Three-dimensional diffraction of plane P, SV & SH waves by a hemispherical alluvial valley

Abstract

The three-dimensional scattering and diffraction of plane waves by a hemispherical alluvial valley in the homogeneous elastic space has been analyzed. The exact series solutions of the mixed boundary value problem for incident P, SV, SH waves are presented. Ground motion on or near the valley has been studied. For plane incident waves, the nature of ground motion will depend on (1) angle of incidence, type, and amplitude of incident waves, (2) η, a dimensionless frequency proportional to the ratio of the diameter of the valley to the wavelength of the incident waves, (3) κ₁, κ₀, the ratio of the longitudinal to transverse wave speeds respectively in the valley and the half-space, (4) ∼μ=μ₁/μ₀, the ratio of the respective shear moduli, (5) ∼α=α₁/α₀, the ratio of the respective longitudinal wave speeds.

The displacement amplitudes on nearby ground surface show significant departure from the uniform half-space motions. The elastic properties of the valley relative to the half-space determine the overall trends of motion on the valley.