Full waveform inversion( FWI) is a high resolution inversion method,which can reveal detailed information of the structure and lithology under complex geological background. It is limited by many kinds of noises when ...Full waveform inversion( FWI) is a high resolution inversion method,which can reveal detailed information of the structure and lithology under complex geological background. It is limited by many kinds of noises when the method applied to the real seismic data. Based on Huber function criterion,the objective function combinates the anti-noise of L1 norm and the stability of L2 norm in theory,the authors derive the gradient formula of the Huber function by using L-BFGS algorithm for FWI. The new method is proved by synthetic seismic data with the Gaussian noise and the impulse noise. Numerical test results show that L-BFGS algorithm is applied to the frequency domain FWI with the convergence speed and high calculation accuracy,and can effectively reduce computer memory usage; and the Huber function is more robust and stable than L2 norm even with the noises.展开更多
In this paper, we develop a novel alternating linearization method for solving convex minimization whose objective function is the sum of two separable functions. The motivation of the paper is to extend the recent wo...In this paper, we develop a novel alternating linearization method for solving convex minimization whose objective function is the sum of two separable functions. The motivation of the paper is to extend the recent work Goldfarb et al.(2013) to cope with more generic convex minimization. For the proposed method,both the separable objective functions and the auxiliary penalty terms are linearized. Provided that the separable objective functions belong to C1,1(Rn), we prove the O(1/?) arithmetical complexity of the new method. Some preliminary numerical simulations involving image processing and compressive sensing are conducted.展开更多
基金Supported by the National "863" Project(No.2014AA06A605)
文摘Full waveform inversion( FWI) is a high resolution inversion method,which can reveal detailed information of the structure and lithology under complex geological background. It is limited by many kinds of noises when the method applied to the real seismic data. Based on Huber function criterion,the objective function combinates the anti-noise of L1 norm and the stability of L2 norm in theory,the authors derive the gradient formula of the Huber function by using L-BFGS algorithm for FWI. The new method is proved by synthetic seismic data with the Gaussian noise and the impulse noise. Numerical test results show that L-BFGS algorithm is applied to the frequency domain FWI with the convergence speed and high calculation accuracy,and can effectively reduce computer memory usage; and the Huber function is more robust and stable than L2 norm even with the noises.
基金supported by National Natural Science Foundation of China(Grant Nos.11301055 and 11401315)Natural Science Foundation of Jiangsu Province(Grant No.BK2009397)the Fundamental Research Funds for the Central Universities(Grant No.ZYGX2013J103)
文摘In this paper, we develop a novel alternating linearization method for solving convex minimization whose objective function is the sum of two separable functions. The motivation of the paper is to extend the recent work Goldfarb et al.(2013) to cope with more generic convex minimization. For the proposed method,both the separable objective functions and the auxiliary penalty terms are linearized. Provided that the separable objective functions belong to C1,1(Rn), we prove the O(1/?) arithmetical complexity of the new method. Some preliminary numerical simulations involving image processing and compressive sensing are conducted.
