Mathematical interpretation of seismic wave scattering and refraction on tunnel structures of circular cross-section

Abstract

Mathematical interpretation of the elastic wave diffraction in circular cylinder coordinates is in the focus of this paper. Firstly, some of the most important properties of Bessel functions, pertinent to the elastic wave scattering problem, have been introduced. Afterwards, basic equations, upon which the method of wave function expansions is established, are given for cylindrical coordinates and for plane-wave representation. In addition, steady-state solutions for the cases of a single cavity and a single tunnel are presented, with respect to the wave scattering and refraction phenomena, considering both incident plane harmonic compressional and shear waves. The last part of the work is dealing with the translational addition theorems having an important role in the problems of diffraction of waves on a pair of circular cylinders.