New Frechet Derivative for Envelope Data and Multi-Scale Envelope Inversion

Seismic envelope inversion can nonlinearly separate the response of large-scale background velocity structure from the high-wavenumber response of the reflection series. However, for strong-nonlinear FWI involved with salt structures or other strong-contrast structures, the standard envelope inversion does not work well. In this paper we generalize the envelope operator and introduce a multi-scale envelope inversion. We use multi-scale window-averaged envelope (WAE) and derive a new envelope Fréchet derivative (sensitivity operator), leading to a multi-scale envelope inversion (MS-EI) which can recover large-scale strong-contrast velocity structure, such as salt domes. Finally, we show some numerical examples of its application to the inversion of the 2D SEG/EAGE salt mode