Computationally Efficient Phase Shift Plus Interpolation Seismic Migration Method

Abstract

In this letter, we propose a computationally efficient implementation of the phase shift plus interpolation (PSPI) seismic migration technique. The PSPI is among the well-known migration techniques in the frequency-wavenumber ( $\omega -k_{x}$ ) domain that accounts for lateral velocity variations in the earth subsurface. However, the large number of complex multiplications required to perform PSPI makes this method computationally expensive. The proposed method replaces the use of complex multiplications in the frequency-wavenumber ( $\omega -k_{x}$ ) domain with real additions, reducing the computational complexity greatly. It also replaces the real-by-complex multiplications with real multiplications. It does so by using the fact that the PSPI technique maintains the amplitude and shifts the phase of seismic wavefields in the passband region of the extrapolators while attenuating the amplitude and maintaining the phase of the wavefield in the evanescent region of the extrapolators. The proposed method was tested by performing 2-D poststack depth migration to the well-known SEG/EAGE Salt Model. The computational complexity in the $\omega -k_{x}$ domain was reduced by 76.9%, while producing an accurate migrated section of the salt model.