Astro-geodetic platform for high accuracy geoid determination (AGEO)

Programme for Research-Development-Innovation for Space Technology and Advanced Research - STAR

Determining Earth shape and size is one of the oldest concerns of our civilization. In solving this problem have contributed various scientific fields among which the most important are: geodesy, astronomy, geodynamics and remote sensing. For starters the obtained solutions were local, based on simplifying assumptions, and later, with technological evolution, the solutions have reached on areas increasingly large and close to reality, up to current models and solutions that provide global high resolution determinations, which in addition, besides Earth geometry determination are studying the associated gravitational field.

Present proposal is a research project framed in "Space Science" scientific area, being connected to "Development of technologies, system, sensors and equipment for space application" expertise domain, through its specific activities following the development of a new technology/system. The project represents an element of space activities sustainability for a medium and long term because it is only a step for complex studies related to Earth observing and monitoring at national territory.

Geoid determination as physical figure of the Earth and reference equipotential surface represents one of the major tasks of geodesy, integrated in the present efforts of understanding the Earth as a system. Development of satellite geodesy, lunar laser ranging (LLR), satellite laser ranging (SLR) and radio-interferometry with very long baseline (VLBI) represented a major change of geodetically concepts as follows: static → dynamic, Earth → Earth system, Newtonian → Einstein's theory of gravity. Earth system means that its constituent parts of different nature, solid, liquid, gaseous, interact between them in a complex manner, showing large variations in space and time and influencing each other. Earth's gravitational potential and Earth's magnetic field represent the basement of research in geodesy and geophysics, which together with complementary data (seismic, global atmosphere, solar and planetary astronomy) represent the most valuable sources of information about the structure, composition, evolutionary processes and the past-present-future behavior of our planet.

The geoid represents the surface, which in land surveying is usual named sea level. This surface closely approximates sea level in the absence of disturbing forces as winds, ocean currents and tides. Practically, the geoid cannot be expressed into a simple mathematical form. We can see the geoid as the equilibrium and rest state of the ocean's surface extended under the continents. In the every point on the Earth's surface we have a reference direction, tangent to the force line of the terrestrial gravity field. This direction is named local vertical or plumb line direction and it is normal to the geoid, not to the Earth's topographical surface. In contrast, the ellipsoid is a man-made surface, with an easy mathematical description and which, theoretically, approximates as good as possible the geoid. Therefore, through the same point on the Earth we have the second reference direction, normal to the ellipsoid. Angular difference between normal to the geoid and normal to the ellipsoid, in the same point on the Earth's topographical surface, represent so called vertical deviation (Helmert definition). In a similar way is defined the vertical deviation at the geoid surface (Pizzetti definition), but this cannot be directly observed because of terrestrial relief (topographic masses). Practically, these angles indicate the relative position ellipsoid-geoid. The astro-geodetic method of geoid determination is the only one that can directly provide vertical deviation at the Earth's surface, by comparisons between astronomical and geodetic coordinates. In fact, this method provides the meridian and prime vertical components of the vertical deviation. Another quantity involved in the geoid modeling is the geoid-ellipsoid separation (sometime named geoid undulation) which represents the distance along the vertical (or plumb line) between geoid and ellipsoid. The separation can be obtained by gravimetric measurements, combined GNSS observations with geodetic geometric levelling or from gravity potential coefficients determined by satellite measurements. Knowing the geoid-ellipsoid separations it is possible to derive vertical deviations at the geoid surface, which is relatively useless since the almost all terrestrial measurements (except spatial distances) are realized towards local vertical at the Earth's topographic surface. The configuration of the vertical and the shape of the geoid are correlated and the astronomical coordinates are determined with respect to the local vertical from observation's point.

The verticals of the points on the Earth's physical surface, rigorously speaking, are not even plane curves, rather crooked curves, naturally with enough small torsion. However, the angle of deviation varies along the local vertical meaning that the vertical deviation at geoid surface, in general, is not equal with vertical deviation at Earth's surface. For linking these two quantities it is necessary to know the curvature of the local vertical (or more exactly the deflection caused by the curvature, named in scientific literature vertical deflection) between geoid and topographical Earth's surface. Unfortunately, the deflection cannot be observed because of terrestrial masses, it can be only estimated at a low accuracy level.

As we have seen, the geoid reflects the anomalies in the masses distribution and the density inhomogeneities in the terrestrial crust over a certain zone or global, for the whole Earth. Satellite missions as CHAMP (CHAllenging Minisatellite Payload), GOCE (Gravity field and steady-state Ocean Circulation Explorer) or GRACE (Gravity Recover and Climate Experiment) provide global long-wave global geoid models (smooth surfaces) which mainly serve as reference for a better global or zonal geoid model. Thus, a combination between satellite derived models and regional data from terrestrial measurements is the suitable solution for obtaining a high resolution geoid. Terrestrial methods as the astro-geodetic one are able to detect short wavelength structures of the geoid beside gravimetric, GNSS and leveling. All this terrestrial methods have both advantages and disadvantages, general rules being their use in various combination.

In the present project it will be develop an astro-geodetic mobile platform, which will allow geoid determinations at a reasonable price. Astro-geodetic method itself offers some sure advantages. In addition, using modern equipments (high accuracy geodetic instruments, CCD micro camera and GPS time transfer) the astro-geodetic geoid determination becomes a feasible solution at a country level and not only locally. A high- resolution geoid obtained by combining astro-geodetic data with other type of measurements (GNSS-levelling combination or/and gravimetric measurements) represents a good choice for our country, characterized by a various relief. The project results can be extended easily at the whole national territory. Many European countries have adopted astro-geodetic geoid determination as a solution for high accuracy local geoid determination, especially in rugged areas. The platform which will be developed in the project, based on a geodetic instrument is cheaper and easy to use than the solutions based on zenithal cameras. It is an important aspect since the created technology from project can be used by personnel without a high level of education in geodesy or astronomy, which decrease the operational costs (personnel costs). An important advantage of the astro-geodetic method is the fact that a local geoid can be determined directly from pointy (un-relative) determination, within the interest area. This is in contrast with the gravimetric method, for instance even if it has to be considered that the astro-geodetic method provides relative geoid undulations (not quasi-geoid).

References

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