Sonic-boom noise penetrating under a deep ocean is affected by its time-dependent interaction with the surface waves, which can significantly influence the perceived sound pressure level and tonal content of the disturbances at depth far greater than expected from the flat-ocean (Sawyers) model. The present theory assumes a small surface slope and a high water-to-air density ratio; the ocean surface in the analysis is modelled by a sinusoidal surface-wave train. The analysis shows that a distinct acoustic wave mode in the form of a packet of wavelets emerges in the sound field far below the surface and attenuates with increasing distance in a manner similar to the cylindrical spreading of monochromatic waves. The latter feature renders the surface waviness influence an effect of first-order importance, overwhelming the primary noise field at large depth. Detailed properties of the deep-water wave fields are examined and illustrated for the case of an incident N-wave, for which an explicit, analytic solution is obtained. The result reveals a similarity structure of the wave field with two distinct time scales and the invariance characteristics of the cylindrically spreading waves, in accord with the group-velocity concept of dispersive waves. An example is given of the interaction, illustrating the underwater waveform, sound-pressure and frequency levels.