Asymptotic Analysis of the Non-Linear Effects on Finite Echo-Pulses From Elastic Half-Space

The one-dimensional deformation waves dependent on the time t and on the Lagrangian coordinate X are considered. In the region 0 ≦ X ≦ L ₀ (medium) the deformation waves (pulses) are described by one, and in the region L ₀ ≦ X ≦∞ (half-space) by another, quasi-linear wave equation. Two kinds of pulse-type input of arbitrary form at X=0 are considered. It is shown that by the analyses of the influence of the non-linear effects on the echo-signal (reflected pulses) not only the error of the linear solution but also the additional information on the physical properties of the half-space might be established.