Combining CEEMD and recursive least square for the extraction of time-varying seismic wavelets

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The vertical resolution of seismic data is greatly affected by time-varying seismic wavelets. To break through the shape restriction in amplitude estimation and the dependency upon the constant or piecewise stationary assumptions in phase estimation in the existing methods, we propose a time-varying wavelet extraction method combining CEEMD (Complementary Ensemble Empirical Mode Decomposition) and RLS (Recursive Least Square). According to the differences that the amplitude spectra of wavelets and reflection coefficient are smooth and oscillating respectively, the logarithm amplitude spectra of the seismogram at different times are decomposed into multi-layer components with different oscillation scales by CEEMD, and the amplitude spectra of time-varying wavelets can be estimated by filtering the oscillating components and reconstructing the smooth components. Hilbert transform is applied to the estimated amplitude spectra to build time-varying minimum-phase wavelets, and the system functions and pole-zeros in Z domain of minimum-phase wavelets can be estimated using RLS. Finally, time-varying mixed-phase wavelets are extracted by reconfiguring the pole-zeros and determining the optimal combinations under the constraint of local similarity. This method does not need to calculate the Q value. The numerical simulation and real seismic data processing results demonstrate that the proposed method can improve the accuracy of time-varying wavelet extraction compared to the conventional method.