Free Air Gravity Correction Calculator

Gravity falls off with height, so a measurement made above the reference ellipsoid must be reduced before it can be compared with theory. Differentiating the Newtonian field of a sphere at Earth's radius gives about 0.3086 mGal per metre, the free-air gradient, and the correction 0.3086 times h is added back to the observed value. One mGal is 10^-5 m/s2, roughly one millionth of surface gravity, and modern field gravimeters resolve about 0.01 mGal, so station elevation must be known to a few centimetres or the correction dominates the error budget. The free-air anomaly is observed gravity minus normal gravity from the international formula, plus this correction; normal gravity itself runs from about 978,033 mGal at the equator to 983,218 mGal at the poles. The free-air reduction removes only the distance effect, not the mass of rock between the station and the datum. Subtracting the attraction of an infinite slab of that rock, 2 pi G rho h, or about 0.04193 times rho times h in mGal for density in kg/m3, produces the Bouguer anomaly, which is what geologists interpret for subsurface density structure. The conventional slab density is 2,670 kg/m3 for continental crust; sedimentary terrain may warrant 2,200 to 2,400 and volcanic terrain 2,800 to 3,000, and Nettleton's method chooses the density that decorrelates the anomaly from topography. Three caveats matter: the flat-slab assumption fails in rugged country and needs a separate terrain correction, a second-order term of roughly -0.0001189 times h squared becomes significant above a few kilometres, and tidal and instrument-drift corrections must be applied before any of this.

Pierre Bouguer measured the deflection of a plumb line near Chimborazo during the French Geodesic Mission to Peru of 1735 to 1744 and published his results in La figure de la terre in 1749, founding the practice of correcting gravity observations for elevation and for the attraction of intervening topography. The elevation reduction on its own came to be associated with Herve Faye in the nineteenth century, and the free-air anomaly is still called the Faye anomaly in parts of the geodetic literature. Field gravity became a practical exploration tool in the twentieth century. The torsion balance developed by Lorand Eotvos in the 1890s located the Nash salt dome in Texas in 1924, the first oil discovery credited to a geophysical instrument. Lucien LaCoste's zero-length spring, devised in 1934 while he was a student at the University of Texas, led to the LaCoste and Romberg gravimeters that made mGal-level surveying routine. Standardized normal gravity followed in stages: the International Gravity Formula of 1930, then the Geodetic Reference System 1967, and GRS80, adopted by the International Union of Geodesy and Geophysics in 1979, whose constants this calculator uses. L.L. Nettleton published his profile method for choosing reduction density in Geophysics in 1939, and it is still applied in the field today.