Physical geodesy

Image:Ocean gravity map.gif|right|thumb|350px|Ocean basins mapped gravitationally. Seafloor features larger than 10 km are detected by resulting gravitational distortion of sea surface.
Physical geodesy is the study of the physical properties of Earth's gravity and its potential field, with a view to their application in geodesy.

Measurement procedure

Traditional geodetic instruments such as theodolites rely on the gravity field for orienting their vertical axis along the local plumb line or local vertical direction with the aid of a spirit level. After that, vertical angles are obtained with respect to this local vertical, and horizontal angles in the plane of the local horizon, perpendicular to the vertical.
Levelling instruments again are used to obtain geopotential differences between points on the Earth's surface. These can then be expressed as "height" differences by conversion to metric units.

Units

Gravity is commonly measured in units of m·s⁻². This also can be expressed as newtons per kilogram of attracted mass.
Potential is expressed as gravity times distance, m²·s⁻². Travelling one metre in the direction of a gravity vector of strength 1 m·s⁻² will increase your potential by 1 m²·s⁻². Again employing G as a multiplier, the units can be changed to joules per kilogram of attracted mass.
A more convenient unit is the GPU, or geopotential unit: it equals 10 m²·s⁻². This means that travelling one metre in the vertical direction, i.e., the direction of the 9.8 m·s⁻² ambient gravity, will approximately change your potential by 1 GPU. Which again means that the difference in geopotential, in GPU, of a point with that of sea level can be used as a rough measure of height "above sea level" in metres.

Geoid

Due to the irregularity of the Earth's true gravity field, the equilibrium figure of sea water, or the geoid, will also be of irregular form. In some places, like west of Ireland, the geoid—mathematical mean sea level—sticks out as much as 100 m above the regular, rotationally symmetric reference ellipsoid of GRS80; in other places, like close to Sri Lanka, it dives under the ellipsoid by nearly the same amount.
The separation between the geoid and the reference ellipsoid is called the undulation of the geoid, symbol.
The geoid, or mathematical mean sea surface, is defined not only on the seas, but also under land; it is the equilibrium water surface that would result, would sea water be allowed to move freely under the land. Technically, an equipotential surface of the true geopotential, chosen to coincide with mean sea level.
As mean sea level is physically realized by tide gauge bench marks on the coasts of different countries and continents, a number of slightly incompatible "near-geoids" will result, with differences of several decimetres to over one metre between them, due to the dynamic sea surface topography. These are referred to as vertical datums or height datums.
For every point on Earth, the local direction of gravity or vertical direction, materialized with the plumb line, is perpendicular to the geoid.

Gravity anomalies

Above we already made use of gravity anomalies. These are computed as the differences between true gravity, and calculated gravity. We thus get
These anomalies are called free-air anomalies, and are the ones to be used in the above Stokes equation.
In geophysics, these anomalies are often further reduced by removing from them the attraction of the topography, which for a flat, horizontal plate of thickness H is given by
The Bouguer reduction to be applied as follows:
so-called Bouguer anomalies. Here, is our earlier, the free-air anomaly.
In case the terrain is not a flat plate we use for H the local terrain height value but apply a further correction called the terrain correction.