Derivation of the adjoint of a wide angle parabolic equation for acoustic inversion

Recently the concept of optimal control by adjoint modelling has been introduced in shallow water acoustics for solving inverse problems. A continuous analytic adjoint model has been derived for the standard parabolic equation (SPE) using both local and non local impedance boundary conditions at the water-sediment interface. In this paper we discuss the extension of this approach to the Claerbout wide-angle approximation (WAPE) for these two different boundary conditions. By applying an “equivalent medium ” approach we develop the WAPE adjoint and present example inversion results based on synthetic acoustic fields. Further ex-amples are given in an accompanying paper which focusses on the application of penalization methods to the adjoint optimization formalism. The overall performance of the resulting in-version procedure seems promising especially with regard to a rapid environmental assessment (REA) system, where it could for example provide a good initial solution. [The research work reported in this paper is supported by the Royal Netherlands Naval College.] 1