CONCLUSION

We presented an explicit depth migration method which is unconditionally stable. This explicit depth-migration scheme is stable even in the case of lateral velocity variation. For 15-degree depth migration, its impulse responses are comparable in accuracy to those produced by the implicit scheme of Crank-Nicholson approximation. To get a more accurate operator at steep dip we can add more terms in the Taylor expansion of the square-root operator and it results in a matrix with thicker bands than a tridiagonal matrix. In such case, we can still use the unconditionally stable, explicit algorithm but it requires expensive computation to get a good accuracy.