Active manipulation of Helmholtz scalar fields in an ocean of two homogeneous layers of constant depth

In this work, we prove the possibility of actively controlling the acoustic field in an ocean consisting of two homogeneous layers of constant depth using a surface source embedded in one of the layers. For a class of prescribed fields on some bounded control regions in either layer, we show the existence of a boundary input on the source, either acoustic pressure or normal velocity so that the propagated field approximates the prescribed fields. Also, we provide a constructive scheme to find the required boundary input using a Morozov discrepancy principle-based Tikhonov regularization scheme. Several numerical simulations are also provided to support our analyses.