ABSTRACTLateral velocity variation causes time migration to misposition events. Black and Brzostowski 1993 quantify this error by developing a first order theory for the positioning error in terms of x and t. The response of a point diffractor in a medium with a simple lateral velocity variation is a distinctive cusp-like shape that we call a ``plume''. The nature of the plume is revealed by making two geometrical constructions based upon point diffractor ray-tracing: superposition of semicircles and summation along hyperbolas. The plume shapes derived by these two techniques are consistent with results obtained by migrating synthetic point diffractors using the Kirchhoff, Stolt, and Gazdag time migration methods. The shapes of these plumes resemble those predicted by Black and Brzostowski's simple first-order theory, but the actual plumes are less symmetric than the predictions. Thus a higher-order theory is needed. |