  We treat the case of a flat stress-free surface (i.e., the ground in
seismological applications) separating air from a homogeneous, isotropic, solid
substratum overlain by a homogeneous, isotropic, solid layer (in contact with
the ground) solicited by a SH plane body wave incident in the substratum. The
analysis is first carried out in the frequency domain and subsequently in the
time domain. The frequency domain response is {\it normal} in that no
resonances are excited (a resonance is here understood to be a situation in
which the response is infinite in the absence of dissipation). The translation
of this in the time domain is that the scattered pulse is of relatively-short
duration. The duration of the pulse is shown to be largely governed by
radiation damping which shows up in the imaginary parts of the complex
eigenfrequencies of the configuration. Three methods are elaborated for the
computation of the time history and give rise to the same numerical solutions
for a large variety of configurations of interest in the geophysical setting
under the hypothesis of non-dissipative, dispersionless media. The method
appealing to the complex eigenfrequency representation is shown to be the
simplest and most physically-explicit way of obtaining the time history (under
the same hypothesis). Moreover, it is particularly suited for the case in which
modes can be excited as occurs when the incident wave is not plane or the
boundary condition is not of the stress-free variety for all transverse
coordinates on the ground plane.
