Laterally dependent surface waves in an elastic medium with a general depth dependence

We consider waves in layered elastic structure with arbitrary vertical dependence of parameters, in assumption of rotation invariance of the problem. The goal is generalisation of the traditional form of the solution u(x,y,z)=exp(ikx)v(z)u(x,y,z)=exp(ikx)v(z) with z   depth and (x,y)(x,y) lateral variables, to general lateral dependence. We derive a general integral representation for surface or interfacial wave field, and consider as its particular cases, waves with plane wavefronts and polynomial amplitudes and waves, showing Gaussian-type localisation with respect to (x,y)(x,y). We mention a possibility of surface and interfacial waves, inhomogeneous with respect to lateral variables.