In my old life I would tend to these instruments (still in operation). Finicky, old, entirely analogue systems ... but they keep "working" 35+ years later.
In fact, the really old Lacoste & Rhomberg style gravimeters are often thought to be more accurate than their modern counterparts because the springs used to be very meticulously hand-crafted instead of mass-produced.
Even Sandwell & Smith's method for inverting for bathymetry from the Free Air Anomaly (i.e. local sea level) has been around for a long time at this point. (Still damned neat, though.)
The cutting edge stuff these days is in satellite methods that can measure gravity anomalies over land (e.g. GRACE and GOCE). They're still much lower spatial resolution than the sea-surface based methods, but you can use them over the entire globe.
GRACE, for example, measures the distance between two satellites ~100km apart to an accuracy of ~1 micrometer. Pretty impressive! GOCE has multiple very precise accelerometers at different ends of the satellite. Because acceleration of the craft will affect accelerometers equally, the differences in acceleration must be due to local changes in the geoid. (In other words, GOCE is gradiometry based.)
If the submarine were a perfect spherical shell of denser and lighter sub-shells, everything would cancel out. However, they're not. They're essentially really dense blobs attached to much less dense blobs.
You get a gravity anomaly due to the lack of spherical symmetry.