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

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 θ (0°<θ<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 R 1 i from the SV‐P source have a larger high‐frequency content than R 1 i from the P ‐source, show less dispersion and have larger amplitudes when caused by shallow and medium‐depth sources. Higher mode surface waves R 2 i 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 R 3 i has larger radial than angular component and is found equally from both sources. The GV &#x006e;̈ 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 GV &#x006e;̈ is 2–3 times larger than its angular component and is similar to the G &#x006e;̈ guided waves from an SH ‐torque source. GV &#x006e;̈ 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.