Two point method
The two-point method is an approximation method for calculating the gravity of a complexly shaped rock body or part of terrain, see also topographical reduction . The body or the shape of the terrain is computationally broken down into narrow vertical prisms , which are usually arranged in a geographical grid. The effect of these narrow columns can be approximated by only two points in the upper and lower area of each column, which represents a significant simplification of very complex formulas of potential theory.
If the force of gravity or the vertical deviation is determined on a measuring point and interpolation is to be made to points in between, the terrain or the geology must first be mathematically "leveled". This reduction of the measured values to the idealized surface of the earth takes place traditionally through the potential of numerous square prisms, which are gradually adapted to the terrain. But since the area i. a. does not run in steps, this mathematically strict solution is not necessary. A simplification developed in the 1930s uses a vertical mass line in their axes for the effect of the individual prisms , which is sufficient for most applications in geophysics and geodesy.
It is even more precise to replace the mass line with two points 15% below the upper prism surface and 15% above its lower limit. The method was empirically developed in a geoid project at the Vienna University of Technology and supported theoretically in a dissertation at the Bergakademie Freiberg .
literature
- K.Ledersteger : Astronomical and Physical Geodesy ( Earth Measurement ) (= Handbook of Surveying . Volume V). JB Metzler-Verlag, Stuttgart 1968, Chapters VI (potential theory) and IX (weight reduction).
Individual evidence
- ↑ G. Gerstbach: A quick method for vertical deviation reduction in the mountains . Festschrift Wilhelm Embacher , Univ. Innsbruck, Geodät.Inst. Volume 7, Innsbruck 1984, pp. 77-98.
- ↑ K. Hanemann: A new method for reduction in underground gravimetry . In: Proceedings of the Alpine Gravimetry Colloquium 1983 in Leoben, Civil Engineering in the Eastern Alps. Issue 12, Vienna 1985, pp. 195-213.