Exact integral expressions for the displacement components as a function of azimuth, in P1P2P1, (S1S2S1)SV, and (S1S2S1)SH head waves due to an impulsive double-couple source of arbitrary orientation in two semi-infinite media separated by a plane horizontal boundary, and the effect of free surface on it, have been obtained. The time variation of the source is assumed to be represented by the Heaviside unit function. The response due to an arbitrary source excitation may, however, be obtained from this solution by superposition. Necessary formulae for the operational interpretation of integral equations occurring in the problem are given.
Illustrative examples showing the waveform in P1P2P1, (S1S2S1)SV, and (S1S2S1)SH head-wave displacement components for a particular fault and a suitably chosen earth model are given. Plots of the projection of particle trajectory for P waves in ur-uz plane, and for S waves in uϕ-ur and uϕ-uz planes are given for different azimuths; where ur, uϕ, uz are the components of displacement in a cylindrical coordinate system (r, ϕ, z).