Occurrence of Precursors of PKP Waves in the Layered Radial-Symmetric Earth

It is generally accepted that PKP precursor waves arriving ahead of PKP-waves observed in real data are explained by scattering on small-scale inhomogeneities in the lower mantle. In this paper, a stable analytical solution (without interference) was obtained for the field of longitudinal waves in a layered (discrete) ball of planetary size. The calculations of the total wave field, rays, and travel-time curves of longitudinal waves for the spherical model of the Earth AK135 with a carrier frequency of 1 Hz are presented. The analytical solution showed that, at angles smaller than 145°, low-amplitude waves with a higher frequency of about 1.3 Hz arrive ahead of the PKP-waves. These high-frequency oscillations indeed appear similar to the waves scattered on a certain object. The ray pattern and the travel-time graph show that these high-frequency oscillations are due exclusively to the spherical geometry of the Earth. This could be explained by the interference of refracted and reflected longitudinal waves in the bottom of outer core. This field persists even at smaller angles due to the interference of diffraction waves.