We propose an adaptive spectrum-broadening method (ASBM) to improve the resolution of nonstationary seismic data. This method assumes that a seismic trace can be split into segments, each of which can be considered as approximately stationary. We construct a set of specific windows, called molecular-Gabor (MG) windows, by solving an optimization problem, such that the seismic trace in each of the MG windows is stationary. A time-frequency (t-f) transform, called MG transform, can be obtained from a MG frame constructed using the MG windows. For a seismic trace, we first transform it into the t-f domain, then spectrum-broadening and/or amplitude compensation are performed in each of the MG windows. Subsequently, a high-resolution version of the nonstationary seismic trace will be obtained after the inverse MG transform. Applications of this method to synthetic and field data show that the ASBM works well for a general earth Q-model that varies with traveltime. It can restore the attenuated energy and expand the frequency bandwidth of a nonstationary seismic trace effectively. One significant advantage of our method is that it automatically estimates all the parameters that are optimal for each trace.

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