Mass line (method)

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A ground line is in the Geosciences a line along which the mass of an elongated body is assumed to be uniformly distributed. This simplifies the computation of the body's gravity from a three-dimensional problem to a one-dimensional problem.

An important application in geophysics is terrain or topographical reduction . It is required if the force of gravity or the deviation from the perpendicular is determined on a measuring point and interpolation is to be made on points in between. Before this step, the gravity field must be smoothed, i.e. H. the terrain or the geology are mathematically “leveled”. Traditionally, the shape of the terrain or a rock body is rasterized by breaking it down into narrow vertical prisms . The effect of these narrow columns can be calculated using formulas from potential theory , which however require a precise definition of the prism surfaces and are therefore very complex.

The calculation is much easier - and almost as accurate - if the volume or the mass of the prism is approximated by a vertical line of mass points . The method was developed in the 1930s for geoid determination projects and reduces the computational effort to less than a tenth, so that it can also be evaluated in the field with pocket calculators.

A similar and equally accurate method is the two-point method , which replaces the mass line with just two points , each placed 15% from the ends of the line.

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).
  • G. Gerstbach: A quick method to reduce vertical deviation in mountains . Festschrift Wilhelm Embacher , Univ. Innsbruck, Geodät.Inst. Volume 7, Innsbruck 1984, pp. 77-98.
  • K. Jung: Gravity Methods in Applied Geophysics (= Geophysical Monographs. Volume 2). Academic Publishing Company, Leipzig 1961.