Two superimposed sounds travel through low- and high-density matter and are recorded from two different positions (see figure). Knowing the two different densities $d_1$ and $d_2$ (I don't actually know them yet but it is just a matter of some research), would it be possible to separate the superimposed sounds from each other?

It is from an actual research problem but this far I have only considered signal processing techniques. I thought people with a different background might see the problem differently. I'd of course acknowledge any contributions that would further tackling the problem.

Two superimposed sounds (at source: $s(t) = s_1(t) + s_2(t)$; the two sound components overlap completely in time, partially in spectra) travel through low- and high-density matter and are recorded from two different positions (see figure). Knowing the two different densities $d_1$ and $d_2$ (I don't actually know them yet but it is just a matter of some research), would it be possible to separate the superimposed sounds from each other?

It is from an actual research problem but this far I have only considered signal processing techniques. I thought people with a different background might see the problem differently. I'd of course acknowledge any contributions that would further tackling the problem.

DSP, including filters and blind source separation has been tested already.