Physical geodesy

Physical geodesy is a specialized branch of science focused on Earth's gravity. It studies the physical properties of the gravity field and the geopotential. The geopotential is a field of gravity potential that scientists use for many applications. Understanding these properties is vital for geodesy, which is the science of measuring Earth's shape. By studying how gravity pulls at different points, we can better map our planet.

To measure these properties, scientists use specific instruments and procedures. Traditional tools include theodolites, which are used to find vertical and horizontal angles. These instruments rely on the local gravity field to find the vertical axis. This axis follows the local plumb line, which is the direction gravity pulls straight down. Scientists also use leveling instruments to find geopotential differences between two points. They then convert these differences into metric units to express the height of a location.

Measuring these values requires specific scientific units. Gravity is commonly measured in meters per second squared (m·s⁻²). Potential is expressed as gravity multiplied by distance, which results in m²·s⁻². A more convenient unit is the geopotential unit, or GPU. One GPU equals 10 m²·s⁻². In our environment, moving one meter vertically changes your potential by approximately 1 GPU. This makes the GPU a useful tool for measuring height above sea level.

Because Earth's gravity is irregular, the sea surface is not a smooth shape. The equilibrium figure of sea water is called the geoid. The geoid represents the mathematical mean sea level. This surface is not just on the oceans; it also exists under the land. If water could move freely through tunnels under the continents, it would follow this geoid shape. The geoid is technically an equipotential surface of the true geopotential.

The geoid does not match a perfect, smooth mathematical model called a reference ellipsoid. The distance between the geoid and this ellipsoid is called the undulation of the geoid. This undulation can be quite large in different parts of the world. For example, west of Ireland, the geoid rises as much as 100 meters above the ellipsoid. Near Sri Lanka, the geoid dives nearly 100 meters below it. These variations show how uneven the Earth's gravity field truly is.

Scientists also study gravity anomalies to understand the Earth's structure. A gravity anomaly is the difference between true, observed gravity and calculated, normal gravity. One type is the free-air anomaly. In geophysics, researchers often use a process called Bouguer reduction. This reduction removes the effect of the attraction from local topography. If the land is a flat, horizontal plate, they use the Bouguer plate formula. If the terrain is not flat, they must also apply a terrain correction.

These measurements are essential for creating accurate vertical datums. A vertical datum is a reference surface used to measure height. Because of dynamic sea surface topography, different coastlines may use slightly different "near-geoids." These can differ by several decimeters or even over one meter. By mastering physical geodesy, scientists can create precise maps of the entire planet. This work connects gravity, math, and geography to define our world.