Extended local Born Fourier migration method

A migration approach based on a local application of the Born approximation within each extrapolation interval contains a singularity that can make direct application unstable. Previous authors have suggested adding an imaginary part to the vertical wavenumber to eliminate the singularity. However, their method requires that the reference slowness must be the maximum slowness of a given layer; consequently, the slowness perturbations are larger than those when the average slowness is selected as a reference slowness. Therefore, its applicability is limited. We develop an extended local Born Fourier migration method that circumvents the singularity problem of the local Born solution and makes it possible to choose the average slowness as a reference slowness. It is computationally efficient because of the use of a fast Fourier transform algorithm. It can handle wider angles (or steeper interfaces) and scattering effects of heterogeneities more accurately than the split-step Fourier (SSF) method, which accounts for only the phase change as a result of the slowness perturbations but not amplitude change. To handle large lateral slowness variations, we introduce different reference slownesses in different regions of a medium to ensure the condition of small perturbation. The migration result obtained using the extended local Born Fourier method with multiple reference slownesses demonstrates that the method can produce high-quality images of complex structures with large lateral slowness variations.