Attempting to image the subsurface in areas of complex geology and rapid lateral velocity variation is a challenging problem. In particular, using prestack Kirchhoff migration in conjunction with first arrival travel times produces poor subsurface images with increasing depth. This problem is not a limitation of Kirchhoff migration, but it is the failure of the finite difference method to compute travel times which correspond to the most energetic arrivals. Dimitri Bevc in 1997 proposed a technique that combines the use of the wave equation datuming with dividing the velocity model into subsets. In each subset, calculation of the travel times with the finite differencing eikonal equation is valid. This thesis applies Bevc's technique using a software package (ProMAX) that is widely used among the academic and the industrial communities. We not only get a superior image at depth but we also enjoy the simplicity and the computational efficiency of using the finite difference method. We use the Marmousi synthetic dataset as input, which satisfies the definitions of structural complexity and rapid lateral velocity variation. To demonstrate the effectiveness of our approach, tests were performed on the Marmsoui dataset before and after the application of the semi-recursive Kirchhoff migration.