Amplitudes of PcP and PcS obtained from Ray and Wave Theory Solutions and Amplitudes Near Shadow Boundary

Abstract

Amplitudes of PcP and PcS phases are derived in terms of ray and wave theory. Numerical computations when the core is assumed to be a spherical cavity or a liquid are presented to show that, as far as periods of the waves concerned are shorter than 40 sec, the ray theory solution gives satisfactory approximation if angle of incidence at the mantle-core boundary is smaller than 70°. Amplitudes of diffracted waves with short periods decay from a shadow boundary to wards the shadow zone more rapidly than those with long periods. Frequency dependence of amplitudes of the diffracted waves is obtained in a wide frequency range from the numerical solution, refering to a short wave solution. Amplitudes of direct waves close to the shadow boundary cannot be explained by simple ray theory because of contamination due to diffraction into a lit zone. Ex-pressions for the amplitudes in this area are also derived, together with epicentral distance where waves recognize the existence of the core.