On Numerical Methods for Migration in Layered Media*

Abstract

Three current migration methods derived from the wave‐equation model and based on approximations by Fourier series, finite‐differences, and a combination of both (mixed method) are reviewed. Each method is examined in the context of horizontally layered media, where the velocity of wave propagation varies with depth alone. It is shown how, under such conditions, the special properties of the linear equations obtained from finite‐difference and mixed approximations can be exploited for computational efficiency. A numerical algorithm is described which substantially reduces the complexity and the computational cost of the solution. This algorithm is directly applicable to vector processing. The description of each method includes derivation, dispersion relation, stability properties, and applicable numerical algorithms. Comparative analyses show that, for the same computational cost, the finite‐difference approximation has poor accuracy characteristics and should be used only when the boundary conditions are difficult to express in the frequency domain. The results are illustrated with numerical experiments on synthetic data.