The distortion of reflection continuity and amplitude by overburden structure in seismic reflection images of the subsurface is easily recognised and modelled when the wavelength of the shallower structure is relatively large. The effects of shorter wavelength structure although giving rise to little reflective response itself, cause significant distortion of the propagating wavefield, particularly when a moderate or strong acoustic impedance contrast is present in the shallow sub-surface. Here we show how short as well as long spatial wavelengths of horizon roughness affect deeper reflection continuity, and develop a new method using fractal interpolation techniques to predict the total roughness of sub-surface horizons from information contained in seismic reflection sections. Fractally complete depth-velocity models are used in forward models, using the finite difference technique, to produce synthetic seismic profiles. The technique is illustrated with data from the Edoras Bank area of the Rockall Plateau, NE Atlantic, where apparently discontinuous reflectors underlying basalt flows are shown to be from continuous sedimentary horizons distorted by overlying rough horizons.¿ 1997 American Geophysical Union