Geoid

The geoid is the equipotential surface that would coincide with the mean ocean surface of the Earth if the oceans and atmosphere were in equilibrium, at rest relative to the rotating Earth, and extended through the continents (such as with very narrow canals). According to 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. Despite being an important concept for almost two hundred years in the history of geodesy and geophysics, it has only been defined to high precision in recent decades, for instance by works of Petr Vaníček and others. It is often described as the true physical figure of the Earth, in contrast to the idealized geometrical figure of a reference ellipsoid.