Seismic pulse in a layered sphere: Normal modes and surface waves

An exact solution is obtained for the displacement of the surface of a layered sphere caused by an explosive point source located within the sphere. The solid elastic mantle and the fluid core have densities and elastic constants taken as averages for Bullen's model B. For all modes of periods 4 sec and longer seismograms were computed at several distances from deep and shallow sources. They show Rayleigh waves, higher-mode surface waves, and reflected and diffracted waves. Stoneley waves are found to be due to a source located on the interface. Rayleigh waves are more highly dispersed in the layered sphere than in the homogeneous sphere. Second-mode surface waves have a larger angular component than radial component, and in most cases under consideration they have a larger angular component than any other arrival. The third higher-mode surface waves have a larger radial component. The correspondence between reflected pulses and several modes of surface waves is discussed.