Asymptotic study of the elastic seadbed effects in ocean acoustics

References

• Ahluwalia , D.S. and Keller , J.B. “ Exact and asymptotic representation of the sound field in a stratified ocean in Wave propagation and Underwater Acoustics ” . Edited by: Keller , J.B. and Papadakis , J.S.
   Google Scholar
• Amnicht , E. and Stickler , D.C. 1984 . Uniform asymptotic evaluation of the continous spectrum contribution for a stratified ocean . J. Acoust. Soc. Am , 76 ( 1 ) : 186 – 191 .
   Web of Science ®Google Scholar
• Amnicht , E. and Stickler , D.C. 1980 . Uniform asymptotic evaluation of the continuous spectrum contributionfor the Pekeris model . J. Acoust. Soc. Am , 67 ( 6 ) : 2018 – 2024 .
   Web of Science ®Google Scholar
• Bleinstein , N. and Handelsman , R.A. 1986 . Asymptotic Expansions of Integrals Dover . 67 ( 6 )
   Google Scholar
• Buchanan , J.L. 1996 . Transmission loss in the far field over a seabed with a rigid substrate assuming the Biot sediment model . J. Comp. Acous , 4 ( 6 ) : 29 – 54 .
   Google Scholar
• Buchanan , J.L. and Gilbert , R.P. 1997 . Transmission loss in the far field over a one-layer seabed assuming the Biot sediment model . Z. Angew. Math. Mech , 77 ( 2 ) : 121 – 135 .
   Web of Science ®Google Scholar
• Coddington , E.A. and Levinson , N. 1955 . Theory of Ordinary Differential Equations . McGraw-Hill Co , 77 ( 2 )
   Google Scholar
• DeSanto , J.A. 1992 . Scalar Wave Theory . 77 ( 2 )
   Google Scholar
• Ditkin , V.A. and Prudnikov , A.P. 1965 . “ Integral Transforms and Operational Calculus ” . New York : Pergamon press .
   Google Scholar
• Dolph , C.L. 1961 . Recent development in some non-selfadjoint problem of mathematical physics . Bull. AMS , 67 : 1 – 69 .
   Google Scholar
• Ewing , W.M. , Jardetzky , W.S. and Press , F. 1957 . Elastic Waves in Layered Media . McGraw-Hill Co , 67
   Google Scholar
• Eringen , A.C. and Suhubi , E.S. 1975 . “ Elastodynamics ” . Vol. 2 , New York : Academic Press .
   Google Scholar
• Gilbert , R.P. and Lin , Z. 1997 . Acoustic field in a shallow stratified ocean with a poro-elastic seabed . Z. Angew. Math. Mech , 77 ( 4 ) : 1 – 13 .
   Google Scholar
• Gilbert , R.P. , Lin , Z. and Buchanan , J.L. 1996 . Direct and inverse problems in ocean acoustics, preprint . 77 ( 4 )
   Google Scholar
• Gilbert , R.P. and Xu , Y. 1989 . Starting fields and far fields in ocean acoustics, Wave Motion . 11 ( 4 ) : 507 – 524 .
   Google Scholar
• Gilbert , R.P. and Xu , Y. 1989 . Dense sets and the projection theorem for acoustic harmonic waves in homogeneous finite depth oceans . Math. Methods Appl.Scis , 12 ( 4 ) : 69 – 76 .
   Google Scholar
• Gilbert , R.P. and Xu , Y. 1990 . The propagation problem and far-field patterns in a stratified finite-depth ocean . Math. Methods Appl. Scis , 12 ( 4 ) : 199 – 208 .
   Google Scholar
• Gilbert , R.P. and Lin , Z.L. 1996 . Acoustic wave in the shallow ocean with a layer of elastic sediment . 82 ( 4 ) : 729 – 737 .
