WAVE-NUMBER-BASED FILTERING OF MARINE POINT-SOURCE DATA

In seismic processing, plane-wave decomposition has played a fundament al role, serving as a basis for developing sophisticated processing te chniques valid for depth-dependent models. By comparing analytical exp ressions for the decomposed wavefields, we review several processing a lgorithms of interest for the geophysicist. The algorithms may be appl ied to marine point-source data acquired over a horizontally layered v iscoelastic and anisotropic medium. The plane-wave decomposition is ba sed on the Fourier transform integral for line-source data and the Han kel transform integral for point-source data. The involved wavenumber integrals of the cosine or Bessel-function type are difficult to evalu ate accurately and efficiently. However, a number of the processing te chniques can easily be run as a filtering operation in the spatial dom ain without transforming to the wavenumber domain. The mathematical ex pressions for the spatial filters are derived using plane wave analysi s. With numerical examples, we demonstrate the separation of upgoing a nd downgoing waves from the pressure, the removal of the source ghost from the pressure, and the transformation of point-source pressure dat a to the corresponding line-source data. The filters for these three p rocesses work satisfactorily. Limited spatial aperture is discussed bo th for point-source and line-source data. The resolution kernels relat ing finite-aperture decomposed data to infinite-aperture decomposed da ta are given. The kernels are approximately equal in the asymptotic li mit when the minimum offset is zero.