Gravity Anomaly Calculator

A gravity anomaly is the residual left after observed gravity has been stripped of everything a simple rotating-ellipsoid Earth would predict. Theoretical gravity comes from the International Gravity Formula; the 1967 version takes 978,031.85 mGal times a latitude term in sin squared and sin to the fourth, rising to about 983,220 mGal at the poles. Adding the free-air correction of 0.3086 mGal per metre yields the free-air anomaly. Removing the attraction of the rock slab between station and datum, 0.04193 times rho times h in mGal, gives the simple Bouguer anomaly. Adding a terrain correction - always positive, since both hills above the station and valleys below it act to reduce observed gravity - gives the complete Bouguer anomaly. What survives is the signal of density contrast at depth. Salt at about 2,200 kg/m3 embedded in 2,500 kg/m3 sediment produces a negative closure of a few mGal over a dome, massive sulphide and iron ore at 4,000 to 5,000 kg/m3 produce sharp positive highs, and sedimentary basins read strongly negative. Over broad regions the Bouguer anomaly is dominated by isostasy, because mountains are underlain by thick low-density crustal roots, driving values to -300 mGal or worse over major ranges; this is why an isostatic anomaly, computed by restoring an Airy or Pratt compensating mass, is used to isolate crustal-scale structure. Reduction density matters throughout: 2,670 kg/m3 is conventional for continental crust, but 2,200 to 2,500 suits sedimentary terrain and 2,800 to 3,000 volcanic terrain, and an error here leaves topography visibly imprinted on the anomaly map.

Gravity anomalies were discovered before they could be measured directly. Pierre Bouguer found during the French expedition to Peru of 1735 to 1744 that Chimborazo deflected a plumb line far less than its visible mass should. The same kind of discrepancy appeared in the Great Trigonometrical Survey of India, where George Everest reported in 1847 an unexplained mismatch in the latitude difference between the stations at Kalianpur and Kaliana. In 1855 John Henry Pratt and George Biddell Airy published competing explanations - lateral density variation in Pratt's model, deep low-density roots in Airy's - and Clarence Dutton named the underlying principle isostasy in 1889. Instrumentation caught up in the twentieth century. The torsion balance of Lorand Eotvos mapped subsurface density gradients from the 1890s and led to the Nash Dome discovery in Texas in 1924. Felix Andries Vening Meinesz carried pendulum apparatus aboard submarines from 1923, revealing the strong negative belts over ocean trenches that were later understood as markers of subduction. John Hayford and William Bowie of the US Coast and Geodetic Survey computed systematic isostatic reductions in the early 1900s, putting Airy's idea to quantitative use. Standard reduction formulae were codified successively as the International Gravity Formula of 1930, GRS67 and GRS80, and satellite missions including GRACE and GOCE now supply global anomaly fields into which ground surveys are tied.