Abstract

In the log/Fourier domain, decomposing the amplitude spectra of seismic data into surface-consistent terms is a linear problem that can be solved, very efficiently, one frequency at a time. However, the nonunique 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 algorithm, which makes it possible to efficiently decompose the phase spectra of normal moveout-corrected (NMO-) data into surface-consistent terms, in the log/Fourier domain. The dual recovery of amplitude and phase spectra yields a surface-consistent deconvolution technique where only the average reflectivity is assumed to be white, and only the average wavelet is required to be minimum-phase. Each individual deconvolution operator may be mixed-phase, depending on its estimated phase spectra. 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 picking horizons or crosscorrelations.

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