A gravity inversion produces two models that fit the observed surface data equally well: Model A places a dense body at 5 km depth, Model B places a less-dense body at 2 km depth. Which model should a geophysicist prefer?
AModel A, because deeper sources produce stronger gravity anomalies
BModel B, because shallower sources are more geologically realistic
CEither — without additional constraints such as seismic data, neither model can be ruled out
DModel A, because Tikhonov regularization always favors deeper solutions
Gravity inversion is fundamentally non-unique: many different density distributions can produce identical surface anomalies. Without external constraints — seismic profiles, well logs, or geologic mapping — both models are equally valid solutions. This non-uniqueness is the central challenge of all potential field methods, and it is why integration with other data types is essential. Regularization like Tikhonov constrains solutions to be smooth or simple, but it does not uniquely determine depth without independent information.
Question 2 Multiple Choice
What does the Bouguer correction accomplish in gravity data reduction?
AIt corrects for the gravitational effect of Earth's rotation and latitude
BIt removes the gravitational contribution of the rock mass between the station and sea level
CIt accounts for the free-air gradient due to the station's elevation above sea level
DIt isolates gravity anomalies caused by surface topography only
The Bouguer correction removes the gravitational effect of the rock slab between the measurement station and sea level. This step goes beyond the free-air correction (which only accounts for elevation) by asking: 'What would gravity look like if we could slice away the topography?' After both corrections, the Bouguer anomaly reflects lateral density variations in the subsurface — the signal geologists actually care about. The free-air correction handles elevation; the Bouguer correction handles the rock mass at that elevation.
Question 3 True / False
Gravity inversion can uniquely recover the subsurface density distribution from a complete set of surface gravity measurements.
TTrue
FFalse
Answer: False
Gravity inversion is inherently non-unique. Infinitely many different density distributions can produce identical gravity observations at the surface — a fundamental mathematical property of potential fields. A deep, dense body may produce the same anomaly as a shallow, less-dense body. Resolving this non-uniqueness requires incorporating independent constraints from seismic surveys, well logs, or geologic knowledge. Regularization techniques like Tikhonov add a smoothness preference but do not eliminate non-uniqueness.
Question 4 True / False
Terrain corrections in gravity data reduction account for nearby hills and valleys, since a simple slab approximation misses the gravitational effect of irregular topography near the station.
TTrue
FFalse
Answer: True
The Bouguer correction uses an infinite slab approximation to remove the topographic mass. But in rugged terrain, nearby peaks add gravitational pull and nearby valleys represent missing mass that reduces it. The terrain correction accounts for both effects, refining the Bouguer correction. Without it, the Bouguer anomaly in mountainous regions would contain significant terrain-related artifacts unrelated to subsurface geology.
Question 5 Short Answer
Why is integration of gravity data with seismic, well-log, and geologic constraints so important in practice? What specific problem does this integration solve?
Think about your answer, then reveal below.
Model answer: It addresses the non-uniqueness of gravity inversion. Because many density models can fit the same surface observations, gravity data alone cannot identify a single correct subsurface model. Independent constraints narrow the solution space: seismic data defines the geometry of subsurface layers, well logs provide direct density measurements at known depths, and geologic mapping constrains which rock types are plausible. Together, these reduce the set of valid models from infinite to a geologically reasonable few.
The inability to uniquely determine subsurface structure is a mathematical property of potential fields — not a limitation of measurement precision. No amount of additional gravity data can solve it. Only independent, non-redundant data types can constrain the solution, which is why integration is the standard practice rather than an optional enhancement.