f A moveout equation for media with lateral velocity gradients

Accurate estimates of velocity are sometimes compromised where the propagation velocity changes in the horizontal direction. Extreme lateral velocity gradients can impair the coherency of a stacked reflection image. To address these problems I extend the standard model used to predict traveltime of reflected waves by allowing the propagation velocity to change in the horizontal direction. The initial model developed here uses a constant thickness layer in which the velocity varies linearly in the horizontal direction. The traveltime equation for a wave reflected off the base of the layer is derived, assuming a source and receiver on the surface. The new traveltime equation has been integrated into a seismic processing system and by reprocessing selected seismic data we have improved reflector continuity and achieved more reasonable velocity distributions. The flat layer model is discussed by Payne (1990a,b). In the present paper the traveltime model has been further extended to allow aplanar, dipping base to the layer, with a velocity gradient parallel to the base of the layer.