The FOCI method versus other wavefield extrapolation methods

Saleh M. Al-Saleh, Gary F. Margrave, Hugh D. Geiger

Recursive wavefield extrapolation methods are more powerful than ray theory based methods because of their great ability to handle strong lateral velocity variations. There are different methods to calculate frequency-space convolution operators for wavefield extrapolation. Wavefield extrapolation methods have two major problems (1) the extrapolator instability and (2) they are computationally expensive.

The forward operator and conjugate inverse (FOCI) method is an appropriate method for designing accurate and efficient extrapolation operators that remain stable in a recursive algorithm. The FOCI's results are comparable with other results obtained with other known methods such as Hale's and the weighted least square (WLSQ) extrapolation methods. Further, the FOCI method is computationally more efficient than the other methods.

The amplitude and phase spectra of the FOCI's, Hale's, and WLSQ's extrapolators are shown to compare their stabilities and accuracies. The impulse responses of these extrapolators are also shown to further compare their accuracies. The Marmousi dataset is used to illustrate the quality of the three extrapolators in a prestack depth migration in the presence of strong lateral velocity variations and steeply dipping events.