Concept of waveguide invariant spectrum and algorithm for its extraction

There are two kinds of definitions for waveguide invariant β. One is defined according to the striation slope of acoustic interference patterns, and the other is defined on the basis of dispersion characteristics of acoustic modes. The first definition is appropriate for engineering applications, while the second is suitable for theoretical analysis. However, the two definitions are not consistent with each other for a waveguide with thermoclines, because modal dispersion in such a waveguide can be very different for different modes and different frequencies. In such cases, the waveguide invariant defined according to modal dispersion can take many different values, which are referred to as the spectrum of waveguide invariant (β spectrum for short) in the paper. Each β spectrum can be related to some interference striation patterns with corresponding striation slopes. The sound field is composed of many modes, so the interference pattern is the summation of many components of different striation slopes and may be very complicated as a result of the diversity of β spectrum. In such a case one single β is not able to describe the complicated interference pattern adequately; instead multiple values of β spectrum are required. From the point of view of engineering application, however, the present β-extracting methods can only give one optimal value, and thus a lot of information is lost. In this paper an algorithm for doing so, called β spectrum separation technique, is proposed. By adopting the concept of integral projection used in digital image processing, the image of acoustic intensity is projected at different angles to separate out the striations of different slopes; and then fast Fourier transform (FFT) is applied to the projected curve in order to isolate striations of different spacing from each other. The values for β spectrum can be computed according to striation slopes, which are also mapped into the positions of their corresponding acoustic modal horizontal wavenumber differences in the wavenumber domain. The applicability of this algorithm for the extraction of β spectrum is tested and verified by simulation results and experiment data. It is shown that the algorithm can separate out each β spectrum of different intensity components from acoustic interference structure. The algorithm maps β spectrum into a two-dimensional plane thereby being able to suppress noise more effectively and work in the condition of low signal-to-noise ratio compared with the already-existing β-extracting algorithms.