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Geoid.
The Geoid is the equipotential surface of the Earth's gravity field which best fits, in a least squares sense, global mean sea level. The Geoid is a representation of the surface of the earth that it would assume if the sea covered the Earth.
The Geoid is often described as the true physical figure of the Earth, in contrast to the idealized geometrical figure of a reference ellipsoid. It is that equipotential surface which would coincide exactly with the mean ocean surface of the Earth, if the oceans were in equilibrium, at rest (relative to the rotating Earth), and extended through the continents (such as with very narrow canals). According to C.F. Gauss, who first described it, it is the "mathematical figure of the Earth", a smooth but highly irregular surface that corresponds not to the actual surface of the Earth's crust, but to a surface which can only be known through extensive gravitational measurements and calculations.
The Geoid surface is irregular, unlike the reference ellipsoid which is a mathematical idealized representation of the physical Earth, but considerably smoother than Earth's physical surface.

Geoid undulations.
The deviation between the Geoid and the reference ellipsoid is called the Geoid undulation. The biggest presently known undulations are the minimum in the Indian Ocean with N = 100 meters and the maximum in the northern part of the Atlantic Ocean with N = +70 meters.
Undulation of the geoid is the mathematical process of determining the height in meters above the geoid (relative to the mean sea level) from the height provided by the GPS system which uses the (WGS84) ellipsoid as reference.
The process of the undulation it is not standardised, as different countries use different mean sea levels as reference but mostly refers to the EGM96 geoid. Calculating the undulation factor is mathematically challenging. This is why many handheld GPS receivers have built in undulation lookup tables to determine the height above sea level.



