Tutorial: Ellipsoid, geoid, gravity, geodesy, and geophysics
Geophysics, 66 (6):
1660--1668 (Nov 1, 2001)DOI: 10.1190/1.1487109
Abstract
Geophysics uses gravity to learn about the density variations of the
Earth's interior, whereas classical geodesy uses gravity to define
the geoid. This difference in purpose has led to some confusion among
geophysicists, and this tutorial attempts to clarify two points of
the confusion. First, it is well known now that gravity anomalies
after the "free-air" correction are still located at their original
positions. However, the "free-air" reduction was thought historically
to relocate gravity from its observation position to the geoid (mean
sea level). Such an understanding is a geodetic fiction, invalid
and unacceptable in geophysics. Second, in gravity corrections and
gravity anomalies, the elevation has been used routinely. The main
reason is that, before the emergence and widespread use of the Global
Positioning System (GPS), height above the geoid was the only height
measurement we could make accurately (i.e., by leveling). The GPS
delivers a measurement of height above the ellipsoid. In principle,
in the geophysical use of gravity, the ellipsoid height rather than
the elevation should be used throughout because a combination of
the latitude correction estimated by the International Gravity Formula
and the height correction is designed to remove the gravity effects
due to an ellipsoid of revolution. In practice, for minerals and
petroleum exploration, use of the elevation rather than the ellipsoid
height hardly introduces significant errors across the region of
investigation because the geoid is very smooth. Furthermore, the
gravity effects due to an ellipsoid actually can be calculated by
a closed-form expression. However, its approximation, by the International
Gravity Formula and the height correction including the second-order
terms, is typically accurate enough worldwide.