Spectral Bandwidth Extension: Invention versus Harmonic Extrapolation



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There are valid and invalid post-processing methods to extend seismic bandwidth for resolution enhancement. Some methods attempt to invent high frequencies without a physical basis, while inversion-based methods extrapolate the spectra in reasonable ways. Frequency invention methods can extend the original seismic spectrum to desired spectral bandwidths. However, those spectral components they invent do not provide new effective information for enhancing resolution. Matching pursuit decomposition has been successfully applied to analyze the available spectrum of seismic data. Consequently, missing spectral components can be directly extrapolated from zero frequency all the way to the Nyquist frequency. Alternatively, the spectral information within the limited band can be modeled as an autoregressive process. Higher and lower frequencies outside the band can thus be predicted by designing a Wiener prediction filter. Spectral decomposition by matching pursuit on the band-limited seismic trace stabilizes the predictions to recover a broad-band reflectivity sequence. Further, continuous wavelet transform can be employed to spectrally decompose the band-limited signal into discrete sub-bands from which missing high and low frequencies could be extrapolated locally using multi-channel operators. Conventional sparse spike deconvolution attempts to retrieve a reflectivity sequence comprising isolated sparse delta functions, which may restore the missing part of the spectrum.



Frequency modulating, Frequency sliding, Frequency doubling, Matching pursuit decomposition (MPD&FMPD), Autoregressive model, Wiener prediction, Continuous wavelet transform, Multichannel operator, L1-norm regularization, Iteratively reweighting strategy