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Adjoint-based control of nonlocal boundary conditions for Claerbout’s wide-angle parabolic approximation
Meyer, M.; Hermand, J.-P. (2005). Adjoint-based control of nonlocal boundary conditions for Claerbout’s wide-angle parabolic approximation. J. Acoust. Soc. Am. 117(4): 2576
In: The Journal of the Acoustical Society of America. American Institute of Physics: New York. ISSN 0001-4966, more
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    This paper applies the concept of optimal boundary control for solving inverse problems in shallow water acoustics. A continuous analytic adjoint model is derived for a wide-angle parabolic equation (WAPE) using a generalized nonlocal impedance condition at the water-bottom interface. While the potential of adjoint methodology has been demonstrated for ocean acoustic tomography, this approach combines the advantages of exact transparent boundary conditions for the WAPE 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, much fewer iterations are required for assessment of environments that are supported by the underlying subbottom model. Furthermore, since regularization is important to enhance performance of full-field acoustic inversion, special attention is devoted to applying penalization methods to the adjoint formalism. Regularization incorporates additional information about the desired solution to stabilize ill-posed problems and identify useful solutions, a feature that is of particular interest for inversion of field data sampled on a vertical array in the presence of measurement noise and modeling uncertainty. Results show that the acoustic fields and the bottom properties embedded in the control parameters are efficiently retrieved.

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