Modelling Of Sound Propagation In Wedge-Like Oceans With Elastic Bottom And Analyzing Of Horizontal Refraction Effects On Vector Fields

Modelling of sound propagation and analyzing of sound fields are important parts in underwater acoustics.With the frequency band of sonar being extended towards low frequency,it is necessary to consider bottom elasticity in sound propagation modelling,because low-frequency sound waves can penetrate deep into the elastic bottom,and then transmit back to the water column after reflection.Meanwhile,with the operating distance of sonar growing,it is important to take account of the horizontal refraction effects,which are due to azimuthal variation of the environment with respect to the source.In this thesis,modelling of sound propagation in wedge-like oceans and analyzing of horizontal refraction effects on vector fields are studied.First,a parabolic-equation(PE)model applicable to wedge-like oceans with elastic bottom is established.Second,with an attempt to verify the PE model,the source images method,which is a benchmark model for the problem of sound propagation in wedge-like oceans,is modified,and the acoustic fields calculated by the source images method and the PE model are compared.Third,the influences of horizontal refraction on vector-field characteristics are analyzed.More details for the studies are listed as following.(1)Establishment of the PE model for wedge-like oceans with elastic bottomA parabolic-equation(PE)model for sound propagation in wedge-like oceans with elastic bottom is established.First,the elastic parabolic equations(PEs)are derived from the elastic motion equations.Second,the mapping approach is used to handle the sloping fluid-elastic interface.Third,by using Fourier transform,the three-dimensional(3D)PEs are simplified to two-dimensional(2D)PEs,which are much easier to solve.Finally,the 3D sound fields are obtained through inverse Fourier transform.The accuracy of the model is tested in a horizontal waweguide and a wedge-like waveguide,and azimuthal limitation of the model is analyzed.According to the theory of Padé approximation,the limitation azimuthal angle can reach between 70 and 80 degrees when the order of Padé approximation is 8,and the limitation azimuthal angle increases with the decreasing of the marching step.An analysis of the sound fields in wedges and in transitional areas between continental slope and continental shelf reveals that,the larger the azimuth in the considered waveguides,the stronger the horizontal refraction effects.In addition,the sound fields in the transitional area indicate that,the horizontal refraction effects in the sloping region affect the sound fields in farther region,though in the farther region the bottom is horizontal.At last,the sound fields calculated by the PE model are compared to the results measured in a tank experiment,where a plastic plate is placed at the tank bottom to play the role of an elastic sea bottom.It is shown that in the case of horizontal bottom,the simulated results and the measured results agree well with each other;while in the case of a sloping bottom,the simulated results and the measured results deviates with each other,and further study is required to know the exact reason.(2)Study on the problem of branch selection for the reflection coefficients in source images methodThe source images method is regarded as a benchmark model for 3D sound fields calculation in wedge-like oceans.An important issue in the source images method is how to choose the correct branch of the reflection coefficients.In principle,the criterion for branch selection is the infinite radiation condition.Nevertheless,for portions of the plane-wave components emitted from the source,the correct branch of the reflection coefficient is not obvious when one tries to judge it according to the infinite radiation condition.P.S.Petrov published a code for the source images method,in which a detailed branch selection rule is given,but a strict proof for this branch selection rule is not found in published literature.In this thesis,we give a systematic discussion of the branch selection problem.In the case of lossless bottom,by combining the infinite radiation condition with a series of numerical examples,a branch selection rule of the reflection coefficients can be concluded: the normal component of the refracted wavenumber should be in the same quadrant with the normal component of the incident wavenumber.The physical meaning of the above branch selection rule is that the propagation direction and the decaying direction of the refracted wave normal component should be the same with those of the incident wave normal component.The branch selection rule in Petrov's code elects the same branches as the above branch selection rule when the bottom is lossless,thus Petrov's code is applicable to the lossless-bottom case.In the case of lossy bottom,it is found that for portions of the plane-wave components,the branch of reflection coefficient can not be judged by the branch selection rule above.Nevertheless,if choosing the branch with the rule of keeping the propagation direction of the refracted wave normal component the same with that of the incident wave normal component,the corresponding acoustic fields produced by the source images method are still with high accuracy.The 3D sound fields in the ASA wedge with lossy bottom is calculated by the source images method with the above branch choice rule,and the results are compared to the results produced by other 3D sound propagation models as well as the results produced by Petrov's code.The comparisons reveal high accuracy of the source images method based on the branch selection rule in this thesis.Meanwhile,it is shown that the results based on the branch selection rule in this thesis is smoother,i.e.,with less oscillation,than those calculated by Petrov's code.Finally,the solutions of sound fields in a series of wedge-like oceans,which differs only in bottom shear-wave speed,are calculated,and these results can be used to verify the accuracy of other 3D sound propagation models.(3)Analysis of the effects of horizontal refraction on acoustic vector-field characteristicsThe effects of horizontal refraction on acoustic vector-field characteristics are studied.Based on the basic difference between a 3D sound propagation problem and a cylindrically symmetric 2D sound propagation problem,i.e.,whether the environmental parameters vary along the azimuth direction with respect to the source,two effects of horizontal refraction on acoustic vector-field characteristics are deduced,i.e.,the elliptical polarization of the horizontal particle displacement and the horizontal deflection of the acoustic energy flux.First,the measured data for particle displacements in a sea trial is analyzed.The results show the horizontal displacement at the receiver point was always elliptically polarized regardless of the change of source position,implying in realistic oceans the propagation of sound waves is usually accompanied with the effects of horizontal refraction due to the horizontal inhomogeneity of the media and the horizontal variation of the bathymetry.Second,the horizontal deflection angle of the acoustic energy flux,which is equal to the deviation between the direction of arrival(DOA)measured by a single vector hydrophone and the true bearing of the source,in coastal wedges with a 2.86o sloping bottom are simulated using the source images method.The results show that the horizontal deflection angle of acoustic energy flux can be larger than 10 degrees in some regions in the considered wedges,indicating that horizontal refraction of sound waves can lead to non-negligible error in bearing estimation.