It is shown that the effect of a slightly curved surface on the behavior of acoustic ‘‘head waves’’ is: (a) to make the head‐wave arrival time weakly dispersive with frequency; (b) to cause a curvature in the head‐wave arrival time with offset, roughly as (offset)3/2; (c) to cause the head wave to arrive earlier (later) than that corresponding to a flat surface for a synclinal (anticlinal) shape. The amplitude behavior of the head wave is also found to be distorted with (d) a lower (higher) high‐frequency/low‐frequency ratio for reflection from a syncline (anticline) and (e) an enhancement (diminution) relative to that for a head wave from a flat surface for a synclinal (anticlinal) surface with the enhancement (diminution) exponentially dependent on offset, roughly as (offset)3/2in the exponent. These calculations have been done in order to point out that it may be possible to use these features of head waves in order to unravel subtle structural traps in the subsurface, which vary slowly and would not be noticed in conventional seismic processing.