Wavefield interpolation in the Fourier wavefield extrapolation

Abstract

The computational cost for seismic migration relies heavily on the methods used for wavefield extrapolation. In general, seismic migration by current industry techniques extrapolates wavefields through a thick slab and then interpolates wavefields in small layers inside the slab. In this paper, I first optimize practical implementation of the Fourier wavefield extrapolation. I then design three interpolation algorithms: Fourier transform, Kirchhoff, and Born‐Kirchhoff for mild, moderate, and large to strong lateral heterogeneities, respectively. The Fourier transform interpolation simultaneously implements wavefield interpolation and imaging without needing to invoke the imaging principle by summing over all frequency components of the interpolated wavefield. The Kirchhoff interpolation is based on the traditional Kirchhoff migration formula and is performed by diffraction summation with a very limited aperture using the average velocity of a laterally heterogeneous slab. The Born‐Kirchhoff interpolation is based on the Lippmann‐Schwinger integral equation. It differs from the Kirchhoff interpolation in that it accounts not only for the obliquity, spherical spreading, and wavelet shaping factors but also for the relative slowness perturbation in a laterally heterogeneous slab. Recursive seismic migration usually accounts for a 20‐ to 40‐ms depth size for wavefield extrapolation in practical applications. Using the above interpolation techniques, Fourier depth migration methods are shown to tolerate a 40‐ to 60‐ms depth size with the SEG/EAGE salt model. Therefore, the Fourier depth migration techniques with thick‐slab extrapolation plus thin‐slab interpolation can be used to image structures with salt‐related complexes.