WAVE-PACKETS, SIGNALING AND RESONANCES IN A HOMOGENEOUS WAVE-GUIDE

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.