Full-wave-equation depth extrapolation for migration using matrix multiplication

Abstract

To investigate wavefield depth extrapolation using the full-wave equation, we have derived a new depth extrapolation scheme for migration using functions of the vertical wavenumber. We develop a complete matrix multiplication formulation and approach to calculate the related mathematical functions of the vertical wavenumber and perform depth extrapolation using matrix multiplication only. Because our depth extrapolation algorithm involves only matrix multiplication, it is naturally applicable to parallel computations. Impulse response experiments demonstrate that our proposed migration method can achieve the same accuracy as full-wave-equation migration using the finite-difference method, in terms of phase information, even for media with strong lateral velocity changes. In numerical experiments using a smoothed version of the 2D SEG/EAGE salt model, our migration method provides an equivalent imaging result compared with reverse time migration (RTM) and a more accurate imaging result than migration using one-way propagators. Our method has certain potential advantages over RTM using the same full-wave equation with fewer internal multiple scatterings and fewer data storage requirements. Our adopted method is a stable depth extrapolation scheme because the evanescent waves are well suppressed. The numerical experimental results on the synthetic model demonstrate the importance of suppressing evanescent waves in a full-wave-equation-based depth extrapolation scheme and migration for imaging quality and computation cost.