Comment by MITSardine

This already exists, it's the domain of inverse problems. Inverse problems consider a forward problem (in this case wave propagation) depending on some physical parameters or domain geometry, and deduce the parameters or geometry from observations.

Conceptually, it's quite simple, you need to derive a gradient of the output error with respect to the sought information. And then use that to minimize the error (= "loss function" or "objective" depending on field terminology), like you do in neural networks.

In many cases, the solution is not unique, unfortunately. The choice of emitters and receivers locations is crucial in the case you're interested in.

There's a lot of literature on this topic already, try "acoustic inverse problem" on google scholar.