Extinction of Stoneley waves in stratified media with diffused interfaces

It is known that along an interface between two isotropic halfspace satisfying the widely used in geophysical applications Wiechert condition, Stoneley waves may propagate with speed of propagation that is independent from frequency. A recent proof on non-existence of Stoneley waves in functionally graded (FG) plates with continuous transverse inhomogeneity may indicate that in real situations, when there is no abrupt change of material properties, the Stoneley waves arise less frequently than it can be supposed. The current analysis is targeted to elucidate the situation of vanishing Stoneley waves, when the initially abrupt interface between elastic layers starts to diffuse.