Wavenumber‐based filtering of marine point‐source data

Abstract

In seismic processing, plane‐wave decomposition has played a fundamental role, serving as a basis for developing sophisticated processing techniques valid for depth‐dependent models. By comparing analytical expressions for the decomposed wavefields, we review several processing algorithms of interest for the geophysicist. The algorithms may be applied to marine point‐source data acquired over a horizontally layered viscoelastic and anisotropic medium. The plane‐wave decomposition is based on the Fourier transform integral for line‐source data and the Hankel transform integral for point‐source data. The involved wavenumber integrals of the cosine or Bessel‐function type are difficult to evaluate accurately and efficiently. However, a number of the processing techniques can easily be run as a filtering operation in the spatial domain without transforming to the wavenumber domain. The mathematical expressions for the spatial filters are derived using plane wave analysis. With numerical examples, we demonstrate the separation of upgoing and downgoing waves from the pressure, the removal of the source ghost from the pressure, and the transformation of point‐source pressure data to the corresponding line‐source data. The filters for these three processes work satisfactorily. Limited spatial aperture is discussed both for point‐source and line‐source data. The resolution kernels relating finite‐aperture decomposed data to infinite‐aperture decomposed data are given. The kernels are approximately equal in the asymptotic limit when the minimum offset is zero.