ Instrument Drift
Drift refers to a gradual change in spring tension with time (t) due to changes in temperature and elastic properties of spring. It is due to changes in the response of the gravimeter over time.
How to Reduce this
- Spring made by materials which are insensitive to temperature.
- Temperature controlled by housing in an evacuated chamber.
ii/ Tidal Effects
It is due to gravitational attraction between the Sun and Moon on the Earth.
The Tidal force (Differential force), is defined as the difference in gravitational force at the Center of the Earth and at any point which is at distance dr.
Recall, Gravitational Force (F) = - GMm/r2
Then dF = (dF/dr)× dr
Then Tidal force can be calculated as dF = 2GMm/r3
2: Spatial Based variation.
These are space dependent variations. They change from place to place like geologic effects but they are not related to geology.
i/ Latitude variation.
Due to ellipsoidal shape and the rotation of the Earth.
The distance between the gravimeter and the Earth's center varies with latitude.
Consider the figure below:
ga = GM/ra2
gb = GM/ rb2
But ra is greater than rb
Then gb is greater than ga
Rotation
Centrifugal force varies with distance between the rotation axes and the gravimeter placed.
Centrifugal is large at the equator and goes to zero at the poles.
components r balance with Centrifugal force, when considering the right angled triangle.
Cos Q = r/R
Then, RQ = ReCosQ
where Q and Re - Is the Latitude and Radius of the Earth respectively.
ii/ Elevation Variation
Due to the difference in elevation of the observation points.
If two gravimeters placed in two different elevations would they record the same gravity?
No! Higher elevated records smaller g than lower elevations. Every 1 Metre increases uphill, gravity is decreasing by 0.3086 mGal.
Since g varies inversely to r2
Consider the figure below.
From
g = GMe/Re2
At point A
gA = GMe/R2
At point B
gB = GMe/ (R + h)2
∆g = gA - gB
iii/ Slab Effects: Due to extra (excess) masses underlying observation points at higher elevations (thickness density)
iv/ Topographic Effect: Related to topography near the observation point. When discussing the topographic effect, we actually consider the topographic masses, in reference to the equipotential surface of the Geoid. However the term Topography is standardly defined in Geodesy and geophysics as topographic density distribution with reference to a lower boundary of the Geoid. When the lower boundary is Ellipsoid it will be described as Ellipsoidal Topography.
Thank you for reading !
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