Full waveform inversion (FWI) is a highly nonlinear optimization problem that aims to reconstruct high-resolution subsurface structures. The success of FWI in reflection seismology relies on appropriate updates of low-wavenumber background velocity structures, which are generally driven by the diving waves in conventional FWI. On the other hand, the reflected waves mainly contribute to updating high-wavenumber components rather than low-wavenumber components. To extract low-wavenumber information from the reflected waves in addition to the diving waves, we propose a two-step FWI strategy that separates a given model into the reflectivity and background velocity models and then alternately update them using the scale-separation technique based on diffraction-angle filtering (DAF; which was proposed to effectively control wavenumber components of the FWI gradient). Our strategy first inverts the high-wavenumber reflectivity model by suppressing energy at large diffraction angles, which are necessary to compute the reflection wavepaths (i.e., the rabbit-ears-shaped kernels) for low-wavenumber updates in the subsequent stage. Then, we extract low-wavenumber components due to the diving (banana-shaped kernels) and reflected waves (rabbit-ears-shaped kernels) from the gradient by suppressing energy at small diffraction angles. Our strategy is similar to reflection waveform inversion (RWI) in that it separates a given model into high- and low- wavenumber components and uses the rabbit-ears-shaped kernels for low-wavenumber updates. The main difference between our strategy and RWI is that our strategy adopts the DAF-based scale-separation technique in the space domain, which makes our algorithm of using both the banana-shaped and rabbit-ears-shaped kernels computationally attractive. By applying our two-step inversion strategy to the synthetic data from the Marmousi-II model and the real ocean-bottom cable (OBC) data from the North sea, we demonstrate that our method properly reconstructs low-wavenumber structures even if initial models deviate from the true models.
Kim, D., Hwang, J., Min, D.-J., Oh, J.-W., & Alkhalifah, T. (2021). Two-step full waveform inversion of diving and reflected waves with the diffraction-angle-filtering-based scale-separation technique. Geophysical Journal International. doi:10.1093/gji/ggab522
This research was supported by the National Research Foundation of Korea (NRF) funded by the Ministry of Science and ICT (NRF-2019K1A3A1A80113341; NRF2020R111A3073977), and the Human Resources Development program (No.20204010600250) of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) funded by the Ministry of Trade, Industry, and Energy of the Korean Government. Research reported in this publication was also supported by competitive research funding from the King Abdullah University of Science and Technology (KAUST) in Thuwal, Saudi Arabia. Also, the North sea data are released by Equinor and former Volve license Partners under Creative Commons License. We greatly appreciate their efforts to disclose the Volve data. The views on the Volve data expressed in this paper are the views of the authors and do not necessarily reflect the views of Equinor and former Volve license Partners. Lastly, we appreciate the editor and anonymous reviewers for their careful reading of our manuscript and their insightful comments and suggestions.