Research on the Air-gun Array Wavelet Decomposition Algorithm in Frequency Domain

The far-field wavelet of air-gun arrays is becoming a requirement in petroleum exploration. Ziolkwski （1982） presented that the signature of the far-field can be calculated by superposition of the decomposed notional sources. Wavelet decomposition in frequency-domain has the potential to address both requirements: it can eliminate the error produced by the interpolation in time-domain, while simultaneously de-ghosting the near-field signatures. Considering the relationship that between the summation of interference in time-domain and the phase delay in frequency-domain, we can decompose the wavelet in frequency-domain using the Fourier transform. Finally, using the inverse Fourier transform, we can get the decomposed wavelet in time-domain. The algorithm to decompose the near field wavelet is demonstrated both on synthetic and real data.