A Note on Three-Dimensional Scattering and Diffraction by a Hemispherical Canyon, II: Normal Incident P- Point Source- Juniper Publishers
Juniper Publishers- Journal of Civil Engineering Abstract This paper revisits the boundary-valued problem of the three-dimensional (3-D) scattering and diffraction of seismic spherical waves by a hemispherical canyon in an elastic half-space, a problem of interest to both earthquake engineers and strong-motion seismologists. The analytical solution of normal incidence of plane P-wave (axi symmetric) has recently been presented in [ 1 ], using the half-range expansion of odd-order Legendre polynomials in terms of even-order Legendre polynomials. The use of excitation by plane harmonic waves is common in many studies of the amplification phenomena by surface and subsurface topographies. It is assumed and reasoned that when the spherical (3-D) and/or cylindrical (2-D) wave fronts are sufficiently far from the earthquake source, such plane wave approximation is adequate. The case of 2-D SH-wave source was recently studied by [ 2 ]. The results are compared with that f...