FWI INVERSION WITH WAVEFORM, ENVELOPE AND PHASE FUNCTIONALS
Seismic Inversion, Full Waveform Inversion, Hilbert Transform
Full waveform inversion (FWI) is a technique that achieves excellent resolution in velocity models. However, its classic waveform functional have multiple local minimum. This problem makes FWI very dependent on the starting model. Moreover, the starting model needs to have a good content of long wavelengths. In order to mitigate these limitations, a popular approach has been to replace the classic waveform functional by other functionals. In this document, using the Marmousi model, we test the functionals of envelope and instantaneous phase of the seismic trace under accoustic approximation, with uniform density, and we compare them with the waveform functional. We used a 3 Hz linear source, supplying enough low frequency content so that it doesn’t become an issue to waveform inversion. The results prove that the envelope is sensitive to smooth model features, and the phase is sensitive to the model reflectivity. A sequential inversion, starting with envelope and ending with phase, leads to a great resolution improvement and removes some artifacts. No functional was able to fit intermediary time reflections, likely because the transmitted component energy of the seismic trace dominates the reflected component energy. We are testing methodologies to mitigate this issue.