On seismic deghosting by spatial deconvolution

Receiver-side deghosting can be derived and implemented in the frequency domain as spatial deterministic deconvolution of marine pressure recordings. The deghosting/deconvolution operator is found analytically as the inverse Fourier transform of the wavenumber-domain wave equation deghosting function. For a sea surface reflection coefficient of -1, the wavenumber-domain deghosting function has well-known poles at fundamental frequencies equal to an integer multiple of a function of the receiver depth and the plane-wave dip angle relative to the depth axis. The first singularity is always at 0 Hz. The spatial deghosting operator has singularities at fundamental frequencies equal to an integer multiple of a function of the receiver depth, independent of its lateral coordinates. The first singularity is again at 0 Hz. In addition, the deghosting operator that is applied to 3D data has singularity when its lateral coordinate is zero. A simple numerical example demonstrates the method.