<p>The sensitivity of the amplitude on the surface of a surface acoustic wave (SAW) to a change in the elastic parameters of a layered half-space with a gradual change in its elastic parameters along the horizontal is considered. Cases of wave transition from a single-layer system to a single-layer system and from a multilayer to a multilayer system are analyzed with the example of a five-layer system with an independent change in the longitudinal and transverse wave velocities in the layers. It is shown that the properties of the reference medium affect the resulting frequency dependences of the relative amplitude. The sensitivity of the wave amplitude to local changes in the parameters in a multilayer system varies significantly depending on the frequency. In the case of a constant Poisson ratio, the mechanism of amplitude variation on the surface is demonstrated based on an analysis of the surface wave profile.</p>