Unambiguous signal recovery above the Nyquist using random‐sample‐interval imaging

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Aliasing is generally understood to mean that sampling causes those frequencies above the Nyquist frequency to be irretrievably “mixed” with those below. As a result, the perceived need to prevent signal aliasing has played a major role in limiting useable signal bandwidth. Yet, the evidence of aliasing in multichannel seismic data is often paradoxical and contradictory, suggesting that aliasing may be more apparent than real. A simple, exact sample‐mapping methodology, random‐sample‐interval imaging, can be used to overcome aliasing in many of the processes used currently for the imaging of seismic data. The robust process recovers broadband signal, on both synthetic and real data, with frequencies significantly above the Nyquist limit predicted by the 1-D sampling theorem. The method appears to be applicable whenever the signal trajectory is intersected irregularly by a sampling grid of two or more dimensions. The results suggest that both spatial and temporal aliasing of signal may be resolved simultaneously by this strategy.