Topographic Gravity Field Models
Topographic gravity field models represent the gravitational potential generated by the Earth’s topographic masses, and any functional derived from it (gravitational attraction, gravity anomalies and disturbances, geoid contributions, gravity gradients). They are also referred to as topographic potential models, topography-related models, synthetic gravity field models or forward models.
The gravitational effect of the topography is computed from two ingredients:
- A model of the geometry of the topography, i.e. a digital elevation model (DEM), possibly complemented by bathymetry and ice-thickness data. For the forward computation, the topographic masses described by the DEM are discretized into elementary bodies (prisms, tesseroids, point masses, polyhedra) whose attraction is evaluated by Newton’s law of universal gravitation and summed; alternatively, the computation is carried out in the spectral domain through a spherical or ellipsoidal harmonic expansion of the topographic potential.
- Assumptions about the density of the topographic masses. Since detailed knowledge of the composition and internal mass distribution of the topography is unavailable, standard density values are adopted for rock, ocean and lake water, and ice, or laterally varying density models are introduced where available.
In contrast to gravity field models estimated from observed gravity data, topographic models are forward models: their output is a prediction, not an adjustment to observations. Their accuracy therefore depends mainly on:
- the spatial resolution of the model;
- the accuracy of the underlying elevation (and bathymetry/ice) models;
- the validity of the mass-density assumptions;
- the approximation adopted for the arrangement of the masses (planar, spherical or ellipsoidal); and
- the forward computation technique.
It should be stressed that forward models capture only the part of the gravity field generated by the modelled topographic masses. They therefore complement, but cannot replace, gravity field models based on actual observations.
Topographic masses usually comprise all solid matter forming the Earth’s topography, such as rock, sand and basalt, but ocean water, lake water and ice sheets may be included as well. The models may or may not account for isostasy, i.e. the buoyant compensation of topographic loads at depth. Models neglecting compensation are referred to as uncompensated topographic potential models, whereas those including it are called topographic-isostatic models.
Typical applications include:
- terrain or topographic gravity reductions;
- smoothing of the gravity field prior to interpolation or geoid computation ;
- modelling of the omission error of truncated global geopotential models (spectral enhancement) ;
- Bouguer anomaly computation ;
- high-resolution synthetic gravity modelling; and
- independent evaluation of satellite-only gravity field models.
IAG Service
Under the umbrella of 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 state-of-the-art archive of topographic global gravity field models. 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 different gravity functionals.
Data Sources
