Examining the phase property of the nonstationary Vibroseis Wavelet

Linping Dong, Gary F. Margrave, and Lawrence E. Mewhort

ABSTRACT

We have observed that Vibroseis wavelets behave very much as if they are minimum phase. This was discovered by applying a minimum-phase Wiener deconvolution to the separated Vibroseis-VSP downgoing waves and observing that the result is effectively a band-limited spike. Our observation was further confirmed by the similarity between Vibroseis-VSP downgoing waves and their minimum-phase equivalents. This finding contradicts the conventional assumption; therefore, it is necessary to investigate the reason for this phase property. By a simple model test, we show that both stationary and nonstationary minimum-phase filters result in an effective minimum-phase wavelet. If the Klauder wavelet is broadband, the phase of the wavelet embedded in the trace will be determined mainly by the minimum-phase factors including instrument and receiver response, far-field differential operators, and earth filtering. Furthermore, we applied a minimum-phase Gabor deconvolution to the correlated Vibroseis data and sweepremoved Vibroseis record, with the residual wavelet being close to minimum phase. For the synthetic data, the deconvolved traces from both approaches are consistent with the input reflectivity. For a real shot-gather, there are few differences between the deconvolved gathers from these two methods. These comparisons further confirm that the nonstationary wavelet embedded in the correlated surface Vibroseis seismic data is effectively minimum phase.

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