Definition of "geoid"

The problem of the form and dimensions of the sea level surface of the earth has been one of peculiar difficulty. The combined efforts of the ablest mathematicians of the past two centuries, supplemented by the most laborious and costly geodetic measurements have yielded us the first approximation only to the complete solution. […] This spheroid, or reference ellipsoid, as it is sometimes called, has its minor axis coincident with the earth's axis of rotation and is usually regarded as sensibly fixed in position and dimensions. With respect to it the actual sea surface or geoid must be imagined to lie partly above and partly below by small but unknown amounts, the determination of which, if possible, will constitute a second approximation to the figure of the earth.

1888, Robert Simpson Woodward, “Introduction”, in On the Form and Position of the Sea Level: With Special Reference to Its Dependence on Superficial Masses Symmetrically Disposed about a Normal to the Earth's Surface (Bulletin of the United States Geological Survey; no. 48), Washington, D.C.: Government Printing Office, page 15

In an earlier paper at Berkeley last year , I suggested correlations between the local crust and the corresponding geoid undulation. Comparisons of crustal thickness with various geoids (gravimetric, astrogeodetic, and satellite) showed a general compatibility, not only in the United States but also in various other parts of the world.

1966, William P. Durbin, Jr., “Geophysical Correlations”, in Hyman Orlin, editor, Gravity Anomalies: Unsurveyed Areas: Papers Presented at the Symposium ‘Extension of Gravity Anomalies to Unsurveyed Areas,’ at Ohio State University, Columbus, November 18–20, 1964 (Geophysical Monograph Series; no. 9; American Geophysical Union Publication; no. 1357), Washington, D.C.: American Geophysical Union of the National Academy of Sciences—National Research Council, page 87, column 2

This paper deals with the accuracy of a geoid computed using local gravity data supplemented by a global potential model. Local gravity can only correct the global model for wavelengths less than about one third of the dimension of local data, so any longer wavelength errors in the global geoid remain in the local model.

1995, Roger G. Hipkin, “How Close are We to a Centrimetric Geoid?”, in Hans Sünkel, Iginio Marson, editors, Gravity and Geoid: Joint Symposium of the International Gravity Commission and the International Geoid Commission: Symposium No. 113, Graz, Austria, September 11–17, 1994 (International Association of Geodesy Symposia; symposium 113), Berlin, Heidelberg: Springer-Verlag, page 529