Bouguer Correction Calculator

Gravity surveying detects lateral density contrasts in the subsurface, but raw gravimeter readings are dominated by effects that have nothing to do with geology, so reductions are applied in a fixed order. The free-air correction of 0.3086 mGal per metre removes the fall-off of gravity with distance from the geocentre, obtained by differentiating the gravitational field of a sphere at Earth radius. The Bouguer correction then removes the pull of the rock that actually lies between the station and the datum, modelled as an infinite horizontal slab of thickness h and density rho, whose attraction is exactly 2 pi G rho h; with G = 6.674e-11 this reduces to about 0.1119 mGal per metre at the standard crustal density of 2670 kg/m3. Subtracting the theoretical gravity given by a reference ellipsoid formula, such as the 1980 Geodetic Reference System expression with an equatorial value near 978032.7 mGal, leaves the Bouguer anomaly. Negative anomalies of tens of mGal typically mark sedimentary basins, salt structures or granitic batholiths; positive anomalies indicate mafic intrusions, ore bodies or shallow dense basement. The density choice is the largest source of error, spanning 2200 to 2500 kg/m3 in young sediments and 2900 to 3000 kg/m3 in basalt terrain, and it can be optimized in the field by the Nettleton method, which selects the density that minimizes correlation between anomaly and topography. This calculation uses the infinite slab approximation only: it omits the terrain correction for nearby hills and valleys, which is always positive and can exceed 10 mGal in rugged country.

The correction carries the name of Pierre Bouguer, the French mathematician and hydrographer who joined the Geodesic Mission to Peru dispatched by the Paris Academy of Sciences in 1735 to measure an arc of meridian near the equator and settle whether the Earth was flattened at the poles. While in the Andes, Bouguer attempted to weigh the Earth by measuring the deflection of a plumb line near the volcano Chimborazo and by comparing pendulum periods at different elevations, and in doing so he confronted the need to account for the attraction of the intervening rock mass. His analysis appeared in La figure de la terre, published in 1749, and the plate model that bears his name follows from it. Bouguer found the mountain deflected the plumb line far less than its bulk implied, an anomaly repeated when Nevil Maskelyne conducted the Schiehallion experiment in Scotland in 1774. The explanation came from surveys in India, where discrepancies in the Great Trigonometrical Survey led John Henry Pratt and George Biddell Airy to propose competing compensation models in 1855, founding the concept of isostasy: mountains have low-density roots that cancel much of their surface attraction. Practical reduction procedures were systematized by Friedrich Robert Helmert in the 1880s, and Sigmund Hammer published his graphical zone chart for terrain corrections in 1939, a template still recognizable in the digital elevation model algorithms that replaced it.