Questions: Gravity Data Reduction: Bouguer, Free-Air, and Terrain Corrections

Question 1

A gravimeter is deployed at a mountain station 1,500 m above sea level. Compared to an identical station at sea level at the same latitude, the mountain station records lower gravity. Which correction specifically accounts for this elevation effect?

• A. The Bouguer correction — it removes the mass of rock beneath the mountain station
• B. The free-air correction — it compensates for the reduced gravity due to greater distance from Earth's center
• C. The terrain correction — it accounts for the gravitational pull of surrounding peaks
• D. The latitude correction — polar stations experience stronger gravity and must be normalized

Answer: (B)

The free-air correction adds back the gravity lost by being farther from Earth's center (~0.3086 mGal per meter of elevation), projecting all stations to a common reference level. The Bouguer correction is applied after — it removes the gravitational attraction of the rock mass between the station and sea level. Confusing these two is a classic error: the free-air correction is purely geometric (elevation), while the Bouguer correction is mass-dependent (density of intervening rock).

Question 2

A geophysicist computes the complete Bouguer anomaly across a sedimentary basin. The anomaly is negative over the basin center. What does this most likely indicate?

• A. The terrain correction was applied incorrectly, subtracting too much gravity
• B. The basin sediments are less dense than the assumed slab density, producing a gravity deficit
• C. The basin is at high elevation, and the free-air correction was not applied
• D. Negative Bouguer anomalies always indicate the presence of water rather than rock

Answer: (B)

A negative Bouguer anomaly means the observed gravity is less than predicted after all corrections — the subsurface contains less mass than the assumed reference model. Sedimentary basin fills (typically 2,200–2,400 kg/m³) are less dense than the standard Bouguer slab density (2,670 kg/m³), creating a mass deficit. The Bouguer anomaly is exactly what is needed to detect this: after removing latitude, elevation, and assumed slab effects, the remaining signal reflects real lateral density variations.

Question 3

The free-air anomaly is the fully reduced gravity signal, ready for geological interpretation without further corrections.

• T. True
• F. False

Answer: False

The free-air anomaly removes only the latitude and elevation effects — it still contains the gravitational attraction of all the rock mass between the station and sea level (the topographic mass). Over mountains, this topographic contribution dominates and masks subsurface signals. The Bouguer correction (and terrain correction in rugged terrain) must be applied to remove this rock mass before the anomaly isolates subsurface density variations.

Question 4

The terrain correction always adds to the Bouguer anomaly — it never subtracts from it.

• T. True
• F. False

Answer: True

The terrain correction accounts for the fact that surrounding topography exerts gravitational attraction in unexpected directions. Nearby hills pull the gravimeter upward (reducing the vertical reading), and nearby valleys lack mass that the infinite-slab model assumed was present (also effectively pulling upward). Both effects reduce measured gravity relative to the slab model, so the terrain correction always adds a positive increment to restore the anomaly to what a flat reference surface would give.

Question 5

Why does the choice of assumed density in the Bouguer correction matter, and what goes wrong if the wrong density is used?

Model answer: The Bouguer correction models the rock between the station and sea level as an infinite horizontal slab of assumed density (typically 2,670 kg/m³ for continental crust). If the actual rock density is higher, the correction under-removes the topographic mass, leaving a positive residual in the Bouguer anomaly that mimics a dense subsurface body. If the actual density is lower, the correction over-removes, creating a spurious negative anomaly. The residual can be used diagnostically: by varying the assumed density until the Bouguer anomaly shows minimum correlation with topography, geophysicists can estimate the actual surface rock density — this is the Nettleton method.

Getting the Bouguer density wrong is especially problematic in areas of unusual surface geology (e.g., igneous intrusions, salt diapirs) where surface and subsurface densities differ from the crust average. The standard 2,670 kg/m³ is a reasonable default for granite-dominated crust but may be wrong by hundreds of kg/m³ in other settings.