A FREQUENCY DOMAIN MAPPING APPROXIMATION OF MOVEOUT FILTERS WITH APPLICATIONS*

Abstract

AbstractWavenumber aliasing is the main limitation of conventional optimum least‐squares linear moveout filters: it prevents adequate reject domain weighting for efficient coherent noise rejection. A general frequency domain multichannel filter design technique based on a one‐to‐one mapping method between two‐dimensional (2D) space and one‐dimensional (1D) space is presented. The 2D desired response is mapped to the 1D frequency axis after a suitable sorting of the coefficients. A min‐max or Tchebycheff approximation to the desired response is obtained in the 1D frequency domain and mapped back to the 2D frequency domain. The algorithm is suitable for multiband 2D filter design. No aliasing damage is inherent in the linear moveout filters designed using this technique because the approximation is done in the frequency‐wavenumber (f, k)‐domain.Linear moveout filters designed by using the present coefficient mapping technique achieve better pass domain approximations than the corresponding conventional least‐squares filters. Compatible reject domain approximations can be obtained from suitable mappings of the origin coefficient of the desired (f k)‐response to the 1D frequency axis. The (fk)‐responses of linear moveout filters designed by using the new technique show equi‐ripple behavior. Synthetic and real data applications show that the present technique is superior to the optimum least‐squares filters and straight stacking in recovering and enhancing the signal events with relatively high residual statics. Their outputs also show higher resolution than those of the optimum least‐squares filters.