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Traditional seismic envelope inversion takes use of a nonlinear misfitfunctional which relates the envelope of seismogram to the observed wavefieldrecords, and then derive the sensitivity kernel of envelope to velocity throughthe use of waveform Frechet derivative by linearizing the nonlinear functional.We know that the waveform Frechet derivative is based on the Born approximationof wave scattering and can only work for the case of weak scattering.Therefore, the traditional envelope inversion using waveform Frechet derivativehas severe limitation in the case of strong-scattering for large-scale,strong-contrast inclusions. In this paper, we derive a new direct envelopeFrechet derivative (sensitivity operator) based on energy scattering physicswithout using the chain rule of differentiation. This new envelope Frechetderivative does not have the weak scattering assumption for the wavefield andcan be applied to the case of strong-nonlinear inversion involving saltstructures. We also extend the envelope data into multi-scale window-averagedenvelope (WAE), which contains much rich low-frequency components correspondingto the long-wavelength velocity structure of the media. Then we develop a jointinversion which combines the new multi-scale direct envelope inversion (MS-DEI)with standard FWI to recover large-scale strong-contrast velocity structure ofcomplex models. Finally, we show some numerical examples of its successfulapplication to the inversion of a 1-D thick salt-layer model and the 2DSEG/EAGE salt model.

Multi-scale seismic envelope inversion using a direct envelope Frechet derivative for strong-nonlinear full waveform inversion