Rayleigh waves in a half-space with bounded variation in density and rigidity

abstract The stress equations of motion of elasticity are solved by the power series method for an inhomogeneous, isotropic elastic semi-space whose rigidity modulus μ and density ρ are defined by ρ = μ ∞ + ( μ 0 − μ ∞ ) exp ( − ε x 2 ) , ρ = ρ ∞ + ( ρ 0 − ρ ∞ ) exp ( − ε x 2 ) , ε > 0 , x 2 ∈ [ 0 , ∞ ]. The period equation for Rayleigh waves is derived and discussed numerically. The solutions may also be useful for body-wave studies.