Weyl filters for linear array data

The Weyl transform, which is closely connected to the Wigner distribution, allows one to reconstruct (temporally and spatially) localized frequency-wavenumber spectral components. Such filters were suggested in time-frequency analysis by Kozek and Hlawatsch (1992). The theory can be naturally extended to signals recorded in space and time. Thereby, wavefield components with predefined varying spectral properties like, for example, wavefront curvature, can be synthesized. The numerical implementation of such filters is in the most general case a computationally expensive task. We present a simplified implementation, which assumes a specially shaped filter pass region. The assumption resembles a ray approximation and allows one to track a temporally and spatially unidimensional wavefield recording for curved wavefronts in reasonable computation times. The suitability of the method is demonstrated by synthetic data and seismic field data, although it is quite general and not restricted to seismic applications.