Extraction of seismic wavelet based on optimal filtering in Fractional Fourier domain

Accurate estimation of seismic wavelet is very important to high-resolution, high-signal-noise ratio and high fidelity petroleum exploration and production data procession. As we known, the underground strata information changes as the depth changes. So it is a time-varying system. Obviously, it´s not accurate enough to describe it with the linear time-invariant system. Fractional Fourier transform is suitable for non-stationary signal filtering, and the wavelet extraction can be transformed into the optimal filtering problem in fractional Fourier domain. This paper proposes a novel seismic wavelet extraction algorithm in fractional Fourier domain and seek the optimal filter which minimize the mean square error of the estimate and the true wavelet. The optimal order is found by searching in the range of [-1, 1] in the fractional domain by step 1/200. Finally, we prove the effectiveness of this algorithm by series of experiments and extract seismic wavelet quickly and accurately.