Bouguer Anomaly

The Bouguer gravity anomaly (Δ*g*_B)—named after eighteenth-century French geophysicist, astronomer, and geodesist Pierre Bouguer (1698–1758)—is the fundamental potential-field observable in solid-Earth geophysics used to map lateral variations in subsurface rock density across the crust and upper mantle. When a gravimeter measures the local gravitational acceleration g_obs at a point on Earth's surface (at elevation h above the geoid or mean sea level), that raw reading reflects not only deep geological structures, but also the station's latitude, its distance from Earth's center of mass, and the downward gravitational pull of the topographic rock mass standing between the station and sea level.

By sequentially subtracting the theoretical reference ellipsoid gravity (g₀(φ)), restoring the vertical elevation gradient (the Free-Air Correction, +Δ*g*_FA), and removing the gravitational attraction of the intervening topographic rock slab (the Bouguer Slab Correction, −Δ*g*_B,slab, plus the Terrain Correction, +*T*), the resulting Complete Bouguer Anomaly isolates gravity perturbations originating below the reference datum: exposing deep Airy isostatic crustal roots beneath mountain belts (strongly negative Δ*g*_B), thin dense oceanic crust over elevated mantle (strongly positive Δ*g*_B), buried sedimentary basins, salt diapirs, magma chambers, and meteorite impact craters (such as the Chicxulub impact structure).

Because Earth's mean surface gravitational acceleration is ~9.80665 m s⁻² (980.665 Gal, where 1 Gal = 1 cm s⁻², named after Galileo Galilei), whereas crustal density anomalies perturb local gravity by only parts per million to parts per hundred million, geophysicists express gravity anomalies in milligals (mGal) or gravity units (gu):

• 1 milligal (1 mGal) = 10⁻³ Gal = 10⁻⁵ m s⁻² = 10 μm s⁻² (approximately 1 part per million of Earth's normal gravity g₀). Modern portable spring/quartz and superconducting gravimeters achieve precision of 0.001 to 0.01 mGal (1–10 μGal).

To reduce a raw surface measurement g_obs at geodetic latitude φ and orthometric elevation h (in meters above the geoid) to the Complete Bouguer Anomaly (Δ*g*_B), four sequential physical corrections are applied:

When Pierre Bouguer conducted pendulum and plumb-line deflection measurements near the 6,263 m volcano Chimborazo in the Ecuadorian Andes during the 1735–1744 French Geodesic Mission to the Equator, he was astonished to discover that the gravitational attraction of the massive Andean mountain range was far smaller than predicted from the volume of visible surface rock. A century later, Sir George Everest and John Henry Pratt (1854–1855) documented the exact same mass deficit along the southern flank of the Himalayas in India.

This apparent "missing mass" under mountain ranges is the geophysical signature of isostasy—the hydrostatic equilibrium of the buoyant crust floating on the denser, ductile asthenospheric mantle:

1. Continental Mountain Belts — Strongly Negative Bouguer Anomalies (Δ*g*_B = −150 to −450 mGal): Under George Biddell Airy's (1855) root-compensation model (and Pratt's thermal/density compensation model), a high mountain range of elevation h and crustal density ρ_c ≈ 2.67–2.75 g cm⁻³ is held up buoyantly by a deep low-density crustal root of thickness r = h · ρ_c / (ρ_m − ρ_c) ≈ 4.5 h to 6 h protruding downward into the denser upper mantle (ρ_m ≈ 3.30 g cm⁻³), depressing the Mohorovičić discontinuity (Moho) from ~35 km under cratons to ~65–75 km beneath the Tibetan Plateau and Central Andes. Because the Bouguer correction removes the positive attraction of the visible surface mountain (h) above sea level, what remains in the Bouguer Anomaly (Δ*g*_B) is the gravitational signature of the subsurface mass deficit (Δρ = ρ_c − ρ_m ≈ −0.55 g cm⁻³) of the deep crustal root:

Meanwhile, because the positive attraction of the surface mountain nearly cancels the negative deficit of the deep root directly beneath it, the Free-Air Anomaly (Δ*g*_F) over wide, isostatically compensated plateaus remains close to 0 mGal.

1. Ocean Basins — Strongly Positive Bouguer Anomalies (Δ*g*_B = +200 to +400 mGal): In deep ocean basins (water depth d ≈ 4–5 km), the oceanic crust is only 6–7 km thick, so dense upper mantle peridotite (ρ_m ≈ 3.30 g cm⁻³) rises to within ~11–12 km of sea level (an "anti-root"). When the marine Bouguer correction mathematically replaces the 4–5 km layer of low-density seawater (ρ_w = 1.03 g cm⁻³) with standard rock (ρ_c = 2.67 g cm⁻³), the shallow high-density mantle underneath produces a +250 to +400 mGal positive Bouguer anomaly:

When long-wavelength regional isostatic trends are subtracted to yield the Residual Bouguer Anomaly, short-wavelength gravity highs and lows map upper-crustal geological targets directly via Gauss's theorem (which enables direct calculation of the total excess or missing mass M = (1 / 2π*G*) ∬ Δ*g*_B dx dy independent of target depth):

