Full-waveform inversion (FWI) is an attractive tool for high-resolution velocity-model building without a high-frequency assumption compared to conventional reflection tomography. However, there are two main challenges to the application of FWI on narrow-azimuth acquisition (NAZ) data: cycle skipping and acquisition footprints. Here, a multistage FWI is proposed to build a high-resolution model for NAZ data. It is well known that FWI may suffer from a cycle-skipping problem when the starting model is not close enough to the true solution. To mitigate this problem, we introduce dynamic-warping preconditioned full-waveform inversion (DWFWI) as the first stage of the velocity inversion. DWFWI iteratively preconditions the observed early arrivals through dynamic warping to avoid cycle skipping in the model, which allows large-scale background updates. The second stage of our workflow is the conventional FWI with image-guided smoothing (IGFWI). On top of DWFWI, more reflection events are included and inverted through the conventional L2-norm FWI, which can add more detailed updates to the velocity model with much higher resolution. Due to poor crossline sampling, there are strong acquisition footprints on FWI updates in the crossline direction. Image-guided smoothing is used to reduce the acquisition footprints in the FWI gradient as well as to preserve the detailed update around the faults. It is then followed by an additional tomography to update the deep portion. This approach was applied on the Hoop Fault Complex data in the southwestern Barents Sea. The results show that a more geologically realistic and higher-resolution model of the Hoop Fault Complex was obtained, and the migration image and gathers were significantly improved.

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