To do this you will need to remove the gravity effect of the density contrast at the seabed from the FAA:

1. Obtain a good quality quality bathymetric grid of the area

2. Calculate the gravity effect of the bathymetry (the Bouguer correction)

3. Subtract the Bouguer correction from the FAA

To calculate the Bouguer correction the most common method is the method of Parker (1972) which uses an FFT method. GMT has a tool called gravfft which you can use to apply it. Otherwise you can write your own implementation. I have a Matlab routine that I could send you. I applied it in a work I did on the Monowai volcano (Paulatto et al., 2014). Another option is to use a numerical approach by modelling the bathymetry with a set of prisms and to calculate their gravitational attraction, perhaps other users will have some suggestions on any tools to do this.

If you use an FFT method like gravfft you will have to define the density constrast at the seabed. I suggest you start with a water density of 1050 kg/m^3 and try different crustal density values between 2000 and of 2800 kg/m^3.

See the references below:

Parker, R.L., 1972. The rapid calculation of potential anomalies, Geophys. J. R. astr. Soc., 31(4), 447–455. http://topex.ucsd.edu/geodynamics/parker.pdf

GMT gravfft: http://gmt.soest.hawaii.edu/doc/5.1.0/supplements/potential/gravfft.html

Paulatto, P., A. B. Watts, and C. Peirce. "Potential field and bathymetric investigation of the Monowai volcanic centre, Kermadec Arc: implications for caldera formation and volcanic evolution." Geophysical journal international. 197, no. 3 (2014): 1484-1499.

Also have a look at this paper that does a comparison of different methods:

http://article.sapub.org/10.5923.j.geo.20140402.02.html

I suggest you could use this simple formula:

ΔgB = Δgf + 0.06889h,

where ΔgB is the Bouguer anomaly, Δgf - the FAA and h is the depth to the ocean bottom in meters (h > 0).

Check this site:

http://bgi.omp.obs-mip.fr/data-products/Documentation/gravity_anomalies_formulas

and the following paper:

http://bgi.omp.obs-mip.fr/content/download/725/4975/file/computations.pdf

More generally, at sea ΔgB =Δgf +2πG(ρ−ρw)h, with 2πG= 0.04193 if gravity anomaly is in mgal, h in meters, and densities are in g/cm3.

Christian Tzankov's answer is, apparently, with a crustal density ρ=2.67 g/cm3 which is the standard Bouguer, and, water density ρw=1.027 g/cm3