Document Type



head waves, second order boundary waves, wave refraction, wave transmission


Geometry and Topology | Geophysics and Seismology | Harmonic Analysis and Representation | Mathematics | Physics


When a combined longitudinal and transverse disturbance, diverging from a localized source, strikes a plane boundary between two solid elastic media, several systems of head waves and second order boundary waves are generated, each associated with grazing incidence of one or the other of the reflected or refracted waves. Associated with grazing incidence of P 1 P2, the refracted P-wave, is the head wave system comprising P1P2P1 (the "refracted wave" of seismic prospectors), and P1P2S1 (a transverse head wave) in the upper medium, and P1P2S2 (a transverse head wave) in the lower medium. There is no boundary wave in the lower medium. These three waves, with the second order term of P1£2 (the first-order term is zero on the boundary) satisfy conditions of continuity of stress and displacement at the boundary. Moreover, the energy of the three head waves is derived completely from the second-order component of P1P2 , which possesses a component of energy flow normal to the boundary. The amplitudes of P1P2P1, P1P2S1 and P1P2,S2 are calculated for certain cases.

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Original Publication data for citation:

Patrick A. Heelan, S.J., "On The Theory of Head Waves," Geophysics, Vol. 18, Issue 4 (1953): 871-893