Nonstationary blind deconvolution using spectral constraints

This study develops a nonstationary blind deconvolution using spectral constraints (NBDSC), a novel method to address the ill-posed nature of wavelet inversion in nonstationary seismic data. NBDSC does not require prior knowledge about the Q-factor of the medium and source wavelet, which are typically unknown. Our power spectrum-guided waveform inversion method corrects a wavelet to match any desired spectral shape. This method can be introduced as a wavelet-smoothing constraint, yielding blind deconvolution with spectral constraints (BDSC). First, based on a segmented stationary convolution model (SSCM), the original nonstationary convolution problem is decomposed into multiple stationary subproblems. Next, an absorption-constrained wavelet power spectrum inversion method is used on the SSCM decomposition results to extract the time-varying wavelet power spectrum. Finally, the estimated time-varying wavelet power spectrum is used as a spectral constraint to perform BDSC on each subseismic trace. We use synthetic and field data examples to demonstrate how the NBDSC enhances the resolution of nonstationary seismic data. Compared with conventional blind deconvolution methods, NBDSC incorporates prior knowledge of the wavelet power spectrum, thereby reducing inversion ambiguity and improving noise robustness. © 2025 Society of Exploration Geophysicists.