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

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 δg_F, and you attach the δgB correction for terrain, the equation δg_top = δg_B + δg_G 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

Δg_B = g(P) + δg_B + δg_G + δd_F - 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

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

Free-air gravity anomaly δg_F

Correction for Terrain δg_G

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: