The Geoid

The geoid can be defined as:

Gravity anomalies, differences in the earth's gravity field due to variations in the mass distribution, create the geoid.  They will only find relatively large features (km scale).

The geoid is a very complex shape.  In contrast, the ellipsoid is simple shape obtained by rotating an elllipse.

Geoid anomalies are measured from the ellipsoid (measured geoid minus ellipsoid).  A positive anomaly means the geoid is above the ellipsoid.  The ellipsoid is the best shape of the earth, creating by rotating an ellipse in three dimensions.  The ellipse has two radii, polar and equatorial.  They differ in size by about one part in 300 (about 20 km, with a 6400 km radius).

The geoid varies from an ellipsoid on three scales, due to imbalances in the mass distribution in the earth. The scales of variation are:

Profiles.  The red line shows the sea floor depths, and the green is the geoid anomaly.  
Long wavelength, large anomalies (100 meters from the ellipsoid, over thousands of km) due to mass differences in the mantle, many of which reflect older plate tectonics and remnants of subducted plates.  Actual slope, 100/1,000,000 is about 1/10,000, or very gentle. 

This profile goes from the southern Indian Ocean to India, which has the largest negative anomaly in the world.  Note that at this scale any changes in the geoid due to features at lat -50,  -30 or -15 do not stand out; you would have to zoom in to see if they create much smaller anomalies, although there is some hint of these at -30 and -15.
Medium wavelength (10 meters from the ellipsoid as modified by the long wavelength anomalies, over hundreds of km) due to mass imbalances in the crust, especially trenches, ridges, or seamounts. Actual slope, 10/100,000, is also very gentle.

This covers a much smaller region that the long wavelength anomaly.

This profile goes over the Indonesian trench at about latitude -7.5.  Here the regional trend of the geoid anomaly goes from -15 on the left to -5 on the right, and the anomaly for the trench is the approximately 2 m departure from that trend line.  Most of the tectonic anomalies are much less than the maximum 10 m size, which typically happen only at the deepest trenches.
Short wavelength, Small anomalies  (1 meters from the ellipsoid as modified by the long and medium wavelength anomalies, over tens of km) due to density imbalances due to the currents in the oceans.   Actual slope, 1/10,000, is also very gentle.

This profile goes over the wall of the Gulf Stream at about latitude 36.5.  Its magnitude is the departure from the local trend line.  There is not much in the bathymetry at this location, and in fact there might be an eddy to the north of the Gulf Stream wall.

All of these changes in the geoid create very gentle slopes in sea surface (note all the vertical changes are in meters, and they occur over many kilometers). However, the changes are real and can be measured by radar altimeters, and they reveal a great deal to oceanographers and geologists.

We report these as anomalies, for departures/differences from the expected value.  The expected value is the ellipsoid, the best simple shape representing the earth

The large and medium wavelength anomalies will change very little over human time, and we will have a good idea of their value after a single pass of the altimeter, and an excellent idea after we average several passes. 

The best anomalies will occur where there is a very steep gradient in the topography.  Deep trenches typically have the most prominent anomalies, and fast spreading rises have very small anomalies.

Data Max value: 85.4 meters, east of New Guinea

Data Min value:-107.0 meters, south of India

This image shows 15'x15' geoid undulations covering the planet Earth from the NIMA/GSFC WGS-84 EGM96 15' Geoid Height File. The undulations refer to the differences from the WGS-84(G873) reference ellipsoid.

Even at 15' resolution, some beautiful features of the global geoid are obvious.

(Map and description from National Geodetic Survey).

Last revision 4/10/2017