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Acoustic Field in a Shallow, Stratified Ocean with a Poro‐Elastic Seabed
Author(s) -
Gilbert R. P.,
Lin Z.
Publication year - 1997
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19970770907
Subject(s) - seabed , poromechanics , representation (politics) , waves and shallow water , geology , mathematics , mathematical analysis , geotechnical engineering , oceanography , porous medium , porosity , politics , political science , law
In this paper we investigate the propagating solutions of the acoustic equation in a stratified shallow ocean with a poroelastic, semi‐infinite seabed. The ocean‐seabed system is first Hankel transformed. Then the method of transmutation is used to generate the transformed solutions in the water column; whereas, the modal seabed equations are solved using the computer algebra Macsyma. In the water column the transformed solutions are first decomposed using the Mittag‐Leffler expansion for the discrete spectrum. Both the discrete and continuous spectrum are then used to give a spectral representation of the solution, from which we develop a numerical scheme. Some numerical examples are given to illustrate the method.