Finite-element adjoint for a fully range-dependent parabolic equation
Asch, M.; Hermand, J.-P.; Berrada, M. (2011). Finite-element adjoint for a fully range-dependent parabolic equation, in: Chen, C.-F. 10th International Conference on Theoretical and Computational Acoustics (ICTCA 2011) - Taipei, Taiwan - April 24-28, 2011. pp. 78 In: Chen, C.-F. (2011). 10th International Conference on Theoretical and Computational Acoustics (ICTCA 2011) - Taipei, Taiwan - April 24-28, 2011. National Taiwan University: Taipei. 88 pp., more |
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| Abstract | Adjoint-based methods have been successfully applied by us to a number of inverse problems in shallow-water geoacoustics and acoustic tomography. These inversions were all performed in a range-independent context, using a finite-difference formulation of the wide-angle parabolic equation. In this study we consider realistic, fully range-dependent cases, where the bathymetry is variable and, more importantly, the medium properties (sound speed, density, attenuation) are variable in depth and range and can exhibit discontinuities. We adopt a finiteelement formulation, recently proposed in, and adapt it to our purposes. The finite-element method permits a geometrization and discretization that are consistent with site-specific boundaries and discontinuities. Finally, a modular graph approach is applied for generating, in a semi-automatic manner, the tangent-linear model and the back propagation needed for the gradient-based minimization of a mismatch cost function. This approach overcomes the two major difficulties of the inversion: the adjoint code is easily obtained (when compared to other automatic differentiation tools) and the subsequent minimization is rapid and robust. Various test cases will be presented that show the versatility of this new approach. |
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