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The origin of computational and numericalacoustics coincides with the emergence of theoretical physics [1] as an intellectual endeavor. Pythagoras developed the theory of the (Western) musical scale in terms of a device called a monochord in which adjacent consonant notes of the musical scale were obtained by plucking two string segments whose relative lengths were ratios of the small integers 1,...
The wave equation in an ideal fluid can be derived from hydrodynamics and the adiabatic relation between pressure and density. The equation for conservation of mass, Euler’s equation (Newton’s second law), and the adiabatic equation of state are respectively 2.1 $$\begin{array}{rcl} & \frac{\partial \rho } {\partial t} = -\mathbf{\nabla }\cdot \rho \mathbf{v},&\end{array}$$ 2.2 $$\begin{array}{rcl}...
Ray-based models have been used for many years in underwater acoustics. In the early 1960s, virtually all modeling was done using either normal modes or ray tracing and primarily the latter. Today, however, ray tracing codes have fallen somewhat out of favor in the research community, the problem being the inherent (high frequency) approximation of the method which leads to somewhat coarse accuracy...
The wavenumber integration technique is basically a numerical implementation of the integral transform technique for horizontally stratified media described in Sect. 2.4.1. The field solution is in the form of a spectral (wavenumber) integral of solutions to the depth-separated wave equation. The normal mode approach described in the next chapter has the same mathematical basis but employs a different...
Normal-mode methods have been used for many years in underwater acoustics. An early and widely cited reference is due to Pekeris [1], who developed the theory for a simple two-layer model of the ocean. At about the same time Ide et al. [2] had been using normal modes to interpret propagation in the Potomac River and Chesapeake Bay. Progress in the development of normal-mode methods is presented in...
The pioneering work on parabolic wave equations goes back to the mid-1940s when Leontovich and Fock [1] applied a PE method to the problem of radio wave propagation in the atmosphere. Since then, parabolic equations have been used in several branches of physics, including the fields of optics, plasma physics, seismics, and underwater acoustics. It is the application of PE methods to wave-propagation...
In the preceding chapters, we have described the numerical solution techniques most commonly applied in ocean-acoustic propagation modeling. One or more of these approaches are numerically efficient for the majority of forward problems occurring in underwater acoustics, including propagation over very long ranges, with or without lateral variations in the environment. However, the numerical efficiency...
While time-series analysis and modeling has always been the approach used by geophysicists for studying low-frequency seismic wave propagation in the Earth’s crust, underwater acousticians have traditionally favored spectral analysis techniques, which only provide information about the band-averaged energy distribution in space. There are several reasons for choosing this approach in ocean acoustics...
In this chapter, we address the modeling of ambient noise as an application of the concepts and methods discussed in the previous chapters. Ambient noise in the ocean impacts underwater acoustics in two ways: It is the resident acoustic field in the ocean and hence also a diagnostic of the ocean environment. It is the interference with respect to detecting or measuring signals.
Ocean acoustics often involves measuring or detecting a signal propagating in the ocean in the presence of noise. If the signal is weak, an array of sensors is used to coherently sum up or accumulate signal energy at a greater rate than noise. A simple example would be an array of hydrophones used to form a directional receiver in isotropic noise. For this case, there is a gain of signal over noise...
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