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nonstationary inversion-based directional deconvolution of airgun array signature

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Applied Geophysics 2019年第1期16卷 116-124页

作者： Li Hao Li Guo-Fa Guo Xiang-Hui Sun Xi-Ping Wang Jian-Fu CNPC Key Laboratory of Geophysical Prospecting China University of PetroleumBeijing 102249China State Key Laboratory of Petroleum Resources and Prospecting China University of PetroleumBeijing 102249China Research Institute of Petroleum Exploration and Development PetrochinaBeijing 100083China Dagang Oil Field PetrochinaTianjin 300280China

Airgun arrays are widely used in marine seismic exploration because signatures excited by airgun arrays have high energy and high-peak bubble ratio, whereas the considerable length and width of the array and ghost reflections make the airgun array signature directional. As a result, the relation of the reflection amplitude with the incident and azimuth angles is variable. This means that the directivity of the airgun array results in a nonstationary wavelet and distorts the relation of the amplitude variation with the incident and azimuth angles. To remove the directivity effect, we propose a nonstationary inversion-based directional deconvolution. At fi rst, the signature as a function of take-off angle and azimuth angle is calculated using the spatial configuration of the airgun array and the near-field signatures. Then, based on the velocity model, the time-variant take-off angles are estimated and directional fi lters are designed using the take-off angles. Finally, the directivity-dependent signatures are shaped to the signature right below the airgun array using nonstationary inversion in the directional deconvolution.

关键词： Airgun array airgun signature directivity nonstationary deconvolution

nonstationary signal inversion based on shaping regularization for random noise attenuation

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Applied Geophysics 2020年第3期17卷 432-442页

作者： Yang Wu-Yang Wang Wei Li Guo-Fa Wei Xin-Jian Wang Wan-Li Chen De-wu Research Institute of Petroleum Exploration&Development-Northwest PetroChinaLanzhou 730020China. State Key Laboratory of Petroleum Resources and Prospecting CUP(Beijing)Beijing 102249China. CNPC Key Laboratory of Geophysical Prospecting CUP(Beijing)Beijing 102249China.

Prediction filtering is one of the most commonly used random noise attenuation methods in the industry;however,it has two drawbacks.First,it assumes that the seismic signals are piecewise stationary and linear.However,the seismic signal exhibits nonstationary due to the complexity of the underground structure.Second,the method predicts noise from seismic data by convolving with a prediction error filter(PEF),which applies inconsistent noise models before and after denoising.Therefore,the assumptions and model inconsistencies weaken conventional prediction filtering's performance in noise attenuation and signal preservation.In this paper,we propose a nonstationary signal inversion based on shaping regularization for random noise attenuation.The main idea of the method is to use the nonstationary prediction operator(NPO)to describe the complex structure and obtain seismic signals using nonstationary signal inversion instead of convolution.Different from the convolutional predicting filtering,the proposed method uses NPO as the regularization constraint to directly invert the eff ective signal from the noisy seismic data.The NPO varies in time and space,enabling the inversion system to describe complex(nonstationary and nonlinear)underground geological structures in detail.Processing synthetic and field data results demonstrate that the method eff ectively suppresses random noise and preserves seismic refl ection signals for nonstationary seismic data.

关键词： noise attenuation nonstationary inversion shaping regularization

Finite difference scheme based on proper orthogonal decomposition for the nonstationary Navier-Stokes equations

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Science China Mathematics 2007年第8期50卷 1186-1196页

作者： Zhen-dong LUO Rui-wen WANG Jiang ZHU School of Science Beijing Jiaotong UniversityBeijing 100044China Institute of Atmospheric Physics Chinese Academy of SciencesBeijing 100029China

The proper orthogonal decomposition(POD)and the singular value decomposition(SVD) are used to study the finite difference scheme(FDS)for the nonstationary Navier-Stokes equations. Ensembles of data are compiled from the transient solutions computed from the discrete equation system derived from the FDS for the nonstationary Navier-Stokes equations.The optimal orthogonal bases are reconstructed by the elements of the ensemble with POD and SVD.Combining the above procedures with a Galerkin projection approach yields a new optimizing FDS model with lower dimensions and a high accuracy for the nonstationary Navier-Stokes equations.The errors between POD approximate solutions and FDS solutions are analyzed.It is shown by considering the results obtained for numerical simulations of cavity flows that the error between POD approximate solution and FDS solution is consistent with theoretical results.Moreover,it is also shown that this validates the feasibility and efficiency of POD method.

