Imaging from topography with Fourier methods

Gary F. Margrave, Zhengsheng Yao

The method of wavefield extrapolation by nonstationary phase shift is extended to the case of data recorded on a topographic surface. Using the NSPS (nonstationary phase shift) algorithm, the space-domain input data is phase shifted to a horizontal datum beneath the lowest topographic point. The nonstationary phase shift simultaneously accounts for lateral velocity variations and the lateral variation of downward step size. The f-k spectrum of the downward continued data is synthesized at the datum. A much more computationally expensive pseudo-inverse technique is also formulated for comparison. Tests on simple synthetics show that the NSPS method works nearly as well as the pseudo-inverse technique.