> [a] submerged neutrally buoyant submarine produces no first order gravitational anomaly; however, because the distribution of mass throughout the submarine is not uniform, second and higher order effects can be produced. [...] For a submarine to be in stable equilibrium while submerged it is necessary that its center of mass be below its center of buoyancy (in submarine-fixed coordinates). That is, the mass of the lower half of a neutrally buoyant submarine's volume (including ballast) must be greater than the mass of the water it displaces whereas the mass of the upper half must be smaller than the mass of water it displaces. Therefore, a submerged submarine may be considered to possess a net vertical gravitational dipole moment having "negative mass" above and "positive mass" below.
Though, that 1989 paper concludes that because gravimeters would need a sensitivity of at least one part in 10^13 for practical usage, far beyond what was capable at the time, "[t]he concept of detecting submarines by means of detecting gravitational anomalies they produce, should be abandoned."
Yes and no. A moving submarine has a bow wave, a combination of compressed water and an actual wave manifest at the surface above. So there is a transiting bunch of extra mass to detect, at least so long as the sub is moving.
