The surface-wave concept in connection with propagation trajectories associated with Sommerfeld problem

Both the continuous-wave solution and the pulse solution of the Sommerfeld problem can be represented as multiple integrals which describe cooperating contributions propagated along continuous sets of trajectories. The latter consist of a number of rectilinear sections that connect the transmitter and receiver. The propagation velocity along each section is in accordance with the corresponding medium. The velocity along section lying in the earth´s surface is that of the well-known surface wave. Transient phenomena at the receiver start after the arrival of a main pulse along the trajectory connecting the transmitter and the receiver in accordance with ordinary geometric optics, ignoring surface-wave effects. Pulses along trajectories containing a surface-wave section may arrive earlier; however, their joint contributions then cancel each other until the arrival of the main pulse.