Nonstationary seismic deconvolution by adaptive molecular decomposition

An approach is proposed to improve the resolution of nonstationary seismic data by adaptive molecular decomposition. For each seismic trace, a set of nonuniform molecular windows is constructed according to the attenuation trend described by smoothed weighted and damped instantaneous frequencies (WDIF) located at the trace´s envelope peaks. Such that in each window, the seismic trace is approximately stationary. These nonuniform molecular windows are used to produce a couple of Molecular-Gabor frames. For the trace segment in each window, the spectrum-broadening and energy compensation are performed in Molecular-Gabor domain. Subsequently, a high-resolution version of the nonstationary seismic data can be obtained after inverse Molecular-Gabor transform. Applications of this method to both synthetic and real data show that the proposed method works well for a general earth Q-model that varies with travel time, and can expand the frequency band and recover the absorbed energy of the nonstationary seismic trace effectively.