The H/V ratio of Rayleigh waves in layered incompressible orthotropic half-spaces and the incompressible limit method

The main purpose of this paper is to derive exact formulas for the H/V ratio (the horizontal-to-vertical displacement ratio at the upper surface of the layer) of Rayleigh waves propagating in an orthotropic elastic half-space coated by an orthotropic elastic layer. The half-space and the layer are in welded contact and at least one of them is incompressible. These formulas are derived by employing the incompressible limit method. One of the obtained formulas recovers Love's H/V ratio formula. When the layer is absent, the obtained formulas are simplified to the formulas derived previously for the H/V ratio of Rayleigh waves propagating in traction-free orthotropic elastic half-spaces. It is numerically shown that the incompressibility of deposited layers has strong impact on the H/V ratio behavior. As the H/V ratio is a dimensionless quantity and it is easily experimentally measured, the obtained formulas will be a useful tool for nondestructively testing mechanical properties of deposited layers.