Truncation error analysis at optimum interrelation of discrete parameters in difference migration

This paper presents a method for obtaining the optimum interrelation of discrete parameters which minimize the truncation error of a discrete equation with multiple parameters. The method forsakes the traditional concept of truncation effort and shows that the truncation error of a discrete equation can be minimized only when discrete parameters satisfy a special interrelation. The optimum parameter interrelation of a difference equation can be derived by applying this method to relevant difference migration. The use of continuation step determined by this method can result in optimum difference migration. The synthetic and real data results which were produced using this optimum interrelation are shown in this paper. The results indicate that good seismic migration can be achieved only when the optimum interrelation is satisfied. Authors prove wrong the old opinion that the smaller the continuation step is, the better the migration effect is. This method may be used in analyzing the truncation error of all discrete equations.