Full waveform inversion is a precise method for parameter inversion,harnessing the complete wavefield information of seismic waves.It holds the potential to intricately characterize the detailed features of the model ...Full waveform inversion is a precise method for parameter inversion,harnessing the complete wavefield information of seismic waves.It holds the potential to intricately characterize the detailed features of the model with high accuracy.However,due to inaccurate initial models,the absence of low-frequency data,and incomplete observational data,full waveform inversion(FWI)exhibits pronounced nonlinear characteristics.When the strata are buried deep,the inversion capability of this method is constrained.To enhance the accuracy and precision of FWI,this paper introduces a novel approach to address the aforementioned challenges—namely,a fractional-order anisotropic total p-variation regularization for full waveform inversion(FATpV-FWI).This method incorporates fractional-order total variation(TV)regularization to construct the inversion objective function,building upon TV regularization,and subsequently employs the alternating direction multiplier method for solving.This approach mitigates the step effect stemming from total variation in seismic inversion,thereby facilitating the reconstruction of sharp interfaces of geophysical parameters while smoothing background variations.Simultaneously,replacing integer-order differences with fractional-order differences bolsters the correlation among seismic data and diminishes the scattering effect caused by integer-order differences in seismic inversion.The outcomes of model tests validate the efficacy of this method,highlighting its ability to enhance the overall accuracy of the inversion process.展开更多
Accurate reconstruction from a reduced data set is highly essential for computed tomography in fast and/or low dose imaging applications. Conventional total variation（TV）-based algorithms apply the L1 norm-based pen...Accurate reconstruction from a reduced data set is highly essential for computed tomography in fast and/or low dose imaging applications. Conventional total variation（TV）-based algorithms apply the L1 norm-based penalties, which are not as efficient as Lp（0〈p〈1） quasi-norm-based penalties. TV with a p-th power-based norm can serve as a feasible alternative of the conventional TV, which is referred to as total p-variation（TpV）. This paper proposes a TpV-based reconstruction model and develops an efficient algorithm. The total p-variation and Kullback-Leibler（KL） data divergence, which has better noise suppression capability compared with the often-used quadratic term, are combined to build the reconstruction model. The proposed algorithm is derived by the alternating direction method（ADM） which offers a stable, efficient, and easily coded implementation. We apply the proposed method in the reconstructions from very few views of projections（7 views evenly acquired within 180°）. The images reconstructed by the new method show clearer edges and higher numerical accuracy than the conventional TV method. Both the simulations and real CT data experiments indicate that the proposed method may be promising for practical applications.展开更多
基金supported by the China Postdoctoral Science Foundation(Grant No.2024MF750281)the Postdoctoral Fellowship Program of CPSF(Grant No.GZC20230326)+1 种基金the Natural Science Foundation Project of Sichuan Province(Grant No.2025ZNSFSC1170)Sichuan Science and Technology Program(Grant No.2023ZYD0158).
文摘Full waveform inversion is a precise method for parameter inversion,harnessing the complete wavefield information of seismic waves.It holds the potential to intricately characterize the detailed features of the model with high accuracy.However,due to inaccurate initial models,the absence of low-frequency data,and incomplete observational data,full waveform inversion(FWI)exhibits pronounced nonlinear characteristics.When the strata are buried deep,the inversion capability of this method is constrained.To enhance the accuracy and precision of FWI,this paper introduces a novel approach to address the aforementioned challenges—namely,a fractional-order anisotropic total p-variation regularization for full waveform inversion(FATpV-FWI).This method incorporates fractional-order total variation(TV)regularization to construct the inversion objective function,building upon TV regularization,and subsequently employs the alternating direction multiplier method for solving.This approach mitigates the step effect stemming from total variation in seismic inversion,thereby facilitating the reconstruction of sharp interfaces of geophysical parameters while smoothing background variations.Simultaneously,replacing integer-order differences with fractional-order differences bolsters the correlation among seismic data and diminishes the scattering effect caused by integer-order differences in seismic inversion.The outcomes of model tests validate the efficacy of this method,highlighting its ability to enhance the overall accuracy of the inversion process.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61372172 and 61601518)
文摘Accurate reconstruction from a reduced data set is highly essential for computed tomography in fast and/or low dose imaging applications. Conventional total variation（TV）-based algorithms apply the L1 norm-based penalties, which are not as efficient as Lp（0〈p〈1） quasi-norm-based penalties. TV with a p-th power-based norm can serve as a feasible alternative of the conventional TV, which is referred to as total p-variation（TpV）. This paper proposes a TpV-based reconstruction model and develops an efficient algorithm. The total p-variation and Kullback-Leibler（KL） data divergence, which has better noise suppression capability compared with the often-used quadratic term, are combined to build the reconstruction model. The proposed algorithm is derived by the alternating direction method（ADM） which offers a stable, efficient, and easily coded implementation. We apply the proposed method in the reconstructions from very few views of projections（7 views evenly acquired within 180°）. The images reconstructed by the new method show clearer edges and higher numerical accuracy than the conventional TV method. Both the simulations and real CT data experiments indicate that the proposed method may be promising for practical applications.
