A CONTRIBUTION TO POSTMODERN GEODESY: PERSPECTIVES AND FORMS IN DESCRIBING SPACE FOR GEODESY

1. A CONTRIBUTION TO POSTMODERN GEODESY:PERSPECTIVES AND FORMS IN DESCRIBING SPACE FOR GEODESY Mairie Doufexopoulu NTUA Athens Greece

2. 1. Engineering Geodesy

3. A rigorous connection between space and measurements should be established. How space is described and how much “information” about its supposed description from a set of data provides a particular perspective. This space is physical and continuous (=definition of space in Physics) BUT by humans is sensed in Cartesian form and this reduces its final description and interpretation in 3D forms. The “geometry” of this space is adapted to the direction along the local plum-line as height. Geometry is mixed with Physics in discreteforms

4. The same space has the perspective of a model spaceand that of measurement or data space. • Thus each set of measurements provides a particular viewpoint about model space. Different NEARBY viewpoints are optimized to receive a UNIQUE representation • Finally we have : • Model space • Data space • Representation space ( various forms )

5. Out of these 3 different perspectives a geometry of model space is rigorously defined by Earth’s standards. The two other perspectives interchange perspectives according to combinations depending on the type of measurements (modes and impacts ) –variable impacts and variable criteria to optimize The “disagreements” between model space and measurement space are assumed to have a statistical distribution(=a collective impact of not known impacts). Statistical momentsdescribe the stochastic distribution by mean value, the variance ( standard deviation), covariance and ( sometimes only ) the amplitude spectrum.

6. Why Geodesy is thought as high-technology implementation Obstacles of estimating 3D coordinates: Gravity measuring “information” is rare and restricted on the terrestrial gravity Paper maps illustrate 3D coordinates separatelyfor surface and for heights Geodesy interpretation has controversies:x=AX +s+u Space of measurements is limited onto the Earth’s topography

7. Different methods in Geodesy to deal with a more complex Mathematical space For model space: separation of surface coordinates from the height For measuring space: interpretation of each measurement through the appropriate form of the model’s space coordinate geometry and a statistical model to account for “discrepancies” between model space and measuring space. The non linear character of this concrete task has been approached through the over-determined shapes by the measurements; use kind of conditional optimization of discrepancies

8. New technologies in Geodesy to deal with a more complex Physical space Using the transmission time of energy pulses to measure distances & the extent of measuring space with the profit of the satellites Considering more impacts on the global representation of measurements fromthe gravity field(geometry or statistics), and more impacts coming frommeasuring modes, inclusion of atmospheric, tropospheric effects The model space keeps a main perspective of simple Riemann geometry and gravity field models. The measured space “can tell” now more about the physical space than its model form

9. How this “new” feature can be used? To improve in a way the geodetic models. In practice this aim leads to increase / extend the statistical modeling of “discrepancies”. To use “new” types of geodetic measurements as “means” that contain information about physical ( environmental ) factors ( varying with respect to space / time domain )

10. 3.The space in the period of Space Geodesy Characterisation of Space Geodesy Observation space is extended into the whole 3D space with respect to the Earth’s Model. Model space and observation space are common. The perspective and the form of their description IS NOT. Model space is described by synchronous X, Y, Z optimal coordinates of a geocentric Cartesian frame. BUT this space includes more physical parameters in the perspective of measurements. The needs of Earth disciplines bring a transformation of the Cartesian X, Y, Z form into an Earth’s datum as φ,λ, h (or H ) description.

12. Treatment of „discrepancies” coming from the extension of observation space into model space As an extra impact, which should be eliminated by applying analytic, statistical methods ( e. g filtering ). In statistical approach the “discrepancies” may be viewed as variables composed by partly known deterministic and stochastic variations. In analytical approach (a quite familiar process in Geodesy) they simply represent a differential variation of a much simpler model space. . As physical data ( “information” ) carrying physical “information” of non stochastic character. This “information” can be used without processing to indicate or evaluate determinism ( causes ).

13. Why using the term post modern Geodesy? Post modernism is known as an ideology term by the middle of 19th century about arts, policy and thinking streams. About the space it came through Geography by the 60s and during 80s it penetrated to technical sciences; meaning is to allow different perspectives in considering the complex models Measurement space in Space Geodesy as a complex continuous space-time entity, which is much more complex than any applied reference frame for Geodetic positioning. Geodesy has reached to an end of its technology evolution for its basic goals. The time to use measurements in the frame of Geodesy for other objectives has arrived and now this space needs increased standards about the Earth’s models. This will be the Earth’s system Post modern Geodesy (in particular to the use of measurements) shows the tendency to extend the Earth’s models to the Earth’s system models.

14. The very first example of such a perspective of model’s complexity has been given long ago by the relativistic theory - as extension of Newtonian Physics. POST MODERN GEODESY DEALS WITH THE PHYSICS OF SPACE-TIME CONTINUUM FOR THE PARTICULAR OBJECTIVE TO DESCRIBE BY CARTESIAN COORDINATE GEOMETRY

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