A model for nonlinear seismic waves in a medium with instability

Experimental investigations show that the earth's crust is elastically nonlinear and contains the sources of accumulated elastic energy, so that it can be considered as a nonlinear active medium. The effects of stimulation of narrow- and broad-band seismic emission and the existence of dominant frequencies for which the medium is transparent have been reported. A model evolutionary equation which takes into account nonlinearity, instability, dissipation of energy and dispersion is proposed and solved numerically. The temporal evolution of chaotic signals results in the formation of quasi-sinusoidal steady-state wave trains. The dependence of their amplitude on the values of coefficients of nonlinearity and dispersion is found. The mathematical model proposed can be used to describe the observed seismic phenomena.