Quasi-Born Fourier migration

Abstract

The Born approximation of the Lippman-Schwinger equation has recently been used to implement a recursive method for seismic migration of pressure wavefields. This Born-based method is stable only when the scattering from heterogeneities within an extrapolation depth interval is weak. To handle strong scattering accurately and efficiently, we propose a quasi-Born approximation of the Lippman-Schwinger equation to extrapolate pressure wavefields downwards recursively. We assume that the scattered wavefield is linearly related to the incident wavefield by a scalar function that varies slowly with lateral position within an extrapolation depth interval. The extrapolation is implemented as a dual-doma in procedure in the frequency-space and frequency-wavenumber domains. Fast Fourier transforms are used to transform data between these two domains. The quasi-Born-based depth-migration algorithm is termed the quasi-Born Fourier method. It can efficiently produce good-quality images of complex structures with strong lateral perturbations of slowness. It is stable for strong scattering and can accurately handle scattering and wave propagation along directions at large angles from the main propagation direction. Image quality obtained using the new method is similar to that of a dual-domain migration method that uses the Rytov approximation within each extrapolation depth interval, but the computational speed of the new method is approximately 27 per cent faster than the latter method for pre-stack migration of an industry standard data set—the Marmousi data set. Compared to the Born-based migration method, the quasi-Born Fourier method is slightly less efficient because it requires an additional multiplication and an additional division for each lateral gridpoint in each step of wavefield extrapolation. For weak scattering, the quasi-Born Fourier method converges to the Born-based method. To improve the efficiency of the quasi-Born Fourier method further without losing its accuracy, we propose a hybrid Born/quasi-Born Fourier method in which the Born-based method is used when the scattering within an extrapolation depth interval is weak, and the quasi-Born Fourier method is used for other cases. This hybrid method is approximately 32 per cent faster than the Rytov-based method for the pre-stack depth migration of the Marmousi data set, while the images obtained using both methods have almost the same quality.