Modified transmission eigenvalues for inverse scattering in a fluid–solid interaction problem

Target signatures are discrete quantities computed from measured scattering data that could potentially be used to classify scatterers or give information about possible defects in the scatterer compared to an ideal object. Here, we study a class of modified interior transmission eigenvalues that are intended to provide target signatures for an inverse fluid–solid interaction problem. The modification is based on an auxiliary problem parametrized by an artificial diffusivity constant. This constant may be chosen strictly positive, or strictly negative. For both choices, we characterize the modified interior transmission eigenvalues by means of a suitable operator so that we can determine their location in the complex plane. Moreover, for the negative sign choice, we also show the existence and discreteness of these eigenvalues. Finally, no matter the choice of the sign, we analyze the approximation of the eigenvalues from far field measurements of the scattered fluid pressure and provide numerical results which show that, even with noisy data, some of the eigenvalues can be determined from far field data.