Theory of head waves for focal mechanism studies

Abstract

Harskell's result for the displacement due to a single-couple source of arbitrary orientation in a homogeneous, isotropic, perfectly elastic infinite space has been used to obtain the P , SV and SH wave potentials in a cylindrical co-ordinate system ( r , ϕ , z ). Approximate, far field, solutions for the components of displacement of the free surface due to P 1 P 2 P 1, ( S 1 S 2 S 1)SV, ( S 1 S 2 S 1)SH head-wave arrivals for a single- and double-couple source in the upper medium of a layer over a half-space have been obtained. Equations of Nuttli, tan e = F h tan γ , tan e = F v tan δ may be used to obtain the polarization angle e from the observation of γ , angle between the horizontal component of the S -wave surface motion and the great circle path to the station, or from δ , angle between the vertical axis and the component of the S -wave surface motion in the plane transverse to the great circle path. In the present case F h and F v depend on the orientation of the forces of the couple, epicentral distance, azimuth of the observing station, wave period and the elastic properties of the earth model chosen for the study. Illustrative examples for the azimuthal radiation pattern for P 1 P 2 P 1 head wave and horizontal radial, cross-radial, and vertical S 1 S 2 S 1 head-wave dis-placement components for a suitably chosen single-layered earth model are given. Plots of the projection of the particle trajectory for the S waves in the horizontal and in the vertical cross-radial planes are given for different azimuths.