Abstract: In this paper, both forward modeling and migration of the full acoustic wave equation are presented using the fourth order finite difference method based on the exploding reflector model. The forward modeling algorithm can create synthetic data profiles for varying velocity and varying density, and the migration algorithm is not limited by dip angle of the reflectors, nor by the velocity variations. Their dispersions is only about half of that of the conventional methods, and the speed of calculatian is fastcr than the other methods with similar functions. The method has been tested by comparison with tank data profile and by migrating the synthetic profile and the tank data profile. The mathematical stability and the relationship between dispersion and space sampling of the modeling method of varying velocity and varying density, as well as some technical problems related to the implementation of the program are discussed.