= Solution
A <gravity anomaly> is the difference between observed gravitational acceleration and a specified reference prediction after defined reductions. A <free-air gravity anomaly>, a <Bouguer gravity anomaly>, and a residual local <gravity anomaly> differ because they remove different reference contributions. State the reference <ellipsoid>, datum, reference <density>, and regional trend before interpreting an anomaly as a subsurface <geophysical density contrast>.
On land, tie <gravimeter> observations to a gravity base, calibrate them, correct instrumental drift and Earth tides, and determine station <latitude> and elevation accurately. Subtract latitude-dependent normal gravity $\gamma(\varphi)$. Reduce to the reference elevation using a positive <free-air correction> for a station above that datum: about $+0.3086h\ \mathrm{mGal}$ for $h$ in metres. A simple <Bouguer gravity anomaly> then subtracts attraction of the intervening rock slab and adds the conventional <terrain correction>:
$$
\Delta g_B\simeq g_{\mathrm{obs,corr}}-\gamma(\varphi)+0.3086h-2\pi G\rho_{\mathrm{ref}}h+C_{\mathrm{terrain}},
$$
with all acceleration terms expressed consistently. In SI units $1\ \mathrm{mGal}=10^{-5}\ \mathrm{m\,s^{-2}}$.
At sea, also correct vessel-motion effects, especially the <Eötvös correction> from east–west vessel motion and Earth rotation, and vertical ship acceleration; average or filter the moving-platform data appropriately. GPS navigation and tide information specify position and measurement height. Sea-surface measurements give a marine <free-air gravity anomaly> after motion, latitude, tide and height reductions. A marine <Bouguer gravity anomaly> additionally allows for measured <bathymetry> and the replacement of low-density <water> by reference <rock>; the simple water-column replacement correction is positive, $2\pi G(\rho_{\mathrm{ref}}-\rho_w)H$, relative to the sea-surface free-air value. A consistent three-dimensional bathymetric correction is preferable near irregular coasts. Remove a justified broad regional field if the intended quantity is a residual anomaly of the local body.
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