Fourier Finite-difference Migration Research Articles

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

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.

Eliminating artifacts in migration of surface-related multiples: An application to marine data

Migration of multiples can use surface-related multiples to provide extra illumination of the subsurface; however, the migrated images usually contain many migration artifacts. We have developed an efficient workflow to eliminate the artifacts in migration of surface-related multiples and applied it to marine data. Our workflow was based on the criterion that true seismic events in angle-domain common-image gathers (ADCIGs) should be flat. The ADCIGs were obtained via the one-way wave-equation migration and then processed by high-resolution parabolic Radon transform to separate the artifacts. Using the adjoint Radon transform, the filtered ADCIGs can be stacked to get the final image with a high signal-to-noise ratio. We also discovered that the ADCIGs can be extracted from Fourier finite-difference migration more efficiently than by reverse time migration. In the application to marine data, most noise generated by the crosscorrelation of undesired seismic events was suppressed. This shows that the final images can be a valuable complement to conventional migration using primaries only.

Wide-angle FD and FFD migration using complex Padé approximations

Seismic migration by downward continuation using the one-way wave-equation approximations has two shortcomings: imaging steep-dip reflectors and handling evanescent waves. Complex Padé approximations allow a better treatment of evanescent modes, stabilizing finite-difference migration without requiring special treatment for the migration domain boundaries. Imaging of steep-dip reflectors can be improved using several terms in the Padé expansion. We discuss the implementation and evaluation of wide-angle complex Padé approximations for finite-difference and Fourier finite-difference migration methods. The dispersion relation and the impulsive response of the migration operator provide criteria to select the number of terms and coefficients in the Padé expansion. This ensures stability for a prescribed maximum propagation direction. The implementations are validated on the Marmousi model data set and SEG/EAGE salt model data.