The phase-shift method of migration is attractive because it allows for arbitrary depth variation in velocity and arbitrary angles of propagation up to 90.Unfortunately, lateral variation in velocity is not permitted because of the Fourier transformation over the x-axis. To alleviate this difficulty, Gazdag and Sguazzero [1984] proposed an interpolation method. Recall from chapter that the phase-shift method 2-D Fourier transforms the data p(x,t) to .Then is downward continued in steps of depth by multiplication with .Gazdag proposed several reference velocities, say, v_{1}, v_{2}, v_{3}, and v_{4}. He downward continued one depth step with each of the velocities, obtaining several reference copies of the downward-continued data, say, P_{1}, P_{2}, P_{3}, and P_{4}. Then he inverse Fourier transformed each of the P_{j} over k_{x} to .At each x, he interpolated the reference waves of nearest velocity to get a final value, say, which he retransformed to ready for another step. This appears to be an inefficient method since it duplicates the usual migration computation for each velocity. Surprisingly, the method seems to be successful, perhaps because of the peculiar nature of computation using an array processor.