An analytic multiple frequency adjoint-based inversion algorithm for parabolic-type approximations in ocean acoustics

References

• Diachok, O, Caiti, A, Gerstoft, P, and Schmidt, H, 1995. Full Field Inversion Methods in Ocean and Seismo Acoustics. Norwell, MA, USA, and Dordrecht, The Netherlands: Kluwer Academic Publisher; 1995, (Eds.).
   Google Scholar
• Wilson, JH, Rajan, SD, and Null, JM, 1996. Inverse techniques and the variability of sound propagation in shallow water, IEEE Journal of Oceanic Engineering, Special issue 21 (4) (1996), (Eds.).
   Google Scholar
• Caiti, A, Hermand, J-P, Porter, MB, and Jesus, S, 2000. Experimental Acoustic Inversion Methods for Exploration of the Shallow Water Environment. Dordrecht: Kluwer Academic; 2000, (Eds.).
   Google Scholar
• Taroudakis, MI, and Markaki, MG, 2001. Inverse Problems in Underwater Acoustics. New York: Springer; 2001.
   Google Scholar
• Chapman, R, Chin-Bin, S, King, D, and Evans, R, 2003. Geoacoustic inversion in range-dependent shallow water environments, IEEE Journal of Oceanic Engineering, Special issue (Pt.1) 28 (3) (2003), (Eds).
   Google Scholar
• Chapman, R, Chin-Bin, S, King, D, and Evans, R, 2004. Geoacoustic inversion in range-dependent shallow water environments, IEEE Journal of Oceanic Engineering, Special issue (Pt.2) 29 (1) (2004), (Eds).
   Google Scholar
• Caiti, A, Chapman, R, Hermand, JP, and Jesus, S, 2004. Acoustic Inversion Methods and Experiments for Assessment of the Shallow Water Environment. Dordrecht: Springer; 2004, (Eds), (in print).
   Google Scholar
• Tolstoy, A, 1993. Matched Field Processing for Underwater Acoustics. Singapore: World Scientific; 1993.
   Google Scholar
• Sen, MK, and Stoffa, PL, 1995. Global Optimization Methods in Geophysical Inversion. The Netherlands: Elsevier Publishing Co.; 1995.
   Google Scholar
• Spall, JC, 2003. Introduction to Stochastic Search and Optimization: Estimation, Simulation and Control. New York: Wiley Publishers; 2003.
   Google Scholar
• Voss, S, Martello, S, Osman, IH, and Roucairol, C, 1998. Meta-heuristics: Advances and Trends in Local Search Paradigms for Optimization. Berlin: Springer; 1998.
   Google Scholar
• Asch, M, Le Gac, J-C, and Helluy, P, An adjoint method for geoacoustic inversions. Presented at Proceedings of the 2nd Conference on Inverse Problems, Control and Shape Optimization. 2002.
   Google Scholar
• Le Gac, J-C, Stéphan, Y, Asch, M, Helluy, P, and Hermand, J-P, 2004. "A variational approach for geoacoustic inversion using adjoint modeling of a PE approximation model with non local impedance boundary conditions". In: Tolstoy, A, Teng, YC, and Shang, EC, eds. Theoretical and Computational Acoustics 2003. Singapore: World Scientific Publishing; 2004. pp. 254–263.
   Google Scholar
• Hermand, J-P, and Gerstoft, P, 1996. Inversion of broad-band multitone acoustic data from the YELLOW SHARK summer experiments, IEEE Journal of Oceanic Engineering 21 (4) (1996), pp. 324–346.
   Web of Science ®Google Scholar
• Hermand, J-P, 1999. Broad-band geoacoustic inversion in shallow water from waveguide impulse response measurements on a single hydrophone: theory and experimental results, IEEE Journal of Oceanic Engineering 24 (1) (1999), pp. 41–66.
   Web of Science ®Google Scholar
• Le Gac, J-C, Asch, M, Stéphan, Y, and Demoulin, X, 2003. Geoacoustic inversion of broadband acoustic data in shallow water on a single hydrophone, IEEE Journal of Oceanic Engineering (2003).
   Web of Science ®Google Scholar
• Meyer, M, and Hermand, J-P, 2005. Optimal nonlocal boundary control of the wide-angle parabolic equation for inversion of a waveguide acoustic field, Journal of the Acoustical Society of America 117 (5) (2005), pp. 2937–2948.
   PubMed Web of Science ®Google Scholar
• Robertson, JS, Siegmann, WL, and Jacobson, MJ, 1995. Low-frequency sound propagation modelling over a locally reacting boundary with the parabolic approximation, Journal of the Acoustical Society of America 98 (2) (1995), pp. 1130–1137.
   Web of Science ®Google Scholar
• Hursky, P, Porter, MB, Hodgkiss, WS, and Kuperman, WA, 2004. Adjoint modeling for acoustic inversion, Journal of the Acoustical Society of America 115 (2) (2004), pp. 607–619.
   PubMed Web of Science ®Google Scholar
• Lions, JL, 1971. Optimal Control of Systems Governed by Partial Differential Equations, volume 170 of A Series of Comprehensive Studies in Mathematics. New York: Springer Verlag; 1971.
   Google Scholar
• Lions, JL, 1988. Exact controllability, stabilization and pertubations for distributed systems, SIAM Review 30 (1988), pp. 71–86.
   Web of Science ®Google Scholar
• Leredde, Y, Lellouche, J-M, Devenon, J-L, and Dekeyser, I, 1998. On initial, boundary conditions and viscosity coefficient control for Burgers' equation, International Journal for Numerical Methods in Fluids 28 (1998), pp. 113–128.
   Web of Science ®Google Scholar
• Colton, D, and Kress, R, 1998. Inverse Acoustic and Electromagnetic Scattering Theory, volume 93 of Applied Mathematical Sciences. Berlin: Springer; 1998.
   Google Scholar
• Giles, MB, and Pierce, NA, 2001. Analytic adjoint solutions for the quasi 1d euler equations, Journal of Fluid Mechanics 426 (2001), pp. 327–345.
   Web of Science ®Google Scholar
• Tarantola, A, 1984. Inversion of seismic reflection data in the acoustic approximation, Geophysics 49 (1984), pp. 1259–1266.
   Web of Science ®Google Scholar
• Talagrand, O, and Courtier, P, 1986. Les équations adjointes – Application à la modélisation numérique. Atelier modélisation de l'atmosphère, Direction de la météorologie. France: Toulouse; 1986.
   Google Scholar
• Carthel, C, Glowinski, R, and Lions, JL, 1994. On exact and approximate boundary controllabilities for the heat equation: a numerical approach, Journal of Optimization Theory and Aplications 82 (3) (1994), pp. 429–484.
   Web of Science ®Google Scholar
• Akkouchi, M, and Bounabat, A, 2001. Optimality conditions and adjoint state for a perturbed boundary optimal control system, Applied Mathematics Letters 14 (7) (2001), pp. 907–912.
   Web of Science ®Google Scholar
• Akkouchi, M, and Bounabat, A, 2001. Some boundary optimal control problems related to a singular cost functional, Annales Mathématiques Blaise Pascal 8 (1) (2001), pp. 7–15.
   Google Scholar
• Alekseev, AK, and Navon, IM, 2001. The analysis of an ill-posed problem using multi-scale resolution and second-order adjoint techniques, Computer Methods in Applied Mechanics and Engineering 190 (2001), pp. 1937–1953.
   Web of Science ®Google Scholar
• Alekseev, AK, and Navon, MI, 2002. On estimation of temperature uncertainty using the second-order adjoint problem, International Journal of Computational Fluid Dynamics 16 (2) (2002), pp. 113–117.
   Web of Science ®Google Scholar
• Le Dimet, FX, Navon, IM, and Daescu, DN, 2002. Second-order information in data assimilation, Monthly Weather Review 130 (3) (2002), pp. 629–648.
   Web of Science ®Google Scholar
• Jensen, FB, Kuperman, WA, Porter, MB, and Schmidt, H, 1994. Computational Ocean Acoustics. New York: American Institute of Physics Press; 1994.
   Google Scholar
• Kravaris, C, and Seinfeld, JH, 1985. Identification of parameters in distributed parameter systems by regularization, SIAM Journal of Control and Optimization 23 (1985), pp. 217–241.
   Web of Science ®Google Scholar
• Engl, HW, Hanke, M, and Neubauer, A, 1999. Regularization of Inverse Problems. Dordrecht: Kluwer Academic Publishers; 1999.
   Google Scholar
• Zhdanov, MS, 2002. Geophysical Inverse Theory and Regularization Problems Number 36 in Methods in Geochemistry and Geophysics. Amsterdam: Elsevier; 2002.
   Google Scholar
• Meyer, M, Hermand, J-P, Le Gac, J-C, and Asch, M, Penalization method for WAPE adjoint-based inversion of an acoustic field. Presented at Proceedings of the 7th European Conference on Underwater Acoustics, ECUA 2004. July, 2004.
   Google Scholar
• Norton, SJ, 1999. Iterative inverse scattering algorithms: Methods of computing Fréchet derivatives, Journal of the Acoustical Society of America 106 (5) (1999), pp. 2653–2660.
   Web of Science ®Google Scholar
• Frandsen, PE, Jonasson, K, Nielsen, HB, and Tingleff, O, 1999. "Unconstrained optimization". Technical University of Denmark; 1999, Lecture note IMM-LEC-2.
   Google Scholar
• Tappert, FD, Nghiem-Phu, L, and Daubin, SC, 1985. Source localization using the PE method, Journal of the Acoustical Society of America 78 (S1) (1985), p. S30.
   Web of Science ®Google Scholar
• Thomson, DJ, Ebbeson, GR, and Maranda, BH, A matched field backpropagation algorithm for source localization. Presented at Proceedings of MTS/IEEE Oceans 1997. 1997.
   Google Scholar
• Gilbert, KE, and White, MJ, 1989. Application of the parabolic equation to sound propagation in a refracting atmosphere, Journal of the Acoustical Society of America 85 (2) (1989), pp. 630–637.
   Web of Science ®Google Scholar
• West, M, Gilbert, KE, and Sack, RA, 1992. A tutorial on the parabolic equation (PE) model used for long range sound propagation in the atmosphere, Applied Acoustics 37 (1992), pp. 31–49.
   Web of Science ®Google Scholar