The Motion of a Sphere Caused by an Impulsive Force and by an Explosive Point-Source

Abstract

Summary An exact solution is obtained for the displacement of the surface of a uniform elastic solid sphere of radius a due to an impulsive force applied in radial direction at a point situated at a depth d below the surface. The theoretical seismograms, which were computed for several epicentral distances 9 (Ok9 < 180), show several modes of surface waves in addition to various reflected and diffracted pulses. The higher modes of surface waves are a result of sphericity only and are compared with the observed higher modes and with the higher modes in a plane layered model. A comparison of the present SV-P source with an explosive P-source shows that the Rayleigh-waves RIi from the SV-P source have a larger high-frequency content than R from the P-source, show less dispersion and have larger amplitudes when caused by shallow and medium-depth sources. Higher mode surface waves R2i have larger angular than radial component. They are larger in the results from the P-source, and smaller from the SV-P source. The mode RSi has larger radial than angular component and is found equally from both sources. The GVv surface-waves are the largest guided waves to arrive from the deep SV-P source, they are largest except for the Rayleigh-wave from the shallow and medium depth SV-P sources. The radial component of CV. is 2-3 times larger than its angular component and is similar to the G, guided waves from an SH-torque source. GVv is absent in results from the P-source. The connection between the higher modes of surface waves and groups of certain reflected pulses is given. ' Refracted' pulses, found in results from the shallow SV-P source, have a larger angular than radial component. In several cases the angular component is larger than that of the direct pulse.