Heights - The Geoid
The geoid can be investigated several ways. Before satellites, the local variations in the geoid could be determined using gravity measurements over a "small" area. The resulting geoid had biases and other systematic errors, but the small scale (high spatial frequency) details were correct. These reflect the near underground structures. (Oil companies make extensive use of gravity data for finding underground areas where oil might be located.)
The very long scale behavior is just the mean gravity field - that due to the mass of the earth as a whole. This has been know since the late 1700's to fairly good accuracy. The intermediate scales were basically unknown until the first satellite was launched in 1957.
All satellites serve to measure the gravity field to some extent. There have also been several satellites launched to map the gravity field. And satellites used to measure the sea surface with radar, Seasat, Topex-Posiden, ERS-1 etc., require accurate gravity fields. This has lead to some very good earth gravity models (EGM's). Lately EGM 96 and EGM 2000 have been published.
Here is a color coded map of the geoid separations (N's) from EGM 96. Blue is lowest and red is highest.
The maximum positive value is about 80 meters and the minimum about -100 m. In fact the mean averaged over the world is almost zero. This is how the size of the ellipsoid is set for modern scientific ellipsoids.
Historical ellipsoids, the ones used for older datums, have no real relationship to the world wide undulations. However modern ellipsoids defined from satellite measurements are different. These have the ellipsoid and gravity model determined together. They will have an average undulation of zero.
Notice that the large mountain ranges and deep ocean trenches seem to show up on the geoid. This is due to the effects of these mass variations on the gravity field. You can see the continents outlined, especially where a trench meets a mountain range such as on the west coast of South America.
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