High-definition frequency decomposition

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Spectral decomposition is a widely used technique in analysis and interpretation of seismic data. According to the uncertainty principle, there exists a lower bound for the joint time–frequency resolution of seismic signals. The highest temporal resolution is achieved by a matching pursuit approach which uses waveforms from a dictionary of functions (atoms). This method, in its pure mathematical form can result in atoms whose shape and phase have no relation to the seismic trace. The high-definition frequency decomposition algorithm presented in this paper interleaves iterations of atom matching and optimization. It divides the seismic trace into independent sections delineated by envelope troughs, and simultaneously matches atoms to all peaks. Co-optimization of overlapping atoms ensures that the effects of interference between them are minimized. Finally, a second atom matching and optimization phase is performed in order to minimize the difference between the original and the reconstructed trace. The fully reconstructed traces can be used as inputs for a frequency-based reconstruction and red–green–blue colour blending. Comparison with the results of the original matching pursuit frequency decomposition illustrates that high-definition frequency decomposition based colour blends provide a very high temporal resolution, even in the low-energy parts of the seismic data, enabling a precise analysis of geometrical variations of geological features.

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