Seismic envelope inversion and modulation signal model

ABSTRACTWe recognized that the envelope fluctuation and decay of seismic records carries ultra low-frequency (ULF, i.e., the frequency below the lowest frequency in the source spectrum) signals that can be used to estimate the long-wavelength velocity structure. We then developed envelope inversion for the recovery of low-wavenumber components of media (smooth background), so that the initial model dependence of waveform inversion can be reduced. We derived the misfit function and the corresponding gradient operator for envelope inversion. To understand the long-wavelength recovery by the envelope inversion, we developed a nonlinear seismic signal model, the modulation signal model, as the basis for retrieving the ULF data and studied the nonlinear scale separation by the envelope operator. To separate the envelope data from the wavefield data (envelope extraction), a demodulation operator (envelope operator) was applied to the waveform data. Numerical tests using synthetic data for the Marmousi model pro...

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