Gravity

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Lecture 2

• Gravity

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UCLA Student taking gravity reading
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As a first approximation the Earth has an
ellipsoidal shape, wider at the equator. A better
approximation is the geoid (height) which
measures the variation of shape relative to the
ellipsoid. This variation is caused by mass
heterogeneities
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Geoid
The Geoid is the potential due to gravity.
Potential is proportional to mass but decreases
with distance away. The geoid is the shape of
the ocean surface, i.e. defines sea level. On
land the geoid is the height the water in a canal
would have if it were connected to the ocean
(this can be calculated using surveying methods,
gravity, GPS) A () mass heterogeneity has more
mass so the geoid rises above it.
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A liquid surface is an equipotential (same
potential)
Surface Ocean
equipotential
seamount
Ocean floor
Ocean floor rise over a seamount (or drops above
a trench) because to keep the potential the same
the increase due to the seamount is compensated
by a decrease as you move away from the rest of
the earth.
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The Global Geoid A ship sailing from s. India to
s. Africa rises 130 m.
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Seamounts, trenches, and pull-apart basin as
detected by the Geoid measured from satellites.
Note underwater seamounts are eroded flat.
Smith and Sandwell
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Gravityis the negative gradient of potential
Since from
Given a gravity survey you can sum the normal
gravity field Times area to obtain the anomalous
mass.
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Calculate excess mass Sum area times g divide
answer by 4pG
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Gravity measures the force of attraction of the
Earth which Depends on the mass distribution
through Newtons law of Gravity
Force G m1m2/r2m1g
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End Lecture 2