Adjoint-based acoustic inversion for the physical characterization of a shallow water environment

Recently the concept of adjoint modeling has been introduced in shallow water acoustics for solving inverse problems. Analytical adjoints have been derived for normal modes and for both the standard parabolic equation and Claerbout’s wide-angle approximation (WAPE). This paper proposes the application of a semiautomatic adjoint approach that has been successfully applied in the past for multidimensional variational data assimilation in meteorological and climate modeling. Starting from a modular graph representation of the underlying forward model, a programming tool facilitates the generation and coding of both the tangent linear and the adjoint models. The potential of this numerical adjoint approach for the physical characterization of a shallow water environment is illustrated with two applications for geoacoustic inversion and ocean acoustic tomography using Claerbout’s WAPE in combination with nonlocal boundary conditions. Furthermore, the adjoint optimization is extended to multiple frequencies and it is shown how a broadband approach can enhance the performance of the inversion process. For a sparse array geometry in particular, the generalization of the adjoint-based approach to a joint optimization across multiple frequencies is necessary to compensate for the lack of vertical sampling of the propagation modes. Results with test data synthesized from geoacoustic inversion experiments in the Mediterranean show that with the numerical adjoint approach the acoustic field, the sound speed profile in the water column and the bottom properties can be efficiently retrieved