关键词： proper orthogonal decomposition singular value decomposition finite difference scheme the nonstationary Navier-Stokes equations

Seismic spatial effects on long-span bridge response in nonstationary inhomogeneous random fields

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Earthquake Engineering and Engineering Vibration 2005年第1期4卷 75-82页

作者：林家浩张亚辉赵岩 State Key Laboratory of Structural Analysis for Industrial Equipment Dalian University of Technology Dalian 116023 ChinaProfessor Chongqing Communications Research & Design Institute Chongqing 400067 ChinaAssociateProfessor State Key Laboratory of Structural Analysis for Industrial Equipment Dalian University of Technology Dalian 116023 China Chongqing Communications Research & Design Institute Chongqing 400067 China Post-doctor

The long-span bridge response to nonstationary multiple seismic random excitations is investigated using the PEM (pseudo excitation method). This method transforms the nonstationary random response analysis into ordinary direct dynamic analysis, and therefore, the analysis can be solved conveniently using the Newmark, Wilson-9 schemes or the precise integration method. Numerical results of the seismic response for an actual long-span bridge using the proposed PEM are given and compared with the results based on the conventional stationary analysis. From the numerical comparisons, it was found that both the seismic spatial effect and the nonstationary effect are quite important, and that both stationary and nonstationary seismic analysis should pay special attention to the wave passage effect.

关键词： earthquake nonstationary random vibration multiple excitation long-span bridge

SUPERCONVERGENCE OF DISCONTINUOUS GALERKIN METHOD FOR nonstationary HYPERBOLIC EQUATION

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Journal of Computational Mathematics 2002年第4期20卷 429-436页

作者： Chen, Y Lin, JF Lin, Q Chinese Acad Sci Acad Math & Syst Sci ICMSEC LSEC Beijing 100080 Peoples R China

For the first order nonstationary hyperbolic equation taking the piecewise linear discontinuous Galerkin solver, we prove that under the uniform rectangular partition, such a discontinuous solver, after postprossesing, can have two and half approximative order which is half order higher than the optimal estimate by Lesaint and Raviart under the rectangular partition.

关键词： discontinuous Galerkin method hyperbolic equation nonstationary superconvergence

Time-varying parameter auto-regressive models for autocovariance nonstationary time series

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Science China Mathematics 2009年第3期52卷 577-584页

作者： FEI WanChun BAI Lun College of Textile and Clothing Engineering Suzhou UniversitySuzhou 215021China

In this paper, autocovariance nonstationary time series is clearly defined on a family of time series. We propose three types of TVPAR (time-varying parameter auto-regressive) models: the full order TVPAR model, the time-unvarying order TVPAR model and the time-varying order TV-PAR model for autocovariance nonstationary time series. Related minimum AIC (Akaike information criterion) estimations are carried out.

关键词： autocovariance nonstationary time series time-varying parameter time-varying or- der auto-regressive model minimum AIC estimation

The　Stability　of　the　nonstationary　Forest　Evolution　System　and　the　Critical　Proliferation　Rate　of　Fo

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Systems Science and Systems Engineering 1997年第2期7卷 191-195页

Ｉｎｔｈｉｓｐａｐｅｒ，ｗｅｄｉｓｃｕｓｓｅｄｔｈｅｎｏｎｓｔａｔｉｏｎａｒｙｆｏｒｅｓｔｅｖｏｌｕｔｉｏｎｓｙｓｔｅｍ，ｄｅｆｉｎｅｄｔｈｅｔｉｍｅ－ｖａｒｙｉｎｇｃｒｉｔｉｃａｌｐｒｏｌｉｆｅｒａｔｉｏｎｒａｔｅ... 详细信息

Ｉｎｔｈｉｓｐａｐｅｒ，ｗｅｄｉｓｃｕｓｓｅｄｔｈｅｎｏｎｓｔａｔｉｏｎａｒｙｆｏｒｅｓｔｅｖｏｌｕｔｉｏｎｓｙｓｔｅｍ，ｄｅｆｉｎｅｄｔｈｅｔｉｍｅ－ｖａｒｙｉｎｇｃｒｉｔｉｃａｌｐｒｏｌｉｆｅｒａｔｉｏｎｒａｔｅａｎｄｔｈｅｃｒｉｔｉｃａｌｐｒｏｌｉｆｅｒａｔｉｏｎｒａｔｅ，ａｎｄｏｂｔａｉｎｅｄｔｈｅｎｅｃｅｓｓａｒｙａｎｄｓｕｆｆｉｃｉｅｎｔｃｏｎｄｉｔｉｏｎｓｆｏｒｔｈｅｓｙｓｔｅｍｔｏｂｅｓｔａｂｌｅ．

关键词： Stability the nonstationary The Critical Evolution

nonstationary Stimulated Raman Scattering by Polaritons in Continuum of Dipole-Active Phonons

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Journal of Applied Mathematics and Physics 2018年第2期6卷 405-417页

作者： Vladimir Feshchenko Galina Feshchenko Dawson College Montreal Canada Vanier College Montreal Canada

The system of equations simulating the processes of nonstationary stimulated Raman scattering (SRS) with the excitation of polar optical phonons is obtained. This system is found by applying such standard methods as the nonstationary theory of perturbations, which resulted in the equations for the amplitudes of probabilities to find the discrete system in certain state, and slowly-varying amplitudes for the electromagnetic waves. It has been shown that the obtained system includes, as extremes, the case of classical interaction between electromagnetic field and resonant medium (including the “area theorem”), and the one related with SRS on optical phonons. We have conducted both theoretical and numerical investigation of simplified system assuming that the amplitudes of all electromagnetic waves (laser, Stokes, and polariton) were real (there was no destructive spatial-temporal phase modulation). Only low-order nonlinear processes are considered. It is shown that this system can be reduced to Sine-Gordon equation. This system can also be simplified to the equation that simulates the motion of physical pendulum from upper equilibrium position. The numerical study of nonstationary SRS when the electromagnetic field of laser radiation and Stokes excite both polariton emission and the continuum of dipole-active phonons has been carried out. The evolution of the intensity of the polariton wave as function of the length of nonlinear medium has been numerically analyzed.

关键词： nonstationary Stimulated Raman Scattering Polaritons

nonstationary Stimulated Raman Scattering by Polaritons in Cubic Crystals

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Journal of Applied Mathematics and Physics 2019年第9期7卷 2122-2129页

作者： Vladimir Feshchenko Galina Feshchenko Dawson College Montreal Canada Vanier College Montreal Canada

The purpose of this article is to consider two aspects of the nonstationary stimulated Raman scattering by polaritons in cubic crystals. The first feature is related to the pump field, which, by deforming the permittivity of the medium, changes its symmetry. As a result, for example, the cubic crystal becomes anisotropic. The second one results from the possibility of exciting anomalous longitudinal waves at the frequency of the mechanical phonons which is the fundamental difference between scattering by dipole-active (polar) phonons and that of by dipole-inactive (nonpolar) ones. When the phonon frequency is approached, the amplitude of the transverse polariton wave decreases due to increased absorption and the wave mismatch. The polariton wave becomes practically longitudinal. Such a wave is maintained by the pump field and exists only in a pumped medium. The system of four shortened nonstationary equations (two for the Stokes waves with perpendicular polarizations and two for both transverse and longitudinal polariton waves) is obtained. The analysis is carried out for a given stationary pump field which is assumed to be a linearly polarized plane electromagnetic wave. Principal attention was paid to the calculation and analysis of the gain factor which defines the intensities of both stimulated (SRS) and spontaneous Raman scattering. The expressions for two proper gain factors gμ are obtained for Stokes waves in nonstationary case. It was shown that the pumped cubic crystal becomes anisotropic. It is also shown that the values of intensities calculated by using the expression for gμ are consistent with the experimental results for spectra of ZnS.

关键词： nonstationary Stimulated Raman Scattering Polaritons Phonons