Gravity Anomaly (Bouguer) Calculator
Find the Bouguer gravity anomaly from an observed gravity reading, station latitude, elevation, and average rock density.
⚖️ What is Gravity Anomaly (Bouguer Anomaly)?
A gravity anomaly is the difference between the gravity actually measured at a location and the gravity theoretically predicted there by an idealized model of Earth. The Bouguer anomaly is a specific, widely used type of gravity anomaly that additionally corrects for both a station's elevation above sea level and the gravitational pull of the actual rock mass beneath it, leaving behind a signal that reflects real subsurface density differences.
Exploration geophysicists and geodesists use Bouguer anomaly constantly, to map buried ore bodies, salt domes, and sedimentary basins by their distinctive density signatures, to study how mountain ranges are isostatically compensated by low-density crustal roots at depth, to estimate crustal thickness variations across a region, and to detect subsurface voids, caves, or engineering hazards from small local anomalies.
A common misconception is that mountains, being large masses of extra rock, should always show a strongly positive gravity anomaly. In practice their Bouguer anomaly is usually negative, because mountain ranges typically "float" on a thick, buoyant, low-density crustal root extending deep beneath them (isostasy), and that deep mass deficit outweighs the visible topographic mass excess.
This calculator applies the 1967 International Gravity Formula for normal gravity, plus the standard free-air and simple Bouguer slab corrections, to compute the final Bouguer anomaly from a station's observed gravity, latitude, elevation, and rock density, and charts how normal gravity itself varies with latitude.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Mid-Latitude Station at Moderate Elevation
gobs = 980480.71 mGal, φ = 45°, h = 500 m, ρ = 2.67 g/cm³
Example 2 — Low-Latitude Mountain Station
gobs = 977634.26 mGal, φ = 10°, h = 2000 m, ρ = 2.67 g/cm³
Example 3 — High-Latitude Coastal Station
gobs = 981920.70 mGal, φ = 60°, h = 10 m, ρ = 2.67 g/cm³
❓ Frequently Asked Questions
🔗 Related Calculators
How do you calculate Bouguer gravity anomaly?
Bouguer anomaly equals observed gravity minus theoretical normal gravity at that latitude, plus the free-air correction, minus the Bouguer slab correction: Delta g_B = g_obs - g_phi + 0.3086h - 0.04193*rho*h, where h is station elevation in meters and rho is average rock density in g/cm3.
What is normal gravity in the Bouguer anomaly formula?
Normal (theoretical) gravity g_phi is the gravity value predicted at sea level for a given latitude by an idealized reference ellipsoid model of Earth, ignoring local geology. This calculator uses the 1967 International Gravity Formula, g_phi = 978031.85 x (1 + 0.0053024 sin^2(phi) - 0.0000059 sin^2(2phi)) in mGal.
What is the difference between free-air and Bouguer correction?
Free-air correction (0.3086 mGal per meter of elevation) accounts only for a station's height above sea level, treating the space beneath it as empty air. Bouguer correction (0.04193 x rho mGal per meter) then adds back the gravitational pull of the actual rock mass that fills that space between the station and sea level.
Why is Bouguer anomaly usually negative over mountains?
Mountain ranges are typically isostatically compensated by a low-density crustal root extending deep beneath them, per the principle that thick, buoyant, less-dense crust floats higher, exactly like a large iceberg extends deeper below the waterline. That deep mass deficit produces a negative Bouguer anomaly, even though the visible topography is a mass excess.
What density value should I use for the Bouguer correction?
The standard default is 2.67 g/cm3, the traditional average density for continental crustal (granite-like) rock, used almost universally unless a survey has independently measured local rock density, in which case that measured value should replace the default for a more accurate correction.
What is a typical range for Bouguer anomaly values?
Over continental crust, Bouguer anomalies typically range from roughly -200 mGal in high mountain ranges with thick crustal roots (like parts of the Himalayas or Andes) up to about +50 mGal over dense mafic or oceanic-affinity crust, with values near zero common over normal-thickness continental crust close to sea level.
Why does the free-air correction depend only on elevation, not density?
Free-air correction accounts purely for the geometric effect of being farther from Earth's center of mass, gravity naturally weakens with distance regardless of what fills that distance. Density only enters once you correct for the actual rock mass physically present between the station and sea level, which is what the separate Bouguer correction handles.
Does this calculator account for terrain corrections?
No, this calculator applies the standard simple Bouguer slab correction, which models the rock beneath the station as an infinite flat slab of uniform density. A full terrain-corrected Bouguer anomaly additionally accounts for the irregular shape of nearby topography, a more advanced correction requiring detailed elevation data beyond a single station's inputs.
Why does latitude affect normal gravity?
Earth is not a perfect sphere, it bulges at the equator and is flattened at the poles due to rotation, and centrifugal force from that rotation is strongest at the equator. Both effects combine so that measured gravity is lower at the equator and higher at the poles, exactly the sin-squared latitude dependence the normal gravity formula captures.
What units does this calculator use?
Observed gravity and all correction results are in milligals (mGal), the standard gravimetry unit (1 mGal = 0.00001 m/s2). Latitude is in decimal degrees, elevation in meters above sea level, and density in grams per cubic centimeter (g/cm3).