Free-Air Correction

Key Takeaways

• The derivation of the free-air correction gradient (0.3086 mGal/m) follows from the inverse-square law of gravitation: the gravitational acceleration at distance r from the center of the Earth is g = GM/r^2, where G is the gravitational constant and M is the Earth's mass; differentiating with respect to r gives dg/dr = -2GM/r^3 = -2g/r; at the Earth's surface (r = 6,371 km, g = 980 Gals), this gives dg/dr = -2 * 980,000 mGal / 6,371,000 m = -0.3086 mGal/m; the negative sign indicates that gravity decreases with increasing elevation, and the free-air correction adds a positive correction (to increase the measured gravity back toward what it would be at the datum level) for stations above datum; the 0.3086 mGal/m gradient is a constant for all practical purposes of land and airborne gravity surveys (it varies slightly with latitude because the Earth's radius and surface gravity are latitude-dependent, but the variation is small relative to the precision of practical gravity surveys and the gradient is treated as constant in standard gravity processing).
• The free-air anomaly (the result of applying the free-air correction plus the latitude correction to the observed gravity) has a specific geological interpretation that distinguishes it from the Bouguer anomaly: the free-air anomaly is approximately zero over regions in isostatic equilibrium (where the mass deficit of topographic highlands is compensated at depth by less dense crustal roots, and the mass excess of ocean basins is compensated by denser mantle material), because the free-air correction removes the elevation effect while the isostatic compensation at depth produces the mass that restores the surface gravity to near the reference value; the free-air anomaly is positive over mass excesses (dense rocks at shallow depths, subducted slabs, or incompletely isostatically compensated topographic highs such as young mountain belts) and negative over mass deficits (deep sedimentary basins, thick continental crust under plateaus, or regions of excess crustal thickness from continental collision); in petroleum exploration, the free-air anomaly over oceanic sedimentary basins reflects the combined effect of the low-density sediment column, the bathymetry (seafloor topography), and the isostatic structure of the crust, and it is one of the primary products used by marine gravity interpreters to map basin structure before seismic data acquisition.
• The precision required for the free-air correction in petroleum gravity surveys is determined by the precision of the elevation survey: because the free-air correction gradient is 0.3086 mGal/m, an elevation error of 1 meter introduces an error of 0.3086 mGal in the free-air corrected gravity; for regional gravity surveys with a precision of 1 to 5 mGal, elevation errors of 3 to 16 meters are acceptable; for high-resolution gravity surveys intended to map dense basement structures or salt bodies with lateral density contrasts of 0.2 to 0.5 g/cc, the required precision is 0.01 to 0.1 mGal, demanding elevation precision of 3 to 30 centimeters; in historical land gravity surveys, elevation was measured by leveling (a traditional geodetic technique with precision of a few centimeters over short distances and a few decimeters over long traverses), making the elevation survey often the most time-consuming and expensive part of the gravity survey operation; the introduction of differential GPS (dGPS) in the 1990s and subsequently RTK-GPS (real-time kinematic GPS) revolutionized gravity survey elevation control by providing 1 to 5 centimeter elevation accuracy at survey vehicle speeds, reducing the elevation survey cost by an order of magnitude and enabling high-resolution gravity surveys that were not practical with leveling.
• In marine and airborne gravity surveys, the free-air correction must account for the continuously varying elevation (depth or altitude) of the measurement platform: a marine gravity meter mounted on a survey vessel measures gravity at a varying depth of sensor below the sea surface as the vessel pitches and rolls in the sea state, and the free-air correction must be computed using the instantaneous sensor depth at each measurement time rather than a single station elevation; the much larger motion corrections required in marine and airborne gravity (the Eotvos correction for the effect of the survey platform's eastward velocity on the measured gravity, and the vertical acceleration correction for the effect of platform heave on the gravimeter reading) are typically larger than the free-air correction and dominate the data processing workflow; airborne gravity gradiometry (which measures the spatial gradient of the gravity field rather than the field itself) is less sensitive to elevation errors because the gradient measurement is inherently referenced to the separation between the two sensors in the gradiometer, rather than to an external elevation datum, reducing the impact of the free-air correction uncertainty on the final data quality.
• The Bouguer correction, applied after the free-air correction in land gravity surveys over areas of significant topographic relief, accounts for the gravitational attraction of the mass of rock between the measurement station elevation and the datum level (the "Bouguer slab" correction, which assumes the intervening mass has infinite horizontal extent and a density of approximately 2.67 g/cc for continental rocks) and the terrain correction (which removes the excess or deficit of attraction from topographic features that deviate from the infinite slab model -- hills near the station attract the gravimeter upward, reducing the measured gravity, and valleys near the station reduce the downward attraction, also reducing the measured gravity relative to the infinite-slab approximation); after applying the free-air correction, the Bouguer correction, and the terrain correction, the resulting Bouguer anomaly reflects only the lateral variations in subsurface density that are of geological interest, with the topographic effects removed; in offshore and airborne gravity surveys where there is no rock mass between the instrument elevation and the seafloor or land surface, only the free-air correction (plus the Eotvos and dynamic corrections) is needed, and the offshore Bouguer anomaly over water is computed using the density contrast between water and the reference crustal density rather than an actual rock slab.