Insofar as acoustic tomography is concerned most basic sciences questions concerning acoustic propagation have been resolved. Some regions are more complicated that others, however; every region requires a careful analysis to understand any complications. Fram Strait, for example, is a particularly complicated region.
Existing acoustic propagation codes can accurately compute the transmission of acoustic signals through any given environment. The main difficulty is obtaining an accurate realization for the environment. Acoustic propagation is particularly sensitive to errors in sound speed gradient; small errors can lead to significant errors in the computed acoustic arrival pattern. Below is a list of acousitic propagation codes that I've developed or used. The links lead to a page describing and benchmarking the code, with links to the source code.
"Eigenray" is a code for ray tracing:
"MPIRAM" is a code for computing acoustic propagation based on M. Collin's RAM:
Parabolic equation (RAM), FORTRAN
M. Dzieciuch developed code for computing acoustic propagation based on RAM
Parabolic equation (RAM), MATLAB
Another approach to acoustic propagation is using acoustic modes:
Acoustic mode propagation