Frequency-space wavefield extrapolation using infinite impulse response digital filters: is it feasible?

The purpose of this paper is to study the possibility of performing practically stable and efficient frequency-space (f−x) wavefield extrapolation for the application of seismic imaging and datuming via infinite impulse response (IIR) filters. The model reduction control theory was adopted to design such IIR f−x extrapolation filters. The model reduction theory reduces the order of a given order system which, in this case, involves reducing a finite impulse response (FIR) f−x extrapolation filter system into an IIR f−x extrapolation filter system. This theory relies on decomposing the states of the given filter system into strong and weakly coupled sub-systems, and then eliminating the weakly coupled states via singular value decomposition of the Hankel and the impulse response Gramian matrices. Simulation results indicate that IIR f−x filters can be obtained, which are stable from an IIR filter design point of view. Simulations also indicate that stable seismic impulse responses and synthetics can be obtained with a reduced system model order and, hence, less computational efforts with respect to the number of complex multiplications and additions per output sample. It is hoped that this study will open new possibilities for researchers to reconsider designing IIR f−x explicit depth extrapolation filters due to their expected computational savings and wavenumber response accuracy, when compared to the FIR f−x explicit depth extrapolation filters.