On the Stability of Seiche and Free Oscillations of the Surface Layer of the Earth's Crust

Abstract

Consider the equation of long wave in one dimensional form:
Here ζ is elevation from free surface and h the depth. We put
then we readily see that in case of no stable wave motion occurs, but in case of there exists stable oscillation. This is hydrodynamically interpretted such that the steep inclination of bottom form makes relatively slow oscillation unstable. In the above equation σ is the frequency of wave. Applying the present derivation some actual numerical examples are discussed here. The same consideration has been applied to the problem of free oscillation of surface layer, viz to that of elastic vibration. The similar characteristic condition has been derived and numerical examples are given.