P-wave scattering at a coastal region in a shallow ocean (Q1108156)

The present problem can be idealized to study diffraction of compressional waves at a coastal region in a shallow ocean. The method of solution is the Wiener-Hopf technique. An exact solution is obtained in terms of Fourier integrals. The evaluation of the integrals along an appropriate contour in a complex plane results in reflected Rayleigh and scattered waves. Near the scatterer, the scattered field has the behaviour of a cylindrical wave and at distant points, it is a plane wave. The scattered field excites the particle motion at right angles to the free surface of the ocean and the horizontal component of the displacement is absent in the surface. Numerical computations for the scattered field in terms of the distance from the scatterer and for the Rayleigh waves versus depth below the free surface reveal a sharp fall for the former and a slow decay in case of the latter.