In areas with a complex surface,the acquisition and processing of seismic data is a great challenge.Although elevation-static corrections can be used to eliminate the influences of topography,the distortions of seismic wavefields caused by simple vertical time shifts still greatly degrade the quality of the migrated images.Ray-based migration methods which can extrapolate and image the wavefields directly from the rugged topography are efficient ways to solve the problems mentioned above.In this paper,we carry out a study of prestack Gaussian beam depth migration under complex surface conditions.We modify the slant stack formula in order to contain the information of surface elevations and get an improved method with more accuracy by compositing local plane-wave components directly from the complex surface.First,we introduce the basic rules and computational procedures of conventional Gaussian beam migration.Then,we give the original method of Gaussian beam migration under complex surface conditions and an improved method in this paper.Finally,we validate the effectiveness of the improved method with trials of model and real data.