On the problem of analyzing the dynamic properties of a layered half-space

Abstract

An efficient method is developed for constructing the Green matrix functions of a layered inhomogeneous half-space. Matrix formulas convenient for programming are proposed, which make it possible to study the properties of a multilayered half-space with high accuracy. As an example of the problem of oscillations of a three-layer half-space, transformation of the dispersion characteristics of a three-layered medium is shown as a function of the relations of the mechanical and geometric parameters of its components. Study of the properties of the Green’s function of a medium with a low-velocity layered inclusion showed that each mode of a surface wave exists in a limited frequency range: in addition to the critical frequency of mode occurrence, the frequency of its disappearance exists—a frequency above which the mode is suppressed because of superposition of the zero of the Green’s function on its pole. A similar study conducted for a medium with a high-velocity layered inclusion has shown that in addition to the cutoff frequency (the frequency at which a surface wave propagating in the low-frequency range disappears), there is the frequency of its recurrent generation—the upper boundary of the “cutoff range” of the first mode. Beyond this range, the first mode propagates, and also the other propagating modes can appear. The critical relation of the geometric parameters of the medium determining the existence and boundaries of the cutoff range of a wave is established.