Physical geodesy
Study of Earth's gravity and its potential field.
Physical geodesy examines Earth’s gravity and its associated potential field, known as the geopotential, and applies this knowledge to geodesy.
To measure the Earth, traditional instruments like theodolites use the gravity field to align their vertical axis with the local plumb line—the true vertical—using a spirit level. From this alignment, vertical angles (zenith or elevation angles) are measured relative to the local vertical, while horizontal angles are taken in the plane of the local horizon, perpendicular to it. Levelling instruments determine geopotential differences between points on the surface, which can then be converted into height differences in metric units.
Gravity is usually measured in metres per second squared (m·s⁻²). Multiplying by the gravitational constant G converts these units to newtons per kilogram of attracted mass. Potential, expressed as gravity times distance, uses units of m²·s⁻². Moving one metre in the direction of a gravity vector of 1 m·s⁻² increases potential by 1 m²·s⁻². Again using G as a multiplier, the units become joules per kilogram. A more practical unit is the geopotential unit (GPU), equal to 10 m²·s⁻². This means moving one metre vertically—in the direction of Earth’s ambient gravity of about 9.8 m·s⁻²—changes potential by roughly 1 GPU. Thus, the difference in geopotential (in GPU) between a point and sea level gives a rough measure of height above sea level in metres.
Because Earth’s true gravity field is irregular, the equilibrium shape of sea water—the geoid—is also irregular. For instance, west of Ireland the geoid (mathematical mean sea level) rises about 100 metres above the regular, rotationally symmetric reference ellipsoid of GRS80, while near Sri Lanka it dips below that ellipsoid by a similar amount. The separation between the geoid and the reference ellipsoid is called the geoid undulation, denoted *N*. The geoid is defined not only over oceans but also under land; it is the equilibrium water surface that would exist if sea water could move freely through tunnels beneath the continents. Technically, it is an equipotential surface of the true geopotential, chosen to coincide on average with mean sea level.
Since mean sea level is physically realized by tide gauge benchmarks on different coasts, several slightly incompatible “near-geoids” arise, with differences of decimetres to over a metre due to dynamic sea surface topography. These are known as vertical or height datums. At any point on Earth, the local direction of gravity—the vertical, materialized by a plumb line—is perpendicular to the geoid (a concept used in astrogeodetic levelling).
Gravity anomalies, denoted Δ*g*, are the differences between observed gravity *g* and calculated normal gravity γ. (In practice, the location where γ is evaluated differs slightly from where *g* is measured.) This gives the free-air anomaly: Δ*g* = *g* − γ. These anomalies are used in Stokes’ equation. In geophysics, they are often further reduced by removing the attraction of the topography. For a flat, horizontal plate (Bouguer plate) of thickness *H*, this attraction is *a_B* = 2π*G*ρ*H*. The Bouguer reduction is then Δ*g_B* = Δ*g_FA* − *a_B*, producing Bouguer anomalies. Here, Δ*g_FA* is the free-air anomaly. If the terrain is not flat, the local terrain height is used for *H*, and an additional terrain correction is applied.
- field
- Geodesy
- known_for
- Study of Earth's gravity field, geoid, and gravity anomalies
Lore & Background
Physical geodesy is the study of the Earth’s gravity field and its associated potential, known as the geopotential, and applies this knowledge to geodetic measurement. The Earth’s true gravity field is irregular, causing the equilibrium surface of sea water—the geoid—to also be irregular. This geoid, defined as an equipotential surface of the true geopotential that on average coincides with mean sea level, can deviate significantly from a smooth reference ellipsoid. For instance, west of Ireland the geoid rises as much as 100 metres above the reference ellipsoid, while near Sri Lanka it dips below by a similar amount. This separation is called the undulation of the geoid. The geoid extends conceptually under land as the water surface that would exist if seawater could flow freely through tunnels. Local vertical direction, materialized by a plumb line, is always perpendicular to the geoid. Gravity anomalies are computed as the difference between observed gravity and calculated normal gravity; these free-air anomalies are used in Stokes’ equation. In geophysics, these anomalies are often further reduced by removing the attraction of topography, applying a Bouguer reduction for a flat plate of given thickness, and a terrain correction where the land is not flat. Mean sea level is physically realized by tide gauge benchmarks on coasts, producing slightly incompatible vertical datums with differences of several decimetres to over one metre, due to dynamic sea surface topography.
Reader's Guide
Physical geodesy is the study of Earth’s gravity field and its associated potential, known as the geopotential, with direct applications in geodesy. Its significance lies in defining the geoid, the irregular equipotential surface that coincides with mean sea level and serves as the fundamental reference for heights. The geoid deviates from a smooth reference ellipsoid; for example, west of Ireland it rises about 100 metres above the ellipsoid, while near Sri Lanka it dips below by a similar amount. This separation is called the geoid undulation. The geoid is not limited to oceans but extends under land as the surface water would reach if allowed to flow freely through hypothetical tunnels. Because mean sea level is realized by tide gauge benchmarks on different coasts, national vertical datums can differ by decimetres to over a metre due to dynamic sea surface topography. Gravity anomalies are computed as the difference between observed gravity and calculated normal gravity, with free-air anomalies used in Stokes’ equation. In geophysics, these anomalies are further reduced by removing the attraction of topography via the Bouguer reduction, which approximates the terrain as a flat plate of given thickness, and a terrain correction is applied where the surface is not flat. Traditional instruments like theodolites rely on the gravity field to orient their vertical axis along the local plumb line using a spirit level, after which vertical and horizontal angles are measured relative to that local vertical and the horizon plane. Levelling instruments measure geopotential differences, which are converted to metric height differences. Gravity is measured in metres per second squared, and potential in square metres per second squared; a practical unit is the geopotential unit (GPU), equal to 10 square metres per second squared, so that a one-metre vertical change in ambient gravity of 9.8 metres per second squared alters potential by roughly one GPU, making GPU differences a rough measure of height above sea level.
Did You Know?
- Gravity is commonly measured in m·s⁻², and potential in m²·s⁻².
- The geopotential unit (GPU) equals 10 m²·s⁻², roughly corresponding to a 1-metre change in height.
- Bouguer anomalies are computed by subtracting the attraction of a flat plate of topography from free-air anomalies.
Frequently Asked Questions
What is Physical geodesy?
Physical geodesy is the branch of geodesy devoted to investigating Earth's gravitational field and its associated potential, known as the geopotential. It treats gravity not just as a force to measure, but as a window into the planet's mass distribution and overall shape.
What are Physical geodesy's core areas of focus?
The discipline revolves around three interconnected pillars: direct gravity measurements, modeling the geoid (the equipotential surface that best approximates mean sea level), and mapping gravity anomalies that betray subsurface density contrasts. Together these give a three-dimensional picture of how mass is arranged inside and around Earth.
Why is Physical geodesy important to real-world applications?
It supplies the gravitational corrections that make satellite positioning, precise leveling, and sea-level benchmarks physically meaningful. Without a solid gravity model, GPS height solutions and geodetic datums would lack the reference frame they depend on.
How does Physical geodesy differ from geometric geodesy?
Geometric geodesy is concerned with the mathematical form and size of the Earth, while physical geodesy adds the gravitational dimension by explaining *why* that form exists through the potential field generated by mass. In short, one describes the shape; the other explains the force behind it.
What single concept anchors the entire field of Physical geodesy?
The geopotential—the scalar potential whose spatial gradient yields the gravity vector—serves as the unifying idea. Every gravity measurement, geoid computation, and anomaly map is ultimately a different way of slicing or visualizing that one potential field.
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