Global Gravity Field Quantities
A global gravity field model is a mathematical representation of the real gravity pull of the Earth over its entire surface. As our planet is not perfectly spherical, has an uneven distribution of mass (due to features such as mountains, ocean trenches and dense rock) and rotates permanently, the gravity varies slightly from place to place and over time. These mathematical models enable scientists and engineers to calculate different gravity-related quantities at any given location or elevation on and outside Earth.
To precisely determine the variations in the Earth’s gravity, geodesists use a mathematical model of the Earth as a reference body. This model is called the reference ellipsoid and is a mathematical apparatus of the planet. The reference ellipsoid has the same size and flattening as the Earth, contains the same mass as the Earth and rotates at the same rate as the Earth. These four properties make it possible to infer the ellipsoid’s gravity field, commonly known as the normal gravity field. Unlike the real Earth, the mass distribution inside the ellipsoid is assumed to be homogeneous. Geodesists therefore focus on identifying the differences in gravity between the real Earth and the ellipsoid.
Using a global gravity field model alone, or in combination with the normal gravity field of the ellipsoid, it is possible to infer different gravity-related quantities, also known as ‘functionals’, at any point on Earth (see e.g., Barthelmes 2013, Ince et al. 2019). Such gravity filed quantities include:
Gravity (g) and gravitation (FG): Any object on Earth’s surface experiences a gravitational force due to the mass of the Earth and other celestial bodies, as well as a centrifugal force resulting from Earth’s rotation. The resultant of these two effects is the force of gravity. Gravitation refers to the attraction produced by mass according to Newton’s law of universal gravitation, excluding the centrifugal contribution. Gravity (g), in contrast, is the effective force (or acceleration) defined as the vector sum of gravitation and centrifugal force.
Gravitational potential (V): The work per unit mass required by gravitational attraction to bring a unit mass from infinity (where gravitational potential vanishes) to the considered point. Equivalently, this is the Newtonian gravitational attraction, excluding centrifugal potential.
Gravity potential (W): The potential of the gravity field of the Earth, being the sum of the gravitational (attraction) potential and the centrifugal potential due to the Earth’s rotation.
Gravity disturbance (dg): The difference between the magnitude of the Earth’s actual gravity and the magnitude of the normal gravity at the same point.
Gravity anomaly on the geoid (Dg): The difference between the magnitude of the Earth’s gravity at a point P₀ on the geoid (obtained by reducing observed surface gravity) and normal gravity at the point Q’₀ on the reference ellipsoid situated on the same ellipsoidal normal, Δg = g(P₀) − g(Q’₀). The two quantities thus refer to different points, in contrast to the gravity disturbance.
Gravity anomaly on the Earth’s surface (Dg): The difference between the magnitude of the Earth’s actual gravity at a point P on the Earth’s surface and normal gravity at the corresponding point Q on the telluroid, located on the same ellipsoidal normal as P, Δg = g(P) − g(Q). The telluroid is the surface formed by the points Q at which the normal potential equals the actual potential at the corresponding surface points P, U(Q) = W(P).
Disturbing potential (T): The difference between the Earth’s actual gravity potential and the normal gravgravity potential at the same point.
Geoid undulation or geoid height (N): The distance, measured along the ellipsoidal normal, between the reference ellipsoid and the geoid (the equipotential surface of the Earth’s gravity field closely approximating mean sea level). It relates ellipsoidal (h) and orthometric (H) heights through h = H + N.
Height anomaly (z): The distance, along the normal plumb line, between a point P on the Earth’s surface and the corresponding point Q on the telluroid. Equivalently, it is the separation between the reference ellipsoid and the quasigeoid. it relates ellipsoidal (h) and normal (H*) heights through h = H + z. Over the oceans the height anomaly practically coincides with the geoid undulation.
Deflections of the vertical (e): The geometric angle between the direction of the plumb line (direction of the Earth’s actual gravity vector) and the direction of the normal plumb line (direction of the normal gravgravity vector, practically coinciding with the ellipsoidal normal). It is customarily decomposed into a north-south and an east-west component.
Gravity gradient: The spatial rate of change of the gravity vector, mathematically the tensor of second derivatives of the gravity potential. It describes how gravity varies with position.
Equivalent water height: A geophysical quantity expressing mass variations as the thickness of a hypothetical water layer producing the same change in surface mass (and hence in gravity) as the observed mass redistribution.
Within the International Gravity Field Service (IGFS) of the International Association of Geodesy (IAG), the International Centre for Global Earth Models (ICGEM), provides the scientific community with a comprehensive archive of static and temporal global gravity field models of the Earth. After a validation procedure, these models are made publicly available in a standardized format with digital object identifiers (DOIs) assigned through GFZ Data Services. ICGEM also provides a web interface to calculate gravity field functionals on freely selected grids or user-defined coordinates, as well as a 3-D interactive visualization service for these functionals (geoid undulations and gravity anomalies) using static and time variable gravity field models. ICGEM’s interactive calculation and 3-D visualization services are excellent tools not only for geodesists but also for students and Earth scientists from other disciplines.
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