ANALYSIS OF HIGHER-ORDER, FINITE-DIFFERENCE SCHEMES IN 3-D REVERSE-TIME MIGRATION

The design and usefulness of practical algorithms for 3-D reverse-time depth migration is examined, while demonstrating data applications of the algorithm. We evaluate quantitatively the accuracy of the finite- difference operator from second-order to eighth-order for the scalar w ave equation by comparing numerical and analytical solutions. The resu lts clearly show the advantage of using higher-order, finite-differenc e schemes, especially from second-order to fourth-order for space deri vatives. Hence, a finite-difference method with the accuracy of fourth -order in space and second-order in time is applied to 3-D full scalar wave equations in reverse-time migration. Considerable savings in CPU and memory are obtained by using larger horizontal grid spacings than the vertical spacings. Therefore, we derive dispersion and stability conditions for such unequal grid spacing. The 3-D reverse-time migrati on of data from the Hibernia Field shows an image improvement over 2-D migrations, despite the fact that much of the structure was considere d to be approximately 2-D. Stable, nondispersive, finite-difference me thods of higher order can allow for tractable and efficient 3-D revers e-time migration solutions.