Free Air Gravity Correction Calculator
Compute air gravity correction using validated scientific equations. See step-by-step derivations, unit analysis, and reference values.
Formula
Free-Air Correction = 0.3086 x h (mGal) | Bouguer Correction = 2piGrho*h
Where h = elevation in meters, G = gravitational constant (6.674e-11 m3/kg/s2), rho = rock density in kg/m3. The free-air gradient of 0.3086 mGal/m represents the rate of gravity decrease with elevation above the reference ellipsoid.
Worked Examples
Example 1: Mountain Gravity Station Correction
Problem: A gravity measurement of 979,500 mGal is recorded at elevation 1200 m, latitude 40 degrees. Calculate the free-air correction and free-air anomaly.
Solution: Free-air correction = 0.3086 x 1200 = 370.32 mGal\nNormal gravity at 40 deg = 978032.7 x (1 + 0.0053024 x sin2(40) - 0.0000058 x sin2(80))\n= 978032.7 x (1 + 0.002189 - 0.0000056) = 980175.0 mGal\nFree-air anomaly = 979500 - 980175.0 + 370.32 = -304.68 mGal
Result: Free-Air Correction: +370.32 mGal | Free-Air Anomaly: -304.68 mGal
Example 2: Bouguer Anomaly at Coastal Station
Problem: At a coastal station (elevation 50 m, latitude 30 deg), observed gravity is 979,400 mGal with rock density 2500 kg/m3. Compute corrections.
Solution: Free-air correction = 0.3086 x 50 = 15.43 mGal\nBouguer correction = 2 x pi x 6.674e-11 x 2500 x 50 x 1e5 = 5.24 mGal\nNormal gravity at 30 deg = 978032.7 x (1 + 0.001326 - 0.0000044) = 979329.7 mGal\nFree-air anomaly = 979400 - 979329.7 + 15.43 = 85.73 mGal\nBouguer anomaly = 85.73 - 5.24 = 80.49 mGal
Result: Free-Air: +15.43 mGal | Bouguer: -5.24 mGal | Bouguer Anomaly: +80.49 mGal
Frequently Asked Questions
What is the free-air gravity correction?
The free-air gravity correction (also called the free-air reduction) accounts for the decrease in gravitational acceleration with increasing elevation above a reference surface, typically the geoid or sea level. Gravity decreases with height because the measurement point is farther from Earth's center of mass. The standard free-air gradient is approximately 0.3086 mGal per meter of elevation. This means for every meter you rise above the reference level, gravity decreases by about 0.3086 milligals. The correction is added to the observed gravity to compute what gravity would be at the reference level, removing the effect of elevation alone without considering the mass of rock between the station and the reference surface.
How is the free-air anomaly different from the Bouguer anomaly?
The free-air anomaly corrects only for the elevation difference between the observation point and the reference surface. It does not account for the gravitational attraction of the rock mass between the two surfaces. The Bouguer anomaly goes one step further by subtracting the gravitational effect of an infinite slab of rock with average crustal density (typically 2670 kg/m3) between the station and sea level. The formula for the Bouguer correction is 2 x pi x G x rho x h, where G is the gravitational constant and rho is rock density. The Bouguer anomaly is more useful for geological interpretation because it reveals subsurface density variations, while the free-air anomaly still contains the signal from topographic mass.
What is normal gravity and how is it calculated?
Normal gravity is the theoretical gravitational acceleration at any point on the reference ellipsoid, which approximates Earth's shape. It varies with latitude because the Earth is an oblate spheroid (flattened at the poles) and rotates. At the equator, normal gravity is about 978,032 mGal, and at the poles it is approximately 983,218 mGal, a difference of about 5,186 mGal. The International Gravity Formula (GRS80) calculates normal gravity using: g = 978032.7 x (1 + 0.0053024 sin2(phi) - 0.0000058 sin2(2phi)) mGal, where phi is geodetic latitude. This formula accounts for both the centrifugal effect of Earth's rotation and the equatorial bulge. Gravity anomalies are computed relative to this normal gravity field.
Why is rock density important in gravity corrections?
Rock density is a critical parameter in the Bouguer correction because it determines the gravitational attraction of the rock slab between the observation point and the reference level. The standard assumed density is 2670 kg/m3, representing average upper continental crust composed primarily of granite and granodiorite. Using incorrect density leads to systematic errors in the Bouguer anomaly. In areas with volcanic rock (density ~2900 kg/m3) or sedimentary basins (density ~2200-2400 kg/m3), the standard density may be inappropriate. The Nettleton method determines optimal density by selecting the value that minimizes correlation between the Bouguer anomaly and topography. Density errors become more significant at higher elevations, where the Bouguer correction magnitude is larger.
What are practical applications of free-air gravity corrections?
Free-air gravity corrections are essential in geophysics and geodesy for numerous practical applications. In mineral exploration, gravity surveys corrected for free-air and Bouguer effects reveal subsurface density anomalies that may indicate ore deposits, cavities, or geological structures. In petroleum exploration, gravity data helps map sedimentary basin depth and locate salt domes. Geodetic applications include determining the geoid shape for precise GPS height conversions. In volcanology, temporal gravity changes corrected for elevation indicate magma movement beneath volcanoes. Civil engineering uses gravity surveys to detect underground voids, abandoned mines, and karst features. Archaeologists employ microgravity surveys to find buried structures. The free-air anomaly itself is important for studying isostatic compensation and tectonic processes.
Does Free Air Gravity Correction Calculator work offline?
Once the page is loaded, the calculation logic runs entirely in your browser. If you have already opened the page, most calculators will continue to work even if your internet connection is lost, since no server requests are needed for computation.