KAUST DepartmentPhysical Sciences and Engineering (PSE) Division
Earth Science and Engineering Program
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AbstractConventional full-waveform inversion (FWI) based on the least-squares misfit function faces problems in converging to the global minimum when using gradient methods because of the cycle-skipping phenomena. An initial model producing data that are at most a half-cycle away from the observed data is needed for convergence to the global minimum. Low frequencies are helpful in updating low-wavenumber components of the velocity model to avoid cycle skipping. However, low enough frequencies are usually unavailable in field cases. The multiplication of wavefields of slightly different frequencies adds artificial low-frequency components in the data, which can be used for FWI to generate a convergent result and avoid cycle skipping. We generalize this process by multiplying the wavefield with itself and then applying a smoothing operator to the multiplied wavefield or its square to derive the nonlinearly smoothed wavefield, which is rich in low frequencies. The global correlation-norm-based objective function can mitigate the dependence on the amplitude information of the nonlinearly smoothed wavefield. Therefore, we have evaluated the use of this objective function when using the nonlinearly smoothed wavefield. The proposed objective function has much larger convexity than the conventional objective functions. We calculate the gradient of the objective function using the adjoint-state technique, which is similar to that of the conventional FWI except for the adjoint source. We progressively reduce the smoothing width applied to the nonlinear wavefield to naturally adopt the multiscale strategy. Using examples on the Marmousi 2 model, we determine that the proposed FWI helps to generate convergent results without the need for low-frequency information.
CitationLi Y, Choi Y, Alkhalifah T, Li Z, Zhang K (2018) Full-waveform inversion using a nonlinearly smoothed wavefield. GEOPHYSICS 83: R117–R127. Available: http://dx.doi.org/10.1190/GEO2017-0312.1.
SponsorsWe thank KAUST for its support and the SWAG for collaborative environment. We also thank Z. Wu for the useful discussions. We would like to thank V. Socco, D. Draganov, D. Komatitsch, and two anonymous reviewers for their valuable comments and suggestions. Author Y. Li wishes to thank the China Scholarship Council for support to study abroad. This research was financially supported by the National Natural Science Foundation of China (grant number 41504100), the Natural Science Foundation of Shandong Province (grant number ZR2017MD014), the National Oil and Gas Program (2016ZX05006-002), and the Fundamental Research Funds for the Central Universities (grant numbers 16CX06039A and 17CX02052).
PublisherSociety of Exploration Geophysicists