Studies of subsurface wave-scattering often rely on wave equation Green's functions for half-planes or half-spaces with plane surfaces. Small deviations from the planar are assumed to have negligible effect away from the surface. Based on extensively-developed perturbation schemes, this article gives analytical first-order approximations for 2D and 3D wave equation Green's functions in the interiors of respectively, half-planes and half-spaces by two approaches. The first approach involves a boundary perturbation, while the second approach invokes a coordinate transformation leading to a perturbation of the governing equations themselves. The cases of, respectively, the functions and their normal derivatives vanishing on the surface are treated. Some numerical results for specific examples are presented and discussed.