• Negative Residual Bouguer Anomalies (Low-Density Deficit Δρ < 0):
• Sedimentary Basins & Halite Salt Diapirs: Thick sequences of porous clastic sediments (ρ ≈ 2.1–2.4 g cm⁻³) or rising rock-salt domes (NaCl, ρ ≈ 2.16 g cm⁻³ intruding denser 2.5 g cm⁻³ shales) produce sharp −5 to −60 mGal gravity lows used since the 1920s to trap petroleum reservoirs along the Gulf of Mexico.
• Felsic Granitic Plutons and Partially Molten Silicic Magma Chambers: Low-density granite batholiths (ρ ≈ 2.60 g cm⁻³) and silicic caldera magma reservoirs (such as Yellowstone and Toba) produce −20 to −60 mGal Bouguer lows.
• Buried Impact Craters (The Chicxulub Crater Discovery): In 1978–1981, geophysicists Glen Penfield and Antonio Camargo analyzing Mexican national oil company (PEMEX) Bouguer gravity surveys across the flat carbonate platform of the northern Yucatán Peninsula discovered a 180 km diameter concentric multi-ring Bouguer gravity low (−20 to −30 mGal, caused by fractured impact breccia and melt rock) surrounding a central +15 to +20 mGal gravity high (uplifted deep basement peak ring)—identifying the buried 66.04 Ma Cretaceous–Paleogene (K–Pg) Chicxulub impact structure.
• Positive Residual Bouguer Anomalies (High-Density Excess Δρ > 0): Mafic/ultramafic intrusions (gabbros, peridotites, ρ ≈ 2.9–3.3 g cm⁻³), ophiolite thrust sheets (such as the Troodos ophiolite on Cyprus, +100 to +200 mGal), massive sulfide (VMS) and chromite/magnetite ore bodies, and failed continental rifts (such as the Midcontinent Rift Gravity High across Lake Superior to Kansas, where 1.1 Ga flood basalts fill the crust).

How does the coherence between Bouguer Gravity and Topography measure the strength (elastic thickness T_e) of tectonic plates?

Not all topographic features are locally compensated directly beneath themselves like floating icebergs (local Airy isostasy, where the plate has zero bending strength, T_e = 0). Instead, the lithosphere behaves as a continuous elastic plate of effective elastic thickness T_e (ranging from T_e ≈ 5–15 km in hot young oceanic plates and active continental rifts to T_e ≈ 60–110 km in cold ancient cratons) with flexural rigidity D = E T_e³ / [12(1 − ν²)]:

• Short-Wavelength Loads (λ < 50–100 km, such as individual volcanic cones or narrow canyons): Supported almost entirely by the mechanical bending stiffness (D) of the lithosphere without deflecting the underlying Moho; consequently, short-wavelength mountains exhibit near-zero Bouguer anomaly correlation with Moho depth and strong positive Free-Air anomalies.
• Long-Wavelength Loads (λ > 500–1,000 km, such as the Tibetan Plateau or Colorado Plateau): Exceed the flexural strength of the plate, forcing the lithosphere to bend downward into the asthenosphere and achieve full Airy isostatic compensation (yielding a coherence of ~1.0 between topography and negative Bouguer gravity). By computing the spectral admittance and coherence between 2D Fourier transforms of topography H(k) and Bouguer gravity Δ*G*_B(k) as a function of wavenumber k = 2π/λ (Forsyth, 1985), geophysicists map the mechanical strength (T_e) of planetary lithospheres on Earth, the Moon (GRAIL mission), Mars, and Venus.

How is Nettleton's Method used to find the true density (ρ_c) of surface hills directly from gravity data?

Although regional gravity maps use a standard nominal continental crustal density of ρ_c = 2.67 g cm⁻³ in the Bouguer slab formula (−0.04192 ρ_c *h*), local surface rocks may actually be porous volcanic tuff (ρ ≈ 1.9 g cm⁻³), sedimentary sandstone (ρ ≈ 2.3 g cm⁻³), or dense basalt (ρ ≈ 2.9 g cm⁻³):

• If the chosen reduction density ρ_c is too low, the Bouguer correction under-subtracts the mass of a local hill, leaving a false positive Δ*g*_B bump that mimics the shape of the hill.
• If the chosen reduction density ρ_c is too high, the Bouguer correction over-subtracts the mass of the hill, creating a false negative Δ*g*_B trough inverted under the hill.
• L. L. Nettleton (1939) showed that by plotting the reduced Bouguer anomaly profile across an isolated topographic hill for a trial series of densities (ρ = 1.8 to 3.0 g cm⁻³), the true bulk in situ density of the hill is the unique value of ρ_c that produces zero correlation (a flat line) between the Bouguer anomaly profile and surface topography.

1. Bouguer, P. (1749). La Figure de la Terre, déterminée par les Observations de Messieurs Bouguer, & de La Condamine. Charles-Antoine Jombert, Paris. https://doi.org/10.3931/e-rara-15226
2. Airy, G. B. (1855). "On the computations of the effect of the attraction of mountain-masses, as disturbing the apparent astronomical latitude of stations in geodetic surveys." Philosophical Transactions of the Royal Society of London, 145, 101–104. https://doi.org/10.1098/rstl.1855.0003
3. Nettleton, L. L. (1939). "Determination of density for reduction of gravimeter observations." Geophysics, 4(3), 176–183. https://doi.org/10.1190/1.1440493
4. Forsyth, D. W. (1985). "Subsurface loading and estimates of the flexural rigidity of continental lithosphere." Journal of Geophysical Research: Solid Earth, 90(B14), 12623–12632. https://doi.org/10.1029/JB090iB14p12623
5. Hildebrand, A. R., Penfield, G. T., Kring, D. A., et al. (1991). "Chicxulub Crater: A possible Cretaceous/Tertiary boundary impact crater on the Yucatán Peninsula, Mexico." Geology, 19(9), 867–871. https://doi.org/10.1130/0091-7613(1991)019<0867:CCAPCT>2.3.CO;2019<0867:CCAPCT>2.3.CO;2)