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.
The Grothendieck conjecture and Padé approximations