We show, from a Huygens-Fresnel integral formulation of the scattered electromagnetic field, that the wave equation for a thin turbulent medium with nonconstant mean characteristics can be reformulated as a problem involving turbulence on a constant background. This is accomplished by a set of simultaneous transformations, which, when reversed and applied to known solutions of the simpler problem involving a constant background, yield results that correctly account for the inhomogeneous ambient atmosphere upon which the turbulence is superimposed. When applied to the mutual coherence function it is found that this quantity is unaltered if the separation of the two field points in the plane of the receiver is replaced by the corresponding separation obtained by projecting these points along the average refracted rays back to the ray periapsis. For the associated spectral broadening function this implies that spectra corresponding to different occultation depths and geometries may be obtained by simple translation of a shape-invariant spectrum along the frequency axis. We also find that the scintillation index approaches asymptotically unity in strong scattering in precisely the same way as if the ambient background were strictly homogeneous, consistent with recent numerical simulations of a one-dimensional scattering model.