Geodetic Data Collection Techniques - Geodesy: Introduction to Geodetic Datum and Geodetic Systems - page 63

surface point can be obtained. Airborne gravimetry is relative gravity measurement,
i.e., prior to taking off, the aircraft is connected to a surface point of known gravity.
Its basic data model is:

ʔ g h ¼ g b þ ʴ g A ˅ A E A h þ 0 : 3086H ʳ 0 , ð 2 : 29 Þ

where g h is the gravity anomaly at a point in space at a height H, g b is the gravity

value at the ground gravity reference station,

ʔ

g is the gravitational variation
relative to g b observed by the airborne gravimeter, A ˅ is the vertical acceleration
correction of the aircraft, A E is the E ¨ tv ¨ s correction, A h is the inclination correction
to the horizontal acceleration,

ʴ

ʳ 0 denotes the normal gravity value (referred to in
Sect. 4.1 ) evaluated on the geometric surface of the reference ellipsoid, and
0.3086H is the spatial correction of normal gravity.
The vertical disturbing acceleration for aircraft A ˅ is mainly induced by the
vertical motion of the aircraft and the self-excited vibration in the body of the
aircraft. This self-excited vibration is chiefly in the high-frequency bandwidth and
can be removed by means of a low-pass filtering technique and high-damping of the
gravimeter's sensing element. Vertical motion of the aircraft can be corrected by
determining the flight altitude in progression with an appropriate computation
method. It is fairly easy to measure changes in flight altitude relative to sea level,
i.e., to measure directly the changes in distance from the aircraft to the sea surface
using an altimeter. However, over land surfaces, what the altimeter measures are
the changes in altitude from the aircraft to the ground; therefore, in order to obtain
changes in the flight altitude, measurements of changes in the topographic surface
of the predetermined flight course are also needed at the same time
To our knowledge, gravity is the resultant of the universal gravitation of the
Earth's masses and the centrifugal force due to the Earth's rotation. When measur-
ing gravity on a moving platform, the centrifugal force will change due to the
resultant force of the carrier's velocity and the rotation velocity of the Earth, and
this change is known as the E¨ tv¨s correction (A E ). The computational formula is
written as:

2 ,

V 2
R

H
R

A E ¼ 1 þ ˉ V sin A cos ˆ þ ð 2 : 30 Þ

where H denotes the flight altitude, R is the average radius of the Earth, V is the
velocity of the carrier, A indicates the azimuth of the motion, ˉ is the angular

velocity of the Earth's rotation, and is the geocentric latitude at a measuring point.

When determining gravity, the gravimeter and the level surface should be
strictly parallel to each other. For airborne gravity measurement, if the platform
of the gravimeter is not strictly parallel to the level surface, it will not only affect the
gravitational acceleration but also exert influence on the vertical component of the
horizontal acceleration. This effect is called inclination correction to the horizontal
acceleration. Assuming that g is the actual gravity value, g t is the value measured by
the gravimeter,

ˆ

ʸ is the inclination between the platform surface and the level