Gravity Bouguer Anomaly Calculator: Free Air and Bouguer Corrections

A raw gravity meter reading mixes together several effects that have nothing to do with the rocks you are actually trying to map. Latitude changes the earth’s normal gravity field by hundreds of milligals on their own, and simply standing on a hill closer to or farther from the earth’s center changes the reading too. The Bouguer anomaly strips all of that away, leaving a number that reflects subsurface density variation, which is what gravity surveys are actually looking for. Use the calculator above to walk through each correction step by step.

The Corrections, One at a Time

Latitude correction accounts for the earth’s flattening and rotation, both of which make normal gravity increase from about 978,032 mGal at the equator to about 983,219 mGal at the poles, using a standard reference formula. Free air correction adds back gravity lost simply from being farther from the earth’s center at higher elevation, at a rate of about 0.3086 mGal per meter. Bouguer correction then removes the extra attraction from the slab of rock between the station and the reference datum, since that slab pulls the reading up and needs to be subtracted back out.

The Formula

Bouguer anomaly = gobs minus gtheory plus free air correction minus Bouguer correction

where gobs is the raw meter reading, gtheory is the latitude dependent normal gravity, the free air correction is 0.3086 times elevation in meters, and the Bouguer correction is 0.04193 times density in g/cm3 times elevation in meters. The calculator above shows every intermediate value so you can see exactly how much each correction contributes to the final anomaly.

Worked Example

At 45 degrees latitude with a station 500 meters above sea level, an observed reading of 980,500 mGal and a rock density of 2.67 g/cm3, the theoretical gravity at that latitude works out to about 980,620 mGal. The free air correction adds about 154.3 mGal, and the Bouguer correction removes about 56.0 mGal, leaving a free air anomaly of about 34.3 mGal and a simple Bouguer anomaly of about negative 21.7 mGal, a small residual that reflects real subsurface density contrasts once every predictable effect has been stripped away.

What a Bouguer Anomaly Tells You

• Positive anomalies often indicate denser rock at depth, such as basic igneous intrusions or ore bodies
• Negative anomalies commonly reflect sedimentary basins, salt bodies, or granite plutons, all lower density than average crust
• Regional gravity trends help constrain basin shape and basement depth over an entire survey area
• Terrain corrections, not covered here, are needed in areas with significant nearby topography for full accuracy

Related Calculator and Reference

For density values used in the slab correction, see the Rock Density Calculator. The correction formulas and the 1980 international gravity formula used here follow the summary in the SEG Wiki entry on the gravity method.