Optimization of the parameters in complex Padé Fourier finite-difference migration

Abstract

Complex Padé Fourier finite-difference migration is a stable one-way wave-equation technique that allows for better treatment of evanescent modes than its real counterpart, in this way producing fewer artifacts. As for real Fourier finite-difference (FFD) migration, its parameters can be optimized to improve the imaging of steeply dipping reflectors. The dip limitation of the FFD operator depends on the variation of the velocity field. We have developed a wide-angle approximation for the one-way continuation operator by means of optimization of the Padé coefficients and the most important velocity-dependent parameter. We have evaluated the achieved quality of the approximate dispersion relation in dependence on the chosen function of the ratio between the model and reference velocities under consideration of the number of terms in the Padé approximation and the branch-cut rotation angle. The optimized parameters are chosen based on the migration results and the computational cost. We found that by using the optimized parameters, a one-term expansion achieves the highest dip angles. The implementations were validated on the Marmousi data set and SEG/EAGE salt model data.