Optimal nonlocal boundary control of the wide-angle parabolic equation for inversion of a waveguide acoustic field

This paper applies the concept of optimal boundary control for solving inverse problems in shallow water acoustics. To treat the controllability problem, a continuous analytic adjoint model is derived for the Claerbout wide-angle parabolic equation (PE) using a generalized nonlocal impedance boundary condition at the water-bottom interface. While the potential of adjoint methodology has been recently demonstrated for ocean acoustic tomography, this approach combines the advantages of exact transparent boundary conditions for the wide-angle PE with the concept of adjoint-based optimal control. In contrast to meta-heuristic approaches the inversion procedure itself is directly controlled by the waveguide physics and, in a numerical implementation based on conjugate gradient optimization, many fewer iterations are required for assessment of an environment that is supported by the underlying subbottom model. Furthermore, since regularization schemes are particularly important to enhance the performance of full-field acoustic inversion, special attention is devoted to the application of penalization methods to the adjoint optimization formalism. Regularization incorporates additional information about the desired solution in order to stabilize ill-posed inverse problems and identify useful solutions, a feature that is of particular importance for inversion of field data sampled on a vertical receiver array in the presence of measurement noise and modeling uncertainty. Results with test data show that the acoustic field and the bottom properties embedded in the control parameters can be efficiently retrieved.