I would argue that the issue discussed here is more closely related to the signal-to-noise ratio (SNR) of the acoustic environment of a towed array than to "dynamic range" of the measurement system per se.
In general, "dynamic range" is more often used to discuss the limits of your data acquisition system - i.e. what is the range between the loudest and the quietest sounds your system can acquire/record without distorting. At the quietest end, your DAQ will only "record" its own noise (i.e. electronic noise generated by the measurement gear itself), which is why this limit is often referred to as the noise floor of the system. This noise floor is related to the electronic design of the device, and the bit depth (i.e. how many bits it uses to store each sample of the signal) is one of the factors involved in it. Increasing the bit depth may reduce the noise floor and improve your dynamic range, but not always.
In practice, it is much more common to have the ambient noise levels much higher than your DAQ noise floor, and this is almost sure the case with towed arrays. Some people would call the increased background noise level as the "noise floor" of the recording, but I would suggest the term "signal-to-noise ratio" is more appropriate in this context and avoids confusion.
As suggested by WMXZ, this issue is better treated at the source - i.e. reduce it before it is recorded. If your recording already contains both signal and noise, traditional filtering (high-pass, band-pass, FIR/IIR, etc) will only attenuate the magnitude of the signal+noise mixture, but won't separate them. Sometimes it's possible to improve your overall SNR by filtering out frequencies where there's mostly noise and very little signal (low SNR) and leave/amplify frequencies where there's little noise and more signal (high SNR).
Actually separating the signal from the noise after acquisition is a very complex task and a very active field of research. If you feel like going down a rabbit hole, some common terms used in this area are "blind source separation" and "independent component analysis", for example. Good luck!