Iterative design of one-dimensional efficient seismic Lp infinite impulse response f-x digital filters

This study proposes a new technique, the Lp iterative reweighted least-square (IRLS) algorithm, to design efficient and accurate non-causal complex-valued seismic infinite impulse response (IIR) frequency-space (f-x) digital filters. Unlike earlier works where the problem is prefiltered and linearised, through this technique, the weights are updated by the trust-region-reflection (TRR) optimisation method, and the non-linear-weighted least-square IIR filter design problem is solved directly. The results of this study show smooth convergence empirically of the proposed IRLS-TRR algorithm for designing efficient complex-valued IIR f-x filter coefficients. Using the same specification parameters, the design for an IIR f-x filter of the order of N=2, a requirement needed for seismic wavefield extrapolation filters, outperforms the same filter designed using the IRLS prefiltering linearised algorithm at the expense of a few additional iterations and a justified running design time.