Ellipsoid, geoid, gravity, geodesy, and geophysics

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.