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Calculation of Bouguer anomalies for the German state of Saarland

K. Seitz (1), H. Bähr (1), F. Wild (1), B. Heck (1) and K. Roth (2)

(1) Geodetic Institute, Englerstraße 7, D-76128 Karlsruhe

(2) State Office for KVK, Saarland

 

Definition of the Bouguer anomaly

The gravity value g(P) is determined gravimetrically (using measurement by weight), and it summarizes the gravity effect of all mass elements in the point P. It particularly looks at the surrounding masses, but local density contrasts also contribute to its variability in the high frequency range. If you take the measured gravity value g(P) and the free-air correction δgF, and you attach the δgB correction for terrain, the equation δgtop = δgB + δgG continues to the geoid where you can then compare that with the normal gravity value γ0 on the ellipsoid, resulting in the refined Bouguer anomaly

ΔgB = g(P) + δgB + δgG + δdF - γ0.

Its interpretation in the context of the prospection permits the localisation of the deposits of raw materials (coal, salt deposits, metallic minerals etc.) which stand out by their density contrast in the Bouguer anomalies. In addition, the formation of gravity anomalies along with digital terrain models (DTM), is an essential database for the calculation of regional and global geoid and quasi-geoid solutions.

 

Data Used

Digital Terrain Models (DTM)

Saarland Datum: DHDN, DHHN 12.5 m x 12.5 m
SRTM3  Datum: WGS84  3” x 3”
SRTM30 Datum: WGS84 30” x 30”
JGP95E Datum: WGS84 5’ x 5’

Interpolation of a DGM for the core zone (49° ≤ φ ≤ 49° 45’; 6° 10’ ≤ λ ≤ 7° 40’)
with a 0.4” x 0.6” grid spacing using the WGS84 coordinate system

 

Point gravity values (4606)

Saarland (820)
Rheinland-Pfalz (249)
Luxemburg (25)
Bureau Gravimétrique International BGI (2582)
Deutsches Schwerearchiv (930)

 

Bouguer reduction

BILD   BILD

BILD
Difference in the gravitational impact between spherical cap and a flat plate

 

Free-air gravity anomaly δgF


BILD

 

Correction for Terrain δgG

Discretisation

For the calculation of the gravitational influence of the residual topography with respect to the reference-point level, the terrain is based on DEMs approximated by suitable mass body:

  • Tesseroide
  • Cuboid (prisms)
  • Point masses
  • Weight lines
  • Surface densities

BILD

s ≤ 10 km; Tesseroid - Quader
  BILD

5 km ≤ s ≤ 10 km; Tesseroid

 

Reduction of the terrain influence δgG on the gravity




With s ≤ 10 km
 

Total core area


5° border around the core area
 

Total long range from JGP95E

 

Calculation variants of the Bouguer anomoly ΔgB for the Saarland


BILD
δgG with s ≤ 5 km; δgB from planar Bouguer anomoly
  BILD
δgG and δgB from spherical cap with s ≤ 10 km
  BILD
δgG global; δgB of spherical shell