   Google Scholar
• Gilbert R.P. Xu Y. Khashanah K. Computation of the acoustic modal solutions in a shallow ocean with an elastic seabed Instabul J. Math. (to appear)
   Google Scholar
• Gohberg , I.T. and Krein , M.G. 1969 . Introduction to the Theory of Linear Non-Selfadjoint Operators . 82 ( 4 ) AMS, Providence, R.I
   Google Scholar
• Gregory , R.D. 1974 . The non-existence of standing modes in certain problems in linear elasticity . Proc. Camb. Phil. Soc , 77 ( 4 ) : 385 – 404 .
   Google Scholar
• Hruščev , S. V. , Nicol'skii , N. K. and Pavlov , B. S. 1981 . “ Unconditional bases of exponentials and of reproducing kernels, in Complex Analysis and Spectral Theory ” . In Lecture Notes in Math , Edited by: Havin , V.P. and Nicolskii , N.K. Vol. 864 , 214 – 235 . Springer-Verlag .
   Google Scholar
• Kravicki[icaron] , A. 0. 1966 . Expansion in a series of eigenfunctiona of a nonselfadjoint boundary value problem . Soviet Math. Dokl. , 7 : 1361 – 1365 .
   Google Scholar
• Kravicki[icaron] , A. 0. 1968 . On the double series expansion in eigenfunctions of a non-selfadjoint boundary value problem . Dig. Eq. , 4 : 165 – 177 .
   Google Scholar
• Livs[icaron]c , M. S. 19727 . “ Operators, Waves and Open Systems ” . Providence, R.I. : AMS .
   Google Scholar
• Mikhlin , S. G. 1975 . The spectrum of a family of operators in the theory of elasticity . Russian Math. Surv. , 28 : 45 – 88 .
   Google Scholar
• Na[icaron]mark , M. A. 1958 . Spectral analysis of non-selfadjoint operators . AMS Trens , 20 : 55 – 752 .
   Google Scholar
• Pekeris , C. L. 1948 . Theory of propagation of explosive sound in shallow water . Geol. Soc. Amer. Memoir , 27 : 19 – 52 .
   Google Scholar
• Regge , T. 1958 . Analytic properties of the scattering matrix . Nuovo Cimento , 8 ( 5 ) : 671 – 679 .
   Google Scholar
• Regge , T. 1958 . Construction of potentials from resonance parameters . Nuovo Cimento , 9 ( 3 ) : 491 – 503 .
   Google Scholar
• Shubov M. A. Basis properties of eigenfunctions of nonselfadjoint operator pencils generated by the equation of non homogeneous damped string, Int. Eq.Oper. Theory (to appear).
   Google Scholar
• Shubov , M.A. 1995 . Asymptotics of resonances and geometry of resonance states in the problem of scattering of acoustic waves by a spherically symmetric inhomogeneity of the density . Dig. Int. Eq. , 8 ( 5 ) : 1073 – 1115 .
   Google Scholar
• Shubov , M. A. 1996 . Asymptotics of resonances and eigenvalues for nonhomogeneousdamped strings . Asymptotic Analysis , 12 : 1 – 48 .
   Google Scholar
• Voitovich , N.N. and Shatov , A.D. 1973 . Normal mode expansion of the field in an underwater sound channel . Sou. Phys. Acoust , 18 ( 4 ) : 434 – 438 .
   Google Scholar
• Wilcox , C. 1976 . Spectral analysis of the Pekeris operator in the theory of acoustic wave propagation in shallow water . Arch. Rat. Mech. Anal. , 60 : 259 – 300 .
   Web of Science ®Google Scholar
• Wilcox , C. 1984 . “ Sound Propagation in Stratified Fluids ” . In Appl. Math. Scic , Vol. 50 , Springer-Verlag .
   Google Scholar
• Xu , Y. 1990 . The propagating solution and far-field patterns for acoustic harmonic waves in a finite depth ocean . Applicable Analysis , 35 : 129 – 151 .
   Google Scholar