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Frequency extension and robust full-waveform inversion based on nth power operation

  • Research Article - Applied Geophysics
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Abstract

The conventional full-waveform inversion (FWI) often minimizes the objective function using some local optimization algorithms. As a result, when the initial model is not good enough, the inversion process will drop into a local minimum. The low-frequency components contained in seismic data are of vital importance for reducing the initial model dependence and mitigating the cycle-skipping phenomenon of FWI. In this research, a frequency extension method using the nth power operation is proposed, which compresses the seismic data in time domain and extends their frequency band. Based on this, we construct a new objective function using the nth power wavefield and derive the corresponding gradient formula. The new objective function shows better property to overcome local minimum than the conventional one. When conduct inversion, we can invert from high-order to low-order successively, which is a new multiscale strategy. Since seismic data is more sensitive to source wavelet errors after high-order operation, we make the method more robust by proposing a source-independent method to mitigate the effects of source wavelet inaccuracy. After that, we extend the proposed method to encoded multisource waveform inversion. The numerical examples on the Marmousi model demonstrate that the proposed method can effectively mitigate the cycle-skipping of FWI, and it also has good anti-noise property.

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Acknowledgements

We would like to thank the co-editor-in-chief Michal Malinowski, the associate editor Junlun Li and two anonymous reviewers for their insightful suggestions and contributions to this paper. This work is jointly supported by the National Natural Science Foundation of China (Nos. 41674124, 41430213, 41590863, 41974138), the Pearl River talent program of China (2017ZT07Z066), the National Key Research and Development Project of China (No. 2016YFC0600301), the China Postdoctoral Science Foundation (No. 2020M670852), the independent (open) research project of the Key Laboratory of Deep-Earth Dynamics of Ministry of Natural Resources (No. J1901) and the “Thirteenth Five-Year Plan” Science and Technology Project of Education Department of Jilin Province (No. JJKH20201001KJ).

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Authors and Affiliations

  1. College of Geo-exploration Science and Technology, Jilin University, Changchun, China

    Pan Zhang, Liguo Han, Fengjiao Zhang & Zhenzhen Xing

  2. School of Earth Science and Geological Engineering, Sun Yat-sen University, Guangzhou, China

    Rui Gao

  3. Key Laboratory of Deep-Earth Dynamics of Ministry of Natural Resources, Institute of Geology, Chinese Academy of Geological Sciences, Beijing, China

    Pan Zhang

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  1. Pan Zhang
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  2. Liguo Han
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  3. Rui Gao
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  4. Fengjiao Zhang
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Correspondence to Liguo Han.

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Zhang, P., Han, L., Gao, R. et al. Frequency extension and robust full-waveform inversion based on nth power operation. Acta Geophys. 68, 1317–1333 (2020). https://doi.org/10.1007/s11600-020-00465-6

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