Topographical reduction
In geodesy and geophysics, topographic reduction is the mathematical elimination of the topography .
This reduction is necessary for a wide variety of tasks in order to take into account the disturbances in the terrestrial gravity field caused by the terrain or to smooth the field . In the high mountains they can deflections up to ± 50 "( arc sec cause) while the gravity z. B. decrease in the Central Alps by about 200 milligals .
Usually, however, the entire topography is not "lifted" down to the geoid , but the terrain is "leveled" at the height of the respective measuring point . This is done up to distances of a few dozen kilometers with the help of different methods:
- by means of a large-scale topographical map and a template with circular ring sectors in order to be able to read off the terrain heights around the measuring point
- through a digital terrain model from a database or
- by approximation methods :
- with mass points or mass lines
- with the two-point method
- with area assignments
- with the potential of the simple layer .
The first method takes a relatively long time, but is theoretically preferable. The second method has the advantage of automation , but it has to take into account some potential theoretical stage effects in the computer program.
With the approximation methods you can - depending on the effort - approximate the strictly determined values up to a few percent.
See also
Literature and web links
- Karl Ledersteger : Astronomical and Physical Geodesy (Earth Measurement) (= Handbook of Surveying . Volume V), JBMetzler-Verlag, Stuttgart 1968, Chapter 4 (vertical deviation, geoid determination) and 11 (gravity reductions).
- Torben Schüler: Calculation of the topographical proportions of vertical deviations. Archived from the original on September 30, 2007 ; accessed on July 15, 2016 .
- High precision Geoid Determination using Astro & Gravimetric Data (N.Kühreiber, TU Graz) ( Memento from August 21, 2010 in the Internet Archive ) (PDF file; 1.56 MB)