We solve the initial-boundary-value linear stability problem for small
localised disturbances in a homogeneous elastic waveguide formally by
applying a combined Laplace-Fourier transform. An asymptotic evaluati
on of the solution, expressed as an inverse Laplace-Fourier integral,
is carried out by means of the mathematical formalism of absolute and
convective instabilities. Wave packets, triggered by perturbations loc
alised in space and finite in time, as well as responses to sources lo
calised in space, with the time dependence satisfying e(-i omega 0t) O (e(-epsilon t)), for t --> infinity where Im omega(0) = 0 and epsil
on > 0, that is, the signaling problem, are treated. For this purpose,
we analyse the dispersion relation of the problem analytically and by
solving numerically the eigenvalue stability problem. It is shown tha
t due to double roots in a wavenumber k of the dispersion relation fun
ction D(k, omega) for real frequencies omega that satisfy a collision
criterion, wave packets with an algebraic temporal decay and signaling
with an algebraic temporal growth, that is, temporal resonances, are
present ina neutrally stable homogeneous waveguide. Moreover, for any
admissible combination of the physical parameters, a homogeneous waveg
uide possesses a countable set of temporally resonant frequencies. Con
sequences of these results for modelling in seismology are discussed.
In particular, a hypothesis is suggested concerning a possible resonan
t triggering mechanism of certain earthquakes.