Frequency extension and robust full-waveform inversion based on n th power operation
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RESEARCH ARTICLE - APPLIED GEOPHYSICS
Frequency extension and robust full‑waveform inversion based on nth power operation Pan Zhang1,3 · Liguo Han1 · Rui Gao2 · Fengjiao Zhang1 · Zhenzhen Xing1 Received: 4 November 2019 / Accepted: 18 July 2020 © Institute of Geophysics, Polish Academy of Sciences & Polish Academy of Sciences 2020
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. Keywords Full-waveform inversion · Low frequency · Frequency extension · Source independent
Introduction Full-waveform inversion (FWI) is a high-accuracy seismic velocity construction method, which simultaneously utilizes the travel time, amplitude, and phase of the observed seismic waveforms (Virieux and Operto 2009). The objective function of FWI is often set as the L-p norm of the residuals between observed data and synthetic data, which demonstrates that FWI is a data-driven and strong nonlinear problem (Tarantola 1984). With the help of Born approximation (weak scattering approximation), FWI can be transformed into a local optimization problem, which makes the inversion * Liguo Han [email protected] 1
College of Geo‑exploration Science and Technology, Jilin University, Changchun, China
2
School of Earth Science and Geological Engineering, Sun Yat-sen University, Guangzhou, China
3
Key Laboratory of Deep‑Earth Dynamics of Ministry of Natural Resources, Institute of Geology, Chinese Academy of Geological Sciences, Beijing, China
process depend on the initial model (Gauthier et al. 1986). The relationship between velocity perturbation and low-frequency wavefield scattering is more linear than that between velocity perturbation and high-frequency wavefield scattering, so t
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