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Reflection and Refraction of Spherical Waves
Reflection of Bounded Wave Beams
The Lateral Wave
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according adiabatic approximation amplitude analogous assume asymptotic expansion axis beam boundary conditions branch point calculations caustic Chap component considered const coordinates corresponding critical section curve density dependence derivative differential discrete spectrum displacement distance eikonal eikonal equation expressed in terms fluid frequency Gaussian beam group velocity halfspace Hence homogeneous horizontal rays incidence angle inhomogeneous integral representation integrand interface irregular waveguide lateral wave layered medium main term medium at rest moving medium Note observation point parabolic cylinder functions phase plane wave point q point source pole problem reference integral reference waveguide reflected field reflection coefficient refraction region relation respect right hand side saddle point Sect solution sound field sound pressure sound velocity spherical wave stationary point Substituting surface taking into account tends to zero theory uniform asymptotics valid vicinity wave equation wave number wave propagation wave vector