In this paper,we explore the use of iterative curvelet thresholding for seismic random noise attenuation.A new method for combining the curvelet transform with iterative thresholding to suppress random noise is demons...In this paper,we explore the use of iterative curvelet thresholding for seismic random noise attenuation.A new method for combining the curvelet transform with iterative thresholding to suppress random noise is demonstrated and the issue is described as a linear inverse optimal problem using the L1 norm.Random noise suppression in seismic data is transformed into an L1 norm optimization problem based on the curvelet sparsity transform. Compared to the conventional methods such as median filter algorithm,FX deconvolution, and wavelet thresholding,the results of synthetic and field data processing show that the iterative curvelet thresholding proposed in this paper can sufficiently improve signal to noise radio(SNR) and give higher signal fidelity at the same time.Furthermore,to make better use of the curvelet transform such as multiple scales and multiple directions,we control the curvelet direction of the result after iterative curvelet thresholding to further improve the SNR.展开更多
For random noise suppression of seismic data, we present a non-local Bayes (NL- Bayes) filtering algorithm. The NL-Bayes algorithm uses the Gaussian model instead of the weighted average of all similar patches in th...For random noise suppression of seismic data, we present a non-local Bayes (NL- Bayes) filtering algorithm. The NL-Bayes algorithm uses the Gaussian model instead of the weighted average of all similar patches in the NL-means algorithm to reduce the fuzzy of structural details, thereby improving the denoising performance. In the denoising process of seismic data, the size and the number of patches in the Gaussian model are adaptively calculated according to the standard deviation of noise. The NL-Bayes algorithm requires two iterations to complete seismic data denoising, but the second iteration makes use of denoised seismic data from the first iteration to calculate the better mean and covariance of the patch Gaussian model for improving the similarity of patches and achieving the purpose of denoising. Tests with synthetic and real data sets demonstrate that the NL-Bayes algorithm can effectively improve the SNR and preserve the fidelity of seismic data.展开更多
The signal-to-noise ratio (SNR) of seismic reflection data in many areas is rather poor and conventional two-dimensional filters designed to suppress noise with different moveout from the signal tend to generate art...The signal-to-noise ratio (SNR) of seismic reflection data in many areas is rather poor and conventional two-dimensional filters designed to suppress noise with different moveout from the signal tend to generate artifacts. We have extended a method of multichannel filtering, based on the hypothesis that signals on adjacent channels are similar, for enhancing the SNR on stacked sections. Using only the mid-range frequencies where the SNR is highest, the event trend is found for overlapping windows on the section and the average signal vector is calculated. Then the data from the full bandwidth section are projected onto the spatially varying unit similarity vectors and the results are merged for the overlapping windows. Application of the method to synthetic data containing steeply dipping events and to a stacked section for a marine 2D line has produced good results. The modifications we have introduced carry a small overhead in computing time but they should enable the method to be used effectively even on sections containing steep dips.展开更多
New sigma point filtering algorithms, including the unscented Kalman filter (UKF) and the divided difference filter (DDF), are designed to solve the nonlinear filtering problem under the condition of correlated no...New sigma point filtering algorithms, including the unscented Kalman filter (UKF) and the divided difference filter (DDF), are designed to solve the nonlinear filtering problem under the condition of correlated noises. Based on the minimum mean square error estimation theory, the nonlinear optimal predictive and correction recursive formulas under the hypothesis that the input noise is correlated with the measurement noise are derived and can be described in a unified framework. Then, UKF and DDF with correlated noises are proposed on the basis of approximation of the posterior mean and covariance in the unified framework by using unscented transformation and second order Stirling's interpolation. The proposed UKF and DDF with correlated noises break through the limitation that input noise and measurement noise must be assumed to be uneorrelated in standard UKF and DDF. Two simulation examples show the effectiveness and feasibility of new algorithms for dealing with nonlinear filtering issue with correlated noises.展开更多
The importance of stochasticity in cellular processes is increasingly recognized in both theoretical andexperimental studies.General features of stochasticity in gene regulation and expression are briefly reviewed in ...The importance of stochasticity in cellular processes is increasingly recognized in both theoretical andexperimental studies.General features of stochasticity in gene regulation and expression are briefly reviewed in thisarticle,which include the main experimental phenomena,classification,quantization and regulation of noises.Thecorrelation and transmission of noise in cascade networks are analyzed further and the stochastic simulation methodsthat can capture effects of intrinsic and extrinsic noise are described.展开更多
This article examines a viscoelastic plate that is driven parametrically by a non-Guassian colored noise,which is simplified to an Ornstein-Uhlenbeck process based on the approximation method.To examine the moment sta...This article examines a viscoelastic plate that is driven parametrically by a non-Guassian colored noise,which is simplified to an Ornstein-Uhlenbeck process based on the approximation method.To examine the moment stability property of the viscoelastic system,we use the stochastic averaging method,Girsanov theorem and Feynmann-Kac formula to derive the approximate analytic expansion of the moment Lyapunov exponent.Furthermore,the Monte Carlo simulation results for the original system are given to check the accuracy of the approximate analytic results.At the end of this paper,results are presented to show some quantitative pictures of the effects of the system parameters,noise parameters and viscoelastic parameters on the stability of the viscoelastic plate.展开更多
First-passage failure of multiple-degree-of-freedom nonlinear oscillators with lightly nonlinear dampings and strongly nonlinear stiffness subject to additive and/or parametric Gaussian white noise excitations is stud...First-passage failure of multiple-degree-of-freedom nonlinear oscillators with lightly nonlinear dampings and strongly nonlinear stiffness subject to additive and/or parametric Gaussian white noise excitations is studied. First, by using the stochastic averaging method based on the generalized harmonic functions, the averaged It stochastic differential equation for the amplitudes of the nonlinear oscillators can be derived. Then the associated backward Kolmogorov equation of the conditional reliability function is established, and the conditional reliability is approximately expressed as a series expansion in terms of Kummer functions with time-dependent coefficients. By using the Galerkin method, the time dependent coefficients of the associated conditional reliability function can be solved by a set of differential equations. Finally, the proposed procedure is applied to Duffing-Van der Pol systems under external and/or parametric excitations of Gaussian white noises. The results are also verified by those obtained from Monte Carlo simulation of the original system. The effects of system parameters on first-passage failure are discussed briefly.展开更多
基金the National Science & Technology Major Projects(Grant No.2008ZX05023-005-013).
文摘In this paper,we explore the use of iterative curvelet thresholding for seismic random noise attenuation.A new method for combining the curvelet transform with iterative thresholding to suppress random noise is demonstrated and the issue is described as a linear inverse optimal problem using the L1 norm.Random noise suppression in seismic data is transformed into an L1 norm optimization problem based on the curvelet sparsity transform. Compared to the conventional methods such as median filter algorithm,FX deconvolution, and wavelet thresholding,the results of synthetic and field data processing show that the iterative curvelet thresholding proposed in this paper can sufficiently improve signal to noise radio(SNR) and give higher signal fidelity at the same time.Furthermore,to make better use of the curvelet transform such as multiple scales and multiple directions,we control the curvelet direction of the result after iterative curvelet thresholding to further improve the SNR.
基金financially sponsored by Research Institute of Petroleum Exploration&Development(PETROCHINA)Scientific Research And Technology Development Projects(No.2016ycq02)China National Petroleum Corporation Science&Technology Development Projects(No.2015B-3712)Ministry of National Science&Technique(No.2016ZX05007-006)
文摘For random noise suppression of seismic data, we present a non-local Bayes (NL- Bayes) filtering algorithm. The NL-Bayes algorithm uses the Gaussian model instead of the weighted average of all similar patches in the NL-means algorithm to reduce the fuzzy of structural details, thereby improving the denoising performance. In the denoising process of seismic data, the size and the number of patches in the Gaussian model are adaptively calculated according to the standard deviation of noise. The NL-Bayes algorithm requires two iterations to complete seismic data denoising, but the second iteration makes use of denoised seismic data from the first iteration to calculate the better mean and covariance of the patch Gaussian model for improving the similarity of patches and achieving the purpose of denoising. Tests with synthetic and real data sets demonstrate that the NL-Bayes algorithm can effectively improve the SNR and preserve the fidelity of seismic data.
文摘The signal-to-noise ratio (SNR) of seismic reflection data in many areas is rather poor and conventional two-dimensional filters designed to suppress noise with different moveout from the signal tend to generate artifacts. We have extended a method of multichannel filtering, based on the hypothesis that signals on adjacent channels are similar, for enhancing the SNR on stacked sections. Using only the mid-range frequencies where the SNR is highest, the event trend is found for overlapping windows on the section and the average signal vector is calculated. Then the data from the full bandwidth section are projected onto the spatially varying unit similarity vectors and the results are merged for the overlapping windows. Application of the method to synthetic data containing steeply dipping events and to a stacked section for a marine 2D line has produced good results. The modifications we have introduced carry a small overhead in computing time but they should enable the method to be used effectively even on sections containing steep dips.
基金Projects(61135001, 61075029, 61074155) supported by the National Natural Science Foundation of ChinaProject(20110491690) supported by the Postdocteral Science Foundation of China
文摘New sigma point filtering algorithms, including the unscented Kalman filter (UKF) and the divided difference filter (DDF), are designed to solve the nonlinear filtering problem under the condition of correlated noises. Based on the minimum mean square error estimation theory, the nonlinear optimal predictive and correction recursive formulas under the hypothesis that the input noise is correlated with the measurement noise are derived and can be described in a unified framework. Then, UKF and DDF with correlated noises are proposed on the basis of approximation of the posterior mean and covariance in the unified framework by using unscented transformation and second order Stirling's interpolation. The proposed UKF and DDF with correlated noises break through the limitation that input noise and measurement noise must be assumed to be uneorrelated in standard UKF and DDF. Two simulation examples show the effectiveness and feasibility of new algorithms for dealing with nonlinear filtering issue with correlated noises.
基金Supported by the Ministry of Science and Technology of China under Grant No. 2012CB934001the National Natural Science Foundation of China under Grant No. 10975019+1 种基金the Scientific Research Foundation for the Returned Overseas Chinese Scholars,Ministry of Personnel of China under Grant No. MOP2006138the Fundamental Research Funds for the Central Universities, and Y1515530U1
文摘The importance of stochasticity in cellular processes is increasingly recognized in both theoretical andexperimental studies.General features of stochasticity in gene regulation and expression are briefly reviewed in thisarticle,which include the main experimental phenomena,classification,quantization and regulation of noises.Thecorrelation and transmission of noise in cascade networks are analyzed further and the stochastic simulation methodsthat can capture effects of intrinsic and extrinsic noise are described.
基金supported by the National Natural Science Foundation of China (Grant Nos. 11072107 and 91016022)the Specialized Research Fund for the Doctoral Program of Higher Education of China (GrantNo.20093218110003)
文摘This article examines a viscoelastic plate that is driven parametrically by a non-Guassian colored noise,which is simplified to an Ornstein-Uhlenbeck process based on the approximation method.To examine the moment stability property of the viscoelastic system,we use the stochastic averaging method,Girsanov theorem and Feynmann-Kac formula to derive the approximate analytic expansion of the moment Lyapunov exponent.Furthermore,the Monte Carlo simulation results for the original system are given to check the accuracy of the approximate analytic results.At the end of this paper,results are presented to show some quantitative pictures of the effects of the system parameters,noise parameters and viscoelastic parameters on the stability of the viscoelastic plate.
基金supported by the National Natural Science Foundation of China (Grant No. 11025211)the Natural Science Foundation of Zhejiang Province (Grant No. 26090125)the Special Fund for National Excellent PhD Dissertation
文摘First-passage failure of multiple-degree-of-freedom nonlinear oscillators with lightly nonlinear dampings and strongly nonlinear stiffness subject to additive and/or parametric Gaussian white noise excitations is studied. First, by using the stochastic averaging method based on the generalized harmonic functions, the averaged It stochastic differential equation for the amplitudes of the nonlinear oscillators can be derived. Then the associated backward Kolmogorov equation of the conditional reliability function is established, and the conditional reliability is approximately expressed as a series expansion in terms of Kummer functions with time-dependent coefficients. By using the Galerkin method, the time dependent coefficients of the associated conditional reliability function can be solved by a set of differential equations. Finally, the proposed procedure is applied to Duffing-Van der Pol systems under external and/or parametric excitations of Gaussian white noises. The results are also verified by those obtained from Monte Carlo simulation of the original system. The effects of system parameters on first-passage failure are discussed briefly.