Reflection of elastic waves from a linear transition layer

A separation of P- and S-wave potentials is achieved for an inhomogeneous medium in which density is constant and Lame's parameters, λ and μ, are assumed to vary as λ/λ1 = μ/μ1 = (1 + bz)2 where λ1, μ1 and b are constants. The resulting equations are solved for an arbitrary angle of incidence. Plane wave reflection coefficients are obtained for the situation when the material mentioned above forms a transition layer between two homogeneous, elastic half-spaces. First and/or second-order discontinuities in material properties are permitted at the boundaries of the transition layer. Some numerical results are given.