SURFACE-CONSISTENT PHASE-DECOMPOSITION IN THE LOG FOURIER DOMAIN

In the log/Fourier domain, decomposing the amplitude spectra of seismi c data into surface-consistent terms is a linear problem that can be s olved, very efficiently, one frequency at a time. However, the nonuniq ue definition of the complex logarithm makes it much more difficult to decompose the phase spectra. The instability of phase unwrapping has previously prevented any attempt to decompose phase spectra in the log /Fourier domain. We develop a fast and robust partial unwrapping algor ithm, which makes it possible to efficiently decompose the phase spect ra of normal moveout-corrected (NMO-) data into surface-consistent ter ms, in the log/Fourier domain. The dual recovery of amplitude and phas e spectra yields a surface-consistent deconvolution technique where on ly the average reflectivity is assumed to be white, and only the avera ge wavelet is required to be minimum-phase. Each individual deconvolut ion operator may be mixed-phase, depending on its estimated phase spec tra. For example, surface-consistent time shifts and phase rotations, as well as any other surface-consistent phase effects, are included in the phase spectra of the surface-consistent deconvolution operators. Consequently, static shifts are estimated and removed without ever pic king horizons or crosscorrelations.