Three-dimensional Sound Propagation Modeling Using Parabolic Equation Approximantion And High Speed Computational Methods

Although two-dimensional(2D)sound propagation models can be used to solve a lot of ocean sound propagation problems,some issues are difficult to figure out using these models.Experimental and numerical results show that,in some specific environment,horizontal refraction effects must be taken into consideration because it can cause unneglectable three-dimensional(3D)effects in the long range.Horizontal variation of sound speed profiles and 3D topography of sea bottom can lead to horizontal deflection of sound rays and thus change the distribution of sound intensity.To consider 3D sound propagation problems efficiently,it is very necessary to build some real 3D sound propagation models.Compared with other methods,parabolic equation(PE)method is flexible and convenient,and is very efficient to handle range-dependent sound propagation problems and 3D problems.To solve3 D problems,a lot of 3D PE models were introduced,but these models still have different disadvantages.To improve calculation precision for sound field,accuracy of some critical steps,eg.,producing the initial field at a close range,approximating of the square root operator and treatment of the coupled cross terms between horizontal operator and depth operator must be improved.Moreover,some methods used to accelerate the speed of sound calculation must be also employed in 3D models.It is obvious that the 3D space is divided into a large number of grids,which slows down the calculation speed significantly and thus limits the real application of 3D models.Therefore,it is meaningful to do some research on3 D PE modeling and its fast calculation method.As one of the existing 3D PE models,the 3D PE model proposed by Lin et.al.in Cartesian coordinates retains a cross term of the horizontal and depth operators and is thus a method of higher-order operator approximation.However,this model can only offer accurate results in a limited angle at close ranges and is not efficient for long-range sound propagation problems.To accelerate the computational speed of this model,some important techniques are adopted in this paper including perfectly matched layer technique and non-uniform numerical grid method.Meanwhile,this thesis presents a new 3D higher-order fluid PE model in cylindrical coordinate which is of high accuracy at close ranges.This model is used to discuss different approximations on square-root operator and 3D sound propagation effects in various submarine topographies.The main researches in this thesis are listed as follows:(1)Limitations and improvements on the 3D Cartesian PE modelLimitations on the 3D PE model presented by Lin are discussed,including anglelimitation in the close range,range limitation in long range calculation,and some improvements are made.To consider 3D problems with environment parameters range-independent in short range and range-dependent in long range,the normal mode method is used to build starting sound field at the distance where range-dependence starts,and afterwards the 3D PE model is used to calculate 3D sound field in the range-dependent area recursively.The sound field in a long-range wedge-shaped waveguide is successfully calculated using this hybrid model,and the results to show a sound intensity enhancement phenomenon in the upslope area.A non-uniform depth and horizontal grid method is applied to the 3D PE model.Some numerical examples show that the improved PE model can calculate long-range sound propagation problems at a higher speed and with higher accuracy.(2)Applications of perfectly matched layer to PE modelsTo eliminate of the reflection waves from the truncated boundary and simulate an unbounded ocean bottom accurately,the perfectly matched layer(PML)technique is used to three PE models,i.e.,RAM,RAMS and a 3D PE model.PML is in essence a stretch of the coordinate in the complex domain,which is used to truncate unbounded domains and simulate infinity radiation conditions as a substitution of artificial absorbing layers(ABL)in these models.The numerical results illustrate that a PML with a half wavelength can keep similar calculation accuracy as an ABL with dozens of wavelengths,which demonstrates that the PML technique is of higher efficiency than the ABL technique in truncating the infinity domain with minimal spurious reflections in PE models.Moreover,PML technique can improve the stability of sound field calculation in the elastic PE model RAMS.(3)3D higher-order fluid PE modelA 3D higher-order fluid PE model in cylindrical coordinates is provided.This model uses alternating direction implicit form and higher-order square-root Helmholtz operator splitting.To improve accuracy,the model considers cross terms of the azimuthal operator and the depth operator.A multi-directional scheme which splits the transverse 2D operator into four 1D operators along the vertical,azimuthal,and two diagonal directions is utilized.Meanwhile,the split-step Padé approximation is used to expand these 1D operators into multiple products of rational fractions,which can be discretized using Galerkin’s method.In the model,vertical interface is handled by energy-conserving correction to study effects from the complicated sea bottom interface on sound propagation.Moreover,the model is used to analyze 3D sound propagation effects and an associated 3D PE model is also implemented to improve the both speed and precision.In the end,this thesis describes results of the data from a Long-Range Ocean AcousticPropagation Experiment carried out in a deep sea.The transmission losses(TL)corresponding to the received scalar and vector data were calculated and compared with the2 D PE model using PML predictions.The comparative results show that the PE model using PML technique is efficient to simulate deep-water and very long-range sound propagation problems including sound pressure and particle velocities in three different directions.