Acoustic normal modes using the propagator matrix technique for a stratified ocean overlaying an inhomogeneous anisotropic porous bed
Abstract
Propogation of acoustic normal modes at excitation frequencies of 50 to 50000 Hz in a shallow stratified ocean overlaying a transverse isotropic poroelastic sediment bed is modeled. The BiotWillis stiffness matrix of the poroelastic anisotropy is defined in terms of physical properties of sediments to model the bed. Propagator matrix method is used to solve the differential equations for the motion stress vectors in both layered sediment and water. The effects of sediment properties on the dispersion and attenuation of acoustic waves are examined numerically. Using the relaxation principle it is observed that the energy loss is maximum at frequency referred to as relaxation frequency of the porous media given by f sub ri = (beta)(nu)/3 pi k (sub si), where beta is the porosity, nu is the kinematic viscosity of the pore fluid and k (sub si) is the anisotropic permeability coefficient. The phase speed of compressional and shear waves in the sediment becomes highly dispersive around this frequency. The sandy bottom's relaxation frequency is the range of several hundred hertz to several kilo hertz. This report presents the derivation of the mathematical expressions used in the model and a complete description of the computer program. Four examples of numerical calculations are provided.
 Publication:

Interim Report Miami Univ
 Pub Date:
 January 1986
 Bibcode:
 1986mufl.rept.....B
 Keywords:

 Anisotropic Fluids;
 Matrix Theory;
 Ocean Bottom;
 Sediments;
 Sound Waves;
 Stiffness Matrix;
 Stratification;
 Biot Number;
 Energy Dissipation;
 Mathematical Models;
 Numerical Analysis;
 Permeability;
 Porosity;
 Relaxation Method (Mathematics);
 Shear Layers;
 Underwater Acoustics;
 Viscous Fluids;
 Acoustics