Seismic-to-well ties are important for seismic interpretation and impedance inversion. Reflectivity can be calculated directly from well logs while its estimation from seismic data requires the determination of the seismic wavelet and the removal of the same. In the presence of anelastic attenuation, the constant-Q theory predicts that the seismic wavelet evolves with amplitude decay and minimum-phase dispersion. Stationary deconvolution estimates and eliminates a single wavelet from the nonstationary trace, resulting in large nonstationary amplitude and phase errors. Gabor deconvolution accurately estimates and eliminates the amplitude spectra of the propagating wavelets, but only corrects the phase to the seismic Nyquist frequency. A phase correction operator is developed to correct the phase to the well logging frequency. Both synthetic and real data examples show seismic-to-well ties can be improved by correcting their time shifts via smooth dynamic time warping and addressing slowly time-variant nonstationarity in a sliding Gaussian window.
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