Inversion of partially spanning array data for normal mode parameters using seabed impedance constraint

Previous work with fully or nearly spanning vertical line arrays has shown that normal mode shapes can be identified as the eigenvectors of the covariance matrix averaged over lengthy source tracks that served to de-correlate the modes. Recent work with partially spanning arrays has used compressed sensing or super-resolution methods like MUSIC to estimate mode wavenumbers. These methods assume the sound speed profile is available, but not the seabed properties. We will present another alternative for inverting for normal modes under these conditions, including a partially spanning vertical line array, in which sets of candidate modes are restricted to modes that satisfy the same impedance boundary condition at the seabed. Each distinct impedance condition defines a physically consistent set of modes. Thus, our inversion is sparse in impedance conditions. We demonstrate how the normal modes resulting from this process are used to form matched field processing replicas that recover source tracks in range and depth.