The design of a homotopy-based 1-D seismic FIR f − x wavefield extrapolation filters

Abstract

This paper proposes a novel application of the homotopy method to design accurate non-causal complex-valued seismic FIR wavefield extrapolation digital filters for the purpose of seismic migration. The FIR filter design problem is solved using the scalar homotopy continuation method, since the filter design system of equations is overdetermined. In addition, the design approach was modified to satisfy the consistency conditions of the scalar homotopy method. Being a novel application to design FIR filters, the scalar homotopy method requires longer running design time compared to other existing methods such as the Weighted Least Squares (WLSQ) and the L1-norm methods. At the same time, the homotopy method is globally convergent and does not require the inversion of the Jacobian matrix, which is a significant advantage for practical purposes. Finally, the designed wavefield extrapolation digital filters were tested using the challenging Marmousi model data set, where prestack migration was performed successfully.

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Recommended citation: W. A. Mousa and A. F. Al-Battal, “The design of a homotopy-based 1-D seismic FIR f − x wavefield extrapolation filters,” Journal of Applied Geophysics, vol. 173, p. 103933, Feb. 2020, doi: 10.1016/j.jappgeo.2019.103933.