In the propagation of seismic waves through layered media, the boundaries play crucial role. The boundaries separating the different layers of the earth are irregular in nature and not perfectly plane. It is, therefore, necessary to take into account the corrugation of the boundaries while dealing with the problem of reflection and refraction of seismic waves. The present study explores the reflection and refraction phenomena of SH-waves at a corrugated interface between visco-elastic half-space and fibre-reinforced half-space. Method of approximation given by Rayleigh is adopted and the expressions for reflection and transmission coefficients are obtained in closed form for the first and second order approximation of the corrugation. The closed form formulae of these coefficients are presented for a corrugated interface of periodic shape (cosine law interface). It is found that these coefficients depend upon the amplitude of corrugation of the boundary, angle of incidence and frequency of the incident wave. Numerical computations for a particular type of corrugated interface are performed and a number of graphs are plotted. Some special cases are derived.

The present paper investigates the propagation of Love-type waves in an initially stressed heterogeneous fibre-reinforced layer with corrugated boundary surfaces, lying over a viscoelastic half-space under hydrostatic state of stress. The dispersion relation is obtained in closed form and found to be in well-agreement with the classical Love wave equation. The substantial effect of reinforcement, position and undulation parameters (i.e. corrugation), heterogeneity, horizontal initial stress and hydrostatic state of stress are discussed briefly. It is established through comparative study that reinforced layer supports more to phase velocity of Love-type wave as compare to reinforced free layer.