Multi-Scale Energy Weighted Envelope-Phase Inversion Using Direct Envelope Fréchet Derivative in Local Time-Frequency

Waveform-phase is closely related to traveltime, it has more linear relationship with the underground structures. Envelopes of seismic traces contain large-scale background structures. Therefore, it is possible for us to use envelope-phase information to build a smooth background initial model for the conventional full waveform inversion. In this work, we explore the multi-scale envelope-phase inversion in the local time-frequency domain. And we incorporate an energy weighting factor into the for the envelope-phase inversion. In this way, we have more flexibility to operate on the local envelope and phase spectra for a stable multi-scale envelope-phase inversion. The traditional phase inversion methods are all based on the weak scattering theory, and using the chain rule to obtain the adjoint source. Therefore, the traditional phase inversion may not work on the salt model. In this abstract, we propose to use the direct envelope Fréchet derivative for the multi-scale energy weighted envelope-phase inversion. Compared to the amplitude-based direct envelope inversion, envelope-phase based inversion have better recovery of salt bottom structures. Finally, we show some numerical examples of its application to the inversion of the 2D SEG/EAGE salt model.