Phase-amplitude-based polarized direct envelope inversion in the time-frequency domain

Large-scale geological structures with strong contrasts present difficulties to seismic imaging and inversion. Direct envelope inversion (DEI) with ultra-low-frequency was previously proposed to retrieve strong-contrast velocity models. However, the envelope signals lose instantaneous phase of the original wavefield, resulting in erroneous seismic inversion results. To solve this problem, instantaneous phase of the wavefield is encoded into envelopes for DEI. In this way, a polarized envelope is created to contain both abundant low-frequencies and the instantaneous phase information of the original seismic waveform. Furthermore, to improve the resolution of deep regions underneath the strong reflections, we propose a phase-amplitude-based polarized direct envelope inversion misfit (PA-PDEI) in the time-frequency domain that uses an amplitude factor to emphasize the phase information. This makes it possible to adjust the amplitude influence, and boost the low-amplitude seismic signals for deep targets. Tests on a model with salt body and on field data showed that combining the PA-PDEI with the phase-amplitude-based full waveform inversion (PA-FWI) made it possible to reliably reconstruct velocity models, especially for deep regions, despite large and strong perturbations.