Abstract

If an optical hologram is broken into pieces, a virtual object can still be reconstructed from each of the fragments. This reconstruction is possible because each diffraction point emits waves that reach every point of the hologram. Thus, the entire object is encoded into each subset of the hologram. Analogous to the broken hologram, the use of undersampled seismic data violating the Nyquist-Shannon sampling theorem may still give a well-resolved image of the subsurface. A theoretical framework of this idea has already been introduced in the literature and denoted as holistic migration. However, the general lack of seismic field data demonstrations has inspired the study presented here. Since the optical hologram is diffraction-driven, we propose to employ diffraction-separated data and not conventional reflection data as input for holistic migration. We follow the original idea and regularly undersample the data spatially. Such a sampling strategy will result in coherent noise in the image domain. We therefore introduce a novel signal processing technique to remove such noise. The feasibility of the proposed approach is demonstrated employing the Sigsbee2a controlled data set and field data from the Barents Sea.

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