Wave packets, signaling and resonances in a homogeneous waveguide
The author presents a fundamental study of a realistic dynamic model of the Earth crust. The Earth crust is assumed to be an infinite homogeneous thick plate whose upper surface is free whereas the lower one can be subjected to dynamic excitations. The associated mathematical problem is to find the displacement depending on \(z\) (directed towards the interior of the Earth), surface coordinate \(x\) and time \(t\). The initial perturbation is a displacement quasicompactly localized in space and in time. The author uses the Laplace and Fourier transforms and obtains asymptotic and approximate solutions. An essential feature of this study is the relevance of localized in space resonances due to multiple contributions of normal modes. It is worthy to say that the approach bases on the study of individual normal modes does not provide this phenomenon.
scientific article; zbMATH DE number 1204384