Ground-motion amplification by topographic depressions for incident P wave under acoustic approximation

Ground-motion amplification caused by a semi-spherical and a semi-cylindrical cavity in a half-space for an incident P wave is calculated from analytic solutions under acoustic approximation. We expect this approximation to be valid for materials with a Poisson's ratio near 0.5, e.g., saturated soils. The ground motion is zero at the edges of the cavity and is normal to the free surface. An amplification of about 2 to 3 occurs near the bottom of the cavity for large wavelengths. Detailed numerical results are given for vertical incidence.