Question

If \(g_{FA}\) and \(g_{BA}\) respectively denote the free-air and Bouguer gravity anomalies over a fully compensated mountain, then which one of the following is CORRECT in case of Airy-isostacy?

• A. \(g_{FA} = 0,\ g_{BA} > 0\)
• B. \(g_{FA} > 0,\ g_{BA} = 0\)
• C. \(g_{FA} > 0,\ g_{BA} < 0\)
• D. \(g_{FA} = 0,\ g_{BA} = 0\)

Hint:

Free-air only corrects for elevation (topographic mass still present, so slightly positive); Bouguer removes that mass and exposes the low-density root (a mass deficit, so negative).

Answer 1

The Correct Option is C

Reach the same conclusion by comparing two vertical mass columns instead of talking about corrections in the abstract.

Step 1: Compare a mountain column to a normal (sea-level) column.
Take one column running from the mountain's summit down through its low-density root to the compensation depth, and a second, reference column of the same cross-section running from sea level down to the same depth through normal-density crust and mantle. In Airy's fully compensated model these two columns have equal total mass - that is the definition of compensation.

Step 2: Gravity at the mountain top vs. at sea level.
A gravimeter on the mountain top still sits directly above and close to the extra rock making up the topography, so, corrected only for elevation (free-air), it records a residual attributable to that nearby mass - a small positive \(g_{FA}\).

Step 3: Strip the topography and expose the root.
Once the Bouguer correction removes exactly the slab of rock above sea level, the remaining signal comes only from the deep root, which is less dense than the mantle it replaces - a negative density contrast at depth gives \(g_{BA} < 0\).

So again: \(g_{FA} > 0,\ g_{BA} < 0\) - option \(\boxed{(C)}\).