Neutral stability and resonant destabilization of the Earth's crust

Responses of tectonic plates of the Earth's crust to spatially localized pe rturbations are a classical problem of theoretical seismology. A characteri zation of such responses is of fundamental importance for the estimation an d interpretation of seismograms, for the prediction and analysis of earthqu akes. In this paper, we model a plate of the Earth's crust as a vertically stratified elastic waveguide of finite thickness and infinite horizontal ex tension rigidly attached to a solid half-space underneath it, and study the propagation of spatially localized linear perturbations in the model. An i nitial boundary-value linear stability problem for three-dimensional (3D) s mall localized disturbances in the plate is treated by using the Laplace tr ansform in time and the Fourier transform in two orthogonal spatial directi ons. By applying an energy-type method it is shown that a plate of the Eart h's crust of an arbitrary vertical stratification is exponentially neutrall y stable. The asymptotic time responses of the plate to sources nearly harm onic in time are studied by applying the mathematical formalism for 3D spat ially amplifying waves to the solution having the form of an inverse Laplac e-Fourier integral. The procedure is an extension of previous analysis by B revdo to the vertically stratified case. The vertical stratification of the plate is modelled by using different seismic measurement data. We show tha t every vertically stratified plate of the Earth's crust considered possess es a rich set of resonant frequencies which is assessed to be countable and unbounded. Sources with resonant frequencies cause a resonant destabilizat ion of the plate, with the growth of the perturbation displacement in time like lnt or roott. The result gives further support to our hypothesis that certain earthquakes can be triggered by localized low-amplitude oscillatory forcings at resonant frequencies. Also, based on the presence of very high resonant frequencies in every tectonic plate, we suggest that the estimati on of seismograms and earthquake prediction can be improved by extending th e frequency range of the existing monitoring tools.