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
Seismic inversion is a highly ill-posed problem, due to many factors such as the limited seismic frequency bandwidth and inappropriate forward modeling. To obtain a unique solution, some smoothing constraints, e.g., t...Seismic inversion is a highly ill-posed problem, due to many factors such as the limited seismic frequency bandwidth and inappropriate forward modeling. To obtain a unique solution, some smoothing constraints, e.g., the Tikhonov regularization are usually applied. The Tikhonov method can maintain a global smooth solution, but cause a fuzzy structure edge. In this paper we use Huber-Markov random-field edge protection method in the procedure of inverting three parameters, P-velocity, S-velocity and density. The method can avoid blurring the structure edge and resist noise. For the parameter to be inverted, the Huber- Markov random-field constructs a neighborhood system, which further acts as the vertical and lateral constraints. We use a quadratic Huber edge penalty function within the layer to suppress noise and a linear one on the edges to avoid a fuzzy result. The effectiveness of our method is proved by inverting the synthetic data without and with noises. The relationship between the adopted constraints and the inversion results is analyzed as well.展开更多
According to the World Health Organization,about 50 million people worldwide suffer from epilepsy.The detection and treatment of epilepsy face great challenges.Electroencephalogram(EEG)is a significant research object...According to the World Health Organization,about 50 million people worldwide suffer from epilepsy.The detection and treatment of epilepsy face great challenges.Electroencephalogram(EEG)is a significant research object widely used in diagnosis and treatment of epilepsy.In this paper,an adaptive feature learning model for EEG signals is proposed,which combines Huber loss function with adaptive weight penalty term.Firstly,each EEG signal is decomposed by intrinsic time-scale decomposition.Secondly,the statistical index values are calculated from the instantaneous amplitude and frequency of every component and fed into the proposed model.Finally,the discriminative features learned by the proposed model are used to detect seizures.Our main innovation is to consider a highly flexible penalization based on Huber loss function,which can set different weights according to the influence of different features on epilepsy detection.Besides,the new model can be solved by proximal alternating direction multiplier method,which can effectively ensure the convergence of the algorithm.The performance of the proposed method is evaluated on three public EEG datasets provided by the Bonn University,Childrens Hospital Boston-Massachusetts Institute of Technology,and Neurological and Sleep Center at Hauz Khas,New Delhi(New Delhi Epilepsy data).The recognition accuracy on these two datasets is 98%and 99.05%,respectively,indicating the application value of the new model.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 the National Basic Research Program of China(973 Program)(No.2013CB228603)National Science and Technology major projects(No.2011ZX05024 and 2011ZX05010)the National Natural Science Foundation of China(No.41174119)
文摘Seismic inversion is a highly ill-posed problem, due to many factors such as the limited seismic frequency bandwidth and inappropriate forward modeling. To obtain a unique solution, some smoothing constraints, e.g., the Tikhonov regularization are usually applied. The Tikhonov method can maintain a global smooth solution, but cause a fuzzy structure edge. In this paper we use Huber-Markov random-field edge protection method in the procedure of inverting three parameters, P-velocity, S-velocity and density. The method can avoid blurring the structure edge and resist noise. For the parameter to be inverted, the Huber- Markov random-field constructs a neighborhood system, which further acts as the vertical and lateral constraints. We use a quadratic Huber edge penalty function within the layer to suppress noise and a linear one on the edges to avoid a fuzzy result. The effectiveness of our method is proved by inverting the synthetic data without and with noises. The relationship between the adopted constraints and the inversion results is analyzed as well.
基金Supported by National Natural Science Foundation of China(Grant Nos.11701144,11971149)Henan Province Key and Promotion Special(Science and Technology)Project(Grant No.212102310305).
文摘According to the World Health Organization,about 50 million people worldwide suffer from epilepsy.The detection and treatment of epilepsy face great challenges.Electroencephalogram(EEG)is a significant research object widely used in diagnosis and treatment of epilepsy.In this paper,an adaptive feature learning model for EEG signals is proposed,which combines Huber loss function with adaptive weight penalty term.Firstly,each EEG signal is decomposed by intrinsic time-scale decomposition.Secondly,the statistical index values are calculated from the instantaneous amplitude and frequency of every component and fed into the proposed model.Finally,the discriminative features learned by the proposed model are used to detect seizures.Our main innovation is to consider a highly flexible penalization based on Huber loss function,which can set different weights according to the influence of different features on epilepsy detection.Besides,the new model can be solved by proximal alternating direction multiplier method,which can effectively ensure the convergence of the algorithm.The performance of the proposed method is evaluated on three public EEG datasets provided by the Bonn University,Childrens Hospital Boston-Massachusetts Institute of Technology,and Neurological and Sleep Center at Hauz Khas,New Delhi(New Delhi Epilepsy data).The recognition accuracy on these two datasets is 98%and 99.05%,respectively,indicating the application value of the new model.
