We experienced difficulties when attempting to perform seismic imaging in complex velocity fields using prestack Kirchhoff depth migration in conjunction with traveltimes computed by finite‐differencing the eikonal equation. The problem arose not because of intrinsic limitations of Kirchhoff migration, but rather from the failure of finite‐differencing to compute traveltimes representative of the energetic part of the wavefield. Further analysis showed that the first arrival is most often associated with a marginally energetic event wherever subsequent arrivals exist. The consequence is that energetic seismic events are imaged with a kinematically incorrect operator and turn out mispositioned at depth. We therefore recommend that first‐arrival traveltime fields, such as those computed by finite‐differencing the eikonal equation, be used in Kirchhoff migration only with great care when the velocity field hosts multiple transmitted arrivals; such a situation is typically met where geological structure creates strong and localized velocity heterogeneities, which partition the incident and reflected wavefields into multiple arrivals; in such an instance, imaging cannot be strictly considered a kinematic process, as it must be performed with explicit reference to the relative amplitudes of multiple arrivals